Key Book Class 3 EASY MATH Project Director: Project Manager: Author: Proofread By: Designed By: Quality Controller: Printed By: Published By: Rana Fiaz Nadeem M. Mohsin Sukhera Naseem Abbas Humayun Nazar MoonLight Designing Lab Irfan Ramzan Ahmed Naveed Printers Sale & Display Center: Head Office: MoonLight Publishers 19-Main Urdu Bazar, Lahore. MoonLight Research Lab. Aahata Shahadriyan, 22 - Urdu Bazar, Lahore. 24/7 UAN: KSA: Ph: Fax: Web: E-mail: Join us: 03 - 1 1 1 - 1 8 6 - 7 8 6 042- 1 1 1 - 1 8 6 - 7 8 6 00966-561- 1 8 6 - 7 8 6 +92- 42-37111000, 37114856 +92- 42-37114420 +92- 42-37210201 www.moonlightpublishers.com [email protected] facebook.com/moonlightpublishers INTERNATIONAL R
Preface This series is designed in accordance with the revised syllabus prescribed by the ministry of education for primary schools in Pakistan. In this series various modern method and techniques have been used to inculcate in the young children the basic mathematical concepts. The approach of treating the subject matter from concert and pictorial to abstract, being still effective in teaching has been maintained in this series. Each concept has been allocated with proper space for incorporation of your colour lively illustrations. Digital pictures and diagram are added which give appreciable look to this book. The series is designed in such a way that even a less experience teacher can easily teach the tough topics of mathematic. Superior paper and high quality printing makes the series acceptable for any prestigious institutes. All possible efforts are made to make this book error free, but still improvement can be made. All suggestions in this regard are welcomed. Publishers.
Contents Numbers 04 12 22 29 38 45 50 58 68 1 2 3 4 5 6 7 8 9 Multiplication and Division Fractions Decimal Fraction Roman Numbers Unitary Method Time Geometry Graph B A C Price of 10 pencils total pencils Price of 1 pencil = 7 10 or 0.7 1 2 9 1 0 8 x 9 108 9 18 18 0 1 2 – –
4 Numbers Student’s Learning Outcomes: After studying this unit, students will be able to: read and write 4-digit numbers. read and write 5-digit numbers. read and write 6-digit numbers. place comma (,) at proper place. represent numbers in expended form. Unit 1 In previous class, we have learnt upto 3-digit numbers. Now we learn numbers, which are greater than 3-digits. We know that a 3-digit number has a format. H T O 4 6 7 The biggest 3-digit number is 999, when we add 1 in it, we get the first and the smallest 4-digit number, which is 1000. It is written in place value form as: TH H T O 1 0 0 0 Let us study some other examples: TH H T O 3 6 8 9 It is read as three thousand six hundred and eighty nine. It is written as 3,689. Remember: After every 3-digits, from right a comma ‘,’ is placed so that reading of numbers becomes more easy. TH H T O 9 9 9 9 It is read as nine thousand nine hundred and ninety nine. It is written as 9,999
5 y Activit 1 Write the numbers names. Th H T O 4 6 0 3 _________________________ (i) Th H T O 5 0 6 0 _________________________ (ii) Th H T O 4 0 5 5 _________________________ (iii) Th H T O 8 8 1 0 _________________________ (iv) 1 1 1 Now we learn numbers which are bigger than 4 digits. We know that a 4-digit number has a format. i.e, TH H T O 4 5 6 7 Maximum value of a 4-digit number is Thousand. This number is read as four thousand five hundred sixty seven. We know that the biggest 4-digit number is 9,999, when we add 1 in it. 9 9 9 9 + 1 1 0 0 0 0 We get the first and the smallest 5-digit number. It is written and read as: T.TH TH H T O 1 0 0 0 0 Ten Thousand. Let us read and write some 5-digit numbers. 2,3468 = T.TH TH H T O 2 3 5 6 8 It is read as: Twenty three thousand five hundred and sixty eight. Four thousand six hundred and three Five thousand and sixty Four thousand and fifty five Eight thousand eight hundred and ten
6 y Activit 2 Write the numbers names. We have a number seventy three thousand one hundred twenty three. It is written as 73123. Consider another example, we can write ninety thousand six hundred forty as 90640. It is read as ninety eight thousand sixty three. T.TH TH H T O 8 3 6 7 2 _________________________ (i) _________________________ (ii) _________________________ (iii) _________________________ (iv) T.TH TH H T O 7 0 6 5 0 T.TH TH H T O 4 5 5 8 8 T.TH TH H T O 1 2 1 9 4 Write a 5-Digit Number Use of Period Remember that number greater than 3-digits are written with the use of a comma. For example: 3624 is written as 3,624 4509 is written as 4,509 Remember: T.TH and TH are read in combination as in above two examples. Twenty Three Thousand and Ninety Eight Thousand, etc. 98063 = T.TH TH H T O 9 8 0 6 3 Eighty three thousand six hundred and seventy two Seventy thousand six hundred and fifty Forty five thousand five hundred and eighty eight Twelve thousand one hundred and ninety four
7 y Activit Place comma (period) at proper place. i. 2356 _______________ ii. 4637 _______________ iii. 28737 _______________ iv. 48484 _______________ v. 77777 _______________ vi. 69520 _______________ vii. 65499 _______________ viii. 80648 _______________ ix. 99872 _______________ x. 28904 _______________ xi. 40558 _______________ xii. 81345 _______________ 23678 is written as 23,678 40505 is written as 40,505 In all these examples, you have seen that after every 3-digits (from right side) a comma (,) is placed, so any number can be read easily. Expanded Form Note: In Pakistani way of writing a number, after every 3rd digit (from right side) a comma (,) is placed. Comma is also called a period. This method of writing a number is used to find the place value of every digit. For example: 43,786 = 40000 + 3000 + 700 + 80 + 6 25,741 = 20000 + 5000 + 700 + 40 + 1 49,999 = 40000 + 9000 + 900 + 90 + 9 10,001 = 10000 + 0000 + 000 + 00 + 1 10,101 = 10000 + 0000 + 100 + 00 + 1 2,356 28,737 77,777 65,499 99,872 40,558 4,637 48,484 69,520 80,648 28,904 81,345
8 y Activit 1 Write these numbers in expanded form. i. 36,734 = ________________________________________________ ii. 24,895 = ________________________________________________ iii. 67,737 = ________________________________________________ iv. 23,405 = ________________________________________________ v. 56,000 = ________________________________________________ i. 40000 + 3000 + 200 + 10 + 6 = ____________ ii. 80000 + 9000 + 800 + 90 + 8 = ____________ iii. 30000 + 7000 + 200 + 70 + 4 = ____________ iv. 20000 + 8000 + 900 + 30 + 0 = ____________ v. 90000 + 5000 + 400 + 60 + 1 = ____________ y Activit 2 Write these numbers in short form. Short Form When we add 1 in the largest 5 digit number 99,999, we get the first and the smallest six digit number. It is called 1 Lakh (or 1 lac) 9 9 9 9 9 + 1 1 0 0 0 0 0 1 1 1 1 This is the reverse process of expanded form. Consider these examples: 40000 + 3000 + 200 + 10 + 5 = 43,215 60000 + 7000 + 000 + 80 + 1 = 67,081 90000 + 3000 + 200 + 00 + 0 = 93,200 70000 + 9000 + 800 + 90 + 4 = 79,894 50000 + 6000 + 200 + 30 + 8 = 56,238 6-Digit Numbers 30000 + 6000 + 700 + 30 + 4 20000 + 4000 + 800 + 90 + 5 60000 + 7000 + 700 + 30 + 7 20000 + 3000 + 400 + 00 + 5 50000 + 6000 + 000 + 00 + 0 43,216 89,898 37,274 28,930 95,461
9 Use of Comma y Activit Write the number names of these numbers. (first one is done for you) i. 2,46,366 = ________________________________________________ ii. 2,43,506 = ________________________________________________ iii. 7,89,123 = ___________________________________________ iv. 2,46,246 = ___________________________________________ v. 3,33,300 = ___________________________________________ vi. 4,44,000 = ___________________________________________ Two lac forty six thousand three hundred sixty six. , It is written in place value form as: L T.TH. TH H T O 1 0 0 0 0 0 A 6-digit number is read and written as: 345682 = Three lac forty five thousand six hundred eighty two. 892304 = Eight lac ninety two thousand three hundred four. 101010 = One lac one thousand ten. In Pakistani style of writing, after every three digits from right a comma (,) is placed and after it is placed after every two digits, so that reading of number becomes easy. Examples: Place ‘,’ in these numbers: i. 235671 = 2,35,671 ii. 808080 = 8,08,080 iii. 100100 = 1,00,100 iv. 361723 = 3,61,723 v. 123456 = 1,23,456 Two lac forty three thousand five hundred six. Seven lac eighty nine thousand one hundred twenty three. Two lac forty six thousand two hundred forty six. Three lac thirty three thousand three hundred. Four lac forty four thousand.
301 Exercise 1. Write the following in numbers. a. Forty six thousand eight hundred thirty nine. ______________ b. Ninety thousand six hundred eighty one. ______________ c. Seventy six thousand six hundred ninety three. ______________ d. Eighty four thousand eighty four. ______________ e. Twelve thousand three hundred forty five. ______________ f. Nine lac eighty thousand four hundred eighty nine. ____________ g. Four lac seventy nine thousand one. ______________ h. One lac one thousand ten. ______________ 2. Write the number names of these numbers. a. 4,307 ________________________________________________________ b. 2,876 ________________________________________________________ c. 8,808 ________________________________________________________ d. 3,754 ________________________________________________________ e. 4,646 ________________________________________________________ f. 35,637 ________________________________________________________ g. 27,253 ________________________________________________________ h. 46,330 ___________________________________________________ i. 97,609 ___________________________________________________ j. 87,003 ___________________________________________________ 46,839 90,681 76,693 84,084 Four thousand three hundred seven Eight thousand eight hundred eight Four thousand six hundred forty six Twenty seven thousand two hundred fifty three Ninety seven thousand six hundred nine Two thousand eight hundred seventy six Three thousand seven hundred fifty four Thirty five thousand six hundred thirty seven Forty six thousand three hundred thirty Eighty seven thousand and three 12,345 9,80,489 4,79,001 1,10,010
11 3. Write the number names of these numbers. a. 146,356 ________________________________________________________ b. 245,639 ________________________________________________________ c. 867,988 ________________________________________________________ d. 303,404 ________________________________________________________ e. 700,707 ________________________________________________________ 4. Write these numbers in expanded form. a. 36,254 ________________________________________________________ b. 76,315 ________________________________________________________ c. 28,503 ________________________________________________________ d. 146,839 ________________________________________________________ e. 273,134 ________________________________________________________ f. 697,314 ________________________________________________________ g. 437,008 ________________________________________________________ h. 808,080 ________________________________________________________ i. 437,008 _________________________________________________ j. 808,080 _________________________________________________ One lac forty six thousand three hundred fifty six. Two lac forty five thousand six hundred thirty nine. Eight lac sixty seven thousand nine hundred eighty eight. Three lac three thousand four hundred four. Seven lac seven hundred seven. 30000 + 6000 + 200 + 50 + 4 70000 + 6000 + 300 + 10 + 5 20000 + 8000 + 500 + 00 + 3 100000 + 40000 + 6000 + 800 + 30 + 9 200000 + 70000 + 3000 + 100 + 30 + 4 600000 + 90000 + 7000 + 300 + 10 + 4 400000 + 30000 + 7000 + 000 + 00 + 8 800000 + 00000 + 8000 + 000 + 80 + 0 400000 + 30000 + 7000 + 000 + 00 + 8 800000 + 00000 + 8000 + 000 + 80 + 0
12 Multiplication and Division We start with a example: Multiply 245 x 4 Student’s Learning Outcomes: After studying this unit, students will be able to: multiply 3-digit numbers with 1-digit numbers. multiply 3-digit numbers with 2-digit numbers. divide numbers with 1-digit and 2 digit numbers solve word problems of multiplication and division. Unit 2 (Converting Tens and Hundreds) Multiplication First, multiply the Ones (5) with the multiplier (4). 4 x 5 = 20 (Convert 20 into 2 Tens) (Convert of Tens) Next multiply the tens (4) with the multiplier (4). 4 x 4 = 16 16 + 2 = 18 Convert 10 Tens into hundred. Finally, multiply the hundreds (2) with the multiplier (4). 4 x 2 = 8 and add 1 which makes 9. The answer is 980 2 4 5 x 4 0 2 4 5 x 4 9 8 0 1 2 4 5 x 4 8 0 2 2 H T O
13 Multiplication of 3-Digit Numbers with 2-Digit Numbers Multiplication of 3-Digit Numbers Example: Multiply 345 x 32 Step 1: First multiply 2 (Ones of multiplier) with all digits. Multiply 2 with 5. (Ones multiplied with Ones) 2 x 5 = 10 Now, Multiply 2 with 4 and add 1. (Ones multiplied with Tens) 2 x 4 = 8 8 + 1 = 9 Multiply 2 with 3. (Ones multiplied with Hundred) 2 x 3 = 6 Step 2: In this step, digit at Tens place (3) is multiplied with all digits. Put a ‘x’ under 0 of 690. Now multiply 3 with 5. (Tens multiplied with Ones) 3 x 5 = 15 Multiply 3 with 4. (Tens with Tens) 3 x 4 = 12 and add 1. 12 + 1 = 13 Finally, multiply 3 with 3. (Tens with Hundred) 3 x 3 = 9 and add 1 = 9 + 1 = 10 Now add both terms, 11040 is the answer. 3 4 5 3 2 6 9 0 3 4 5 3 2 0 0 0 0 1 0 3 5 x 3 4 5 3 2 6 9 0 1 0 3 5 x 1 1 0 4 0 1 1 H T O H T O H T O x x x
14 Multiplication with 10, 1000 and 1000 Look at Result: (i) When we multiplied 463 with 10. (10 has one zero) We put one zero at the end of 463. (ii) When we multiplied 463 with 100, ( 100 has two zeros) We put two zeros at the end of 463. Some multiplications are very easy and simple. We can do these multiplications mentally. Multiplication with 10, 1000 and 1000 are very easy. Lets us multiply on paper and then do this mentally. Examples: Multiply 463 with 10,100 and 1000 H T O 4 6 3 x 1 0 0 0 0 4 6 3 x 4 6 3 0 H T O 4 6 3 x 1 0 0 0 0 0 0 0 0 x 4 6 3 x x 4 6 3 0 0 H T O 4 6 3 x 1 0 0 0 0 0 0 0 0 0 x 0 0 0 x x 4 6 3 x x x 4 6 3 0 0 0 y Activit Solve these. H T O 2 3 4 1 2 4 6 8 2 3 4 0 2 8 0 8 x H T O 3 4 5 3 4 1 3 8 0 1 0 3 5 0 1 1 7 3 0 x H T O 4 5 5 8 8 3 6 4 0 3 6 4 0 0 4 0 0 4 0 x H T O 3 4 5 4 5 1 7 2 5 1 3 8 0 0 1 5 5 2 5 x
15 y Activit Multiply 369 with 10, 100 and 1000. (iii) When we multiplied 463 with 1000 ( 1000 has three zero) We put three zeros at the end of 463. It means, in case of multiplication with 10, 100 or 1000, only zeros are added in the multiplicand and all digits remain same. Word Problems H T U 3 6 9 x 1 0 0 0 0 3 6 9 0 3 6 9 0 H T U 3 6 9 x 1 0 0 0 0 0 0 0 0 0 3 6 9 0 0 3 6 9 0 0 H T U 3 6 9 x 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 6 9 0 0 0 3 6 9 0 0 0 Multiplication is very important not only in mathematics but also in our daily life. Let us solve some everyday problems. Example 1: Price of a toy car is Rs. 346. What is the price of such 24 cars? Solution: Price of a car = Rs. 346 Price of 24 cars = Rs. 346 x 24 Price of 24 cars = Rs. 8,304 3 4 6 2 4 1 3 8 4 6 9 2 x 8 3 0 4 2 x 1 1 Rough Work
0516 Example 2: Price of a cricket bat is Rs 275. What will be the price of such 38 bats? Solution: Price of one bat = Rs. 275 Price of such38 bats = Rs. 275 x 38 So, price of such 38 bats = Rs. 10,450 Divison It is the reverse process of multiplication. With the help of division, we can divide things equally. Let us start with specific name which are related with division. Quotient Remainder 3 19 –18 6 1 Divisor Dividend Example 1: Divide 99 with 11. Solution: We found that 11 x 9 = 99 So, we write 9 as quotient and 99 below the dividend. Now subtraction of 99 from 99 gives 0 as remainder. So, 9 is the answer. 11 99 –99 0 9 Rough Work Multiply 11 with different numbers, such as: 1 1 4 4 4 1 1 5 5 5 1 1 6 6 6 1 1 9 9 9 x x x x 2 7 5 3 8 2 2 0 0 8 2 5 x 1 0 4 5 0 4 1 6 2 Rough Work x
17 Example 2: Divide 108 by 9. Solution: Here 9 x 1 = 9 write 1 in quotient and 9 below 10 and subtract. 1 is remainder bring 8 down with 1. It makes it 18. Now, 9 x 2 = 18 Subtraction given 0 So, 12 is the answer. Division Of 3 Digit Numbers By 2-Digit Numbers Division Of 3 Digit Numbers Example: Divide 192 by 16. Solution: It is not possible to learn table of every number orally. So, use rough work for multiplication. 16 192 16 32 32 0 12 – – y Activit Divide the following. 1 6 1 1 6 1 2 2 3 2 Rough Work 9 108 9 18 18 0 1 2 – – Rough Work x x 8 72 72 0 – 9 12 252 24 12 12 0 – 21 23 299 23 69 69 0 – 13 8 96 8 16 16 0 – 12
12 420 36 60 60 0 35 – – Word Problems Like multiplication, division is also very important in our daily life. Let us solve some everyday problem. Example: Price of a dozen tennis balls is Rs. 120. What is the price of one tennis ball? (1 dozen = 12) Solution: Price of 12 tennis balls = Rs. 420 Price of 1 tennis ball = Rs. 420 12 So, price of one ball = Rs. 35 Exercise 1. Multiply the following. 1 2 1 1 2 1 2 2 2 4 1 2 3 3 6 1 2 4 4 8 1 2 5 6 0 Rough Work x x x x x 18 1 2 3 x 3 3 6 9 a. 2 3 4 x 2 4 6 8 b. 3 4 5 x 4 1 3 8 0 c. 3 4 8 x 7 2 4 3 6 e. 4 3 2 x 6 2 5 9 2 f. 6 0 8 x 8 4 8 6 4 g. 4 5 6 x 5 2 2 8 0 d.
19 2 3 4 x 1 2 4 6 8 2 3 4 0 2 8 0 8 a. 2. Multiply the following. 3 2 3 x 3 2 6 4 6 9 6 9 0 1 0 3 3 6 b. 3 4 6 x 2 3 1 0 3 8 6 9 2 0 7 9 5 8 c. 4 5 6 x 3 4 1 8 2 4 1 3 6 8 0 1 5 5 0 4 d. 3 7 2 x 2 5 1 8 6 0 7 4 4 0 9 3 0 0 e. 4 7 4 x 5 6 2 8 4 4 2 3 7 0 0 2 6 5 4 4 f. 6 3 5 x 4 7 4 4 4 5 2 5 4 0 0 2 9 8 4 5 g. 8 7 9 x 8 9 7 9 1 1 7 0 3 2 0 7 8 2 3 1 h. 3. Multiply the given by 10, 100 and 1000. a. 5 x 10 = ________ b. 12 x 10 = _________ 5 x 100 = ________ 12 x 100 = _________ 5 x 1000= ________ 12 x 1000 = _________ c. 10 x 10 = ________ d. 15 x 10 = _________ 10 x 100= ________ 15 x 100 = _________ 10 x 1000= ________ 15 x 1000 = _________ e. 18 x 10 = _______ f. 80 x 10 = _______ 18 x 100 = _______ 80 x 100 = _______ 18 x 1000 = _______ 80 x 1000 = _______ g. 134 x 10 = _______ h. 260 x 10 = _______ 134 x 100 = _______ 260 x 100 = _______ 134 x 1000 = _______ 260 x 1000 = _______ 50 500 5000 100 1000 10000 120 1200 12000 150 1500 15000 180 1800 18000 1340 13400 134000 800 8000 80000 2600 26000 260000
20 4. Write “T” for true and “F” for false statements. a. 13 x 100 = 130 b. 99 x 10 = 9900 c. 20 x 10 = 200 d. 73 x 100 = 7300 e. 36 x 1000 = 30600 f. 60 x 1000 = 60000 g. 40 x 100 = 40000 h. 707 x 100 = 77000 i. 100 x 1000 = 10000 j. 27 x 100 = 2700 k. 106 x 10 = 10600 l. 100 x 10 = 1000 m. 110 x 100 = 11010 n. 100 x 100 = 1000 o. 210 x 1000 = 210000 p. 700 x 100 = 70000 7. Divide the following. 5. Ali bought 5 footballs. Price of one football is Rs. 235. How much amount did he pay? 6. Price of one litre pack of ice-cream is Rs.175. Find the price of such 23 litre ice-cream packs. O P O O O O O P O P P O P P O P 2 3 5 x 5 1 1 7 5 1 7 5 x 2 3 5 2 5 3 5 0 0 4 0 2 5 6 54 54 0 a. 9 7 84 7 14 14 0 b. 12 8 112 8 32 32 0 c. 14
21 9 180 180 0 d. 20 11 121 11 11 11 0 e. 11 13 325 26 65 65 0 f. 25 18 1134 108 54 54 0 h. 63 15 5580 45 108 105 30 30 0 i. 375 8. Price of one dozen copies of mathematics is Rs. 540. Find the price of one copy. 9. Price of 15 cricket bats is Rs.3975. What is the price of one cricket bat? 10. Fahad bought 12 kg of sugar for Rs. 1212. Find the price of 1 kg sugar. 15 675 60 75 75 0 g. 45 12 540 48 60 60 0 45 8. 540 ¸ 12 = 45 15 3975 30 97 90 75 75 0 265 12 1212 12 12 12 0 101 9. 3975 ¸ 15 = 265 10. 1212 ¸ 12 = 11
22 Fractions Student’s Learning Outcomes: After studying this unit, students will be able to: identify basics of fraction. differentiate between numerator and denominator. form a fraction with the help of numerator and denominator. divide a picture in different fractions. Fig (i) Fig (ii) Fig (iii) On my birthday my father brought a cake. Then again cut it into 2 more equal parts. My mother first cut it into two equal parts. In figure (ii) there are two equal parts of a whole. In mathematics each part is called a half and written as . Writing of a number in this style is called a fraction. It is read as one by two (or one over two). The upper part (1) of a fraction is called numerator and the lower part (2) is called a denominator. In figure (iii) a whole is divided in four equal parts. Four equal parts of a whole are called quarter. A quarter is written as and read as one by four. (or one over four). In , 1 is numerator and 4 is denominator. 1 2 1 4 Unit 3 1 4
23 y Activit 1 i. Take a rectangular piece of paper ii. Fold it at the middle. iii. Open it and divide into two equal parts. Each part is equal to of the whole. 1 2 Challange i. Take a square paper. ii. Fold it from middle. iii. Again fold it from middle. iv. Again fold it from middle. v. Again fold it from middle. Now open the paper and count the total number of squares. Write them as a friction. y Activit 2 Write them as a friction. a. b. c. d. e. f. I know the Answer! 1 2 1 4 1 4 1 3 1 4 1 2
24 Exercise 1. Tick (P) the shapes that are cut in half. 2. Colour one half of each shape. 3. Tick (P) the shapes which have four equal parts and colour th of them. 1 4 a. b. c. d. e. f. g. h. i. j. a. b. c. d. e. f. a. b. c. P P P P P P P P
25 4 Draw lines to divide these things into . 1 4 Fig (a) Fig (b) Fig (c) Fig (d) d. e. f. g. We have a square paper we divide into 4 equal parts. P P
26 There are many types of fractions. Lets us start with easy one. If we colour its one part it is written as: (fig b) If we colour its two parts it is written as: (fig c) If we colour its three parts it is written as: (fig d) 1 4 2 4 3 4 More Fractions Shapes One Whole One Half One Third One Fourth One Fifth One Sixth One Seventh One Eighth One Ninth One Tenth 2 parts 3 parts 4 parts 5 parts 6 parts 7 parts 8 parts 9 parts 10 parts Written as Each part called Divide into equal parts 1 2 1 3 1 4 1 5 1 6 1 7 1 1 8 1 9 1 10
27 Parts of a Fraction The upper part of a fraction is called numerator and lower part of a fraction is called denominator. For example, if we have a fraction then 3 is its numerator and 4 is its denominator. Numerator = 3 Denominator = 7 Fraction = Numerator = 2 Denominator = 4 Fraction = a. c. Numerator = 6 Denominator = 7 Fraction = Numerator = 3 Denominator = 8 Fraction = b. d. 6 7 3 8 3 7 2 4 Exercise 1. Write the fractions of shaded parts. Examples: Write the fraction with the help of given information. Remember: Numerator is always the upper part of fraction and denominator is the lower part of fraction. a. b. c. d. 3 4 1 4 2 4 2 3 1 2
28 e. f. 2. Write the fraction of unshaded parts of given figures. 3. Write the fractions with given information. Numerator = 3 Denominator = 4 Fraction = Numerator = 1 Denominator = 8 Fraction = Numerator = 11 Denominator = 10 Fraction = Numerator = 8 Denominator = 3 Fraction = Numerator = 8 Denominator = 1 Fraction = Numerator = 11 Denominator = 3 Fraction = Numerator = 4 Denominator = 7 Fraction = Numerator = 2 Denominator = 5 Fraction = a. b. c. d. e. f. g. h. a. b. c. d. e. 5 10 3 4 5 8 3 8 4 7 4 10 4 12 8 1 11 3 4 7 3 4 11 10 2 5 1 8 8 3
29 Decimal Fraction We can written the fraction in other way, which is called decimal fraction. = 0.1 (It is read as 0 point 1) In 0.1, ‘.’ is called a decimal point. It separates a whole number from a fractional number. The whole number is to the left of the decimal point. We use these numbers in buying, purchasing or solving mathematical problems. For example, price of sugar per kg is Rs. 57.50, price of petrol per litre is Rs. 64.66, etc. The coloured part of fig (i) shows the fraction or 0.4 and fig (ii) shows the fraction or 0.7. Student’s Learning Outcomes: After studying this unit, students will be able to: understand basics of decimal fraction. find place value of digits in a decimal fraction. add simple decimal numbers. subtract simple decimal numbers. Unit 4 We already know that when we divide a whole number in 10 equal parts then each of these parts is called a tenth and is written as: 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 It means one whole = ten tenth 1 10 fig (i) fig (ii) Part is shaded Part is shaded 7 10 or 0.7 4 10 or 0.4 0.4 is read as 0 point 4 and 0.7 is read as 0 point 7. 1 10 Remember In decimal fraction denominator is always 10 or multiple of 10. 4 10 1 10 7 10
30 So far we have learnt the place value of whole numbers. Now we will learn, what is the place value of decimal numbers? Place value of 3 is 3 Ones or 3. Place value of 2 is 2 Tens or 20. Place value of 1 is 1 Hundreds or 100. ( . ) is called a decimal point. Place value if 4 is 4 tenths or or .4. y Activit 1 Write the coloured part of given shapes as a fraction and also as a decimal. y Activit 2 Write these fractions as decimals. a. b. c. a. 2 10 = b. 6 10 = c. 8 10 = d. 9 10 = e. 5 10 = f. 3 10 = Place Value of a Decimal Number 4 10 Hundred 1 Tens 2 Ones 3 Tenths 4 3 10 or 0.3 5 10 or 0.5 0.2 0.9 0.6 0.5 0.8 0.3 6 10 or 0.6
31 a. 2 3 . 4 = ________ b. 4 6 8 . 6 = ________ c. 3 7 1 . 8 = ________ d. 8 0 7 . 1 = ________ e. 3 6 7 . 3 = ________ f. 7 8 5 . 4 = ________ g. 4 0 5 . 5 = ________ h. 8 8 1 . 1 = ________ i. 9 9 7 . 7 = ________ j. 8 5 0 . 9 = ________ Consider a mixed number 3 . In this number 3 is a whole number and is a fraction, it is written as 0.8 or ‘.8’. So 3 can be written as ‘3.8’. Now consider another example 14 . 14 is the whole number, so it is written as it as and the fraction is written as ‘.9’. Hence, 14 can be written as 14.9 (read as 14 point 9). y Activit Find the place values of circled digits. How to write Mixed Number ed Number ed Numbers as Decimal Number s as Decimal Number s as Decimal Numbers 8 10 8 10 8 10 9 10 9 10 9 10 y Activit Write given whole numbers as decimal numbers. a. 3 5 10 = ___________ b. 15 1 10 = ___________ c. 23 4 10 = ___________ d. 31 7 10 = ___________ e. 34 8 10 = ___________ f. 55 9 10 = ___________ 3.5 23.4 15.1 31.7 34.8 55.9 3 Ones 3 Hundreds 6 Tens 5 Tenths 9 Tens 6 Tenths 7 Ones 7 Hundreds 1 Tenths 8 Hundreds
32 Addition of Decimal Numbers Addition of decimal numbers is same as the addition of whole numbers. Look at the given examples. Example 1: Add 13.4 and 26.3 Step 1: Write the numbers in such a way that decimal sign of both numbers must be exactly above or below of the other number. Tenth place number of first number must be exactly below the Tenth place number of second number. Step 2: Firstly, add tenths is tents, i.e, 4 + 3 = 7 and write the answers. Step 3: Place (.) below the points. Step 4: Add 3 and 6 i.e. 3 + 6 = 9 Step 5: Add 1 and 2 i.e, 1 + 2 = 3 So, the answer is 39.7 Example 2: Add 38.7 and 44.6 Step 1: 7 + 6 = 13, in this 3 is tenths place number and write 1 at the top of 8 (the ones place number). Step 2: Place a decimal sign below the decimal sign. Step 3: Add 1 + 8 + 4, in this 3 is ones place number and write 1 at the top of 3 (tens place number). 3 8 . 7 + 4 4 . 6 8 3 . 3 Tens Ones Tenths 1 1 1 3 . 4 + 2 6 . 3 3 9 . 7 Tens Ones Tenths
33 Step 4: Add 1 + 3 + 4 = 8 write it below the tens place number. So, the answer is 83.3 (read as 83 point 3) y Activit Add the following decimal numbers. 3 4 . 4 + 2 5 . 1 5 9 . 5 a. Tens Ones Tenths 4 5 . 3 + 2 2 . 4 6 7 . 7 b. Tens Ones Tenths 6 4 . 5 + 2 6 . 5 9 1 . 0 c. Tens Ones Tenths 8 4 . 8 + 1 7 . 9 1 0 2 . 7 d. Tens Ones Tenths 3 5 . 6 + 2 7 . 6 6 3 . 2 e. Tens Ones Tenths 4 3 . 8 + 2 8 . 6 7 2 . 4 f. Tens Ones Tenths Subtraction of Decimal Numbers Subtraction of Subtraction of decimal numbers is same as of whole numbers. Look at the given example. Example 1: Subtract 23.2 from 86.7 Step 1: Write given number such that decimal sign of smaller number is exactly below the decimal sign. Step 2: 7 – 2 = 5. (Tenths is subtracted from tenths) Step 3: Place a decimal sign below the decimal sign. Step 4: Subtract 6 – 3 = 4 (ones from ones) Step 5: Subtract 8 – 2 = 6 (tens from tens) So, answer is 63.5. Tens Ones Tenths 8 6 . 7 – 2 3 . 2 6 3 . 5
34 Example 2: Subtract 46.8 from 93.6 Step 1: 8 cannot be subtracted from 6, so take 1 borrow from ones place digit 3. Now 6 becomes 16 and subtract 16 – 8 = 8. (Tenths from Tenths) Step 2: Place a decimal sign below decimal sign. Step 3: 6 cannot be subtracted from 2, so take 1 borrow from tens place number 9. (2 becomes 12) So, 12 – 6 = 6. (Ones from Ones) Step 4: Subtract 8 – 4 = 4. (Tens from Tens) Hence the answer is 46.8. 9 3 . 6 – 4 6 . 8 4 6 . 8 Tens Ones Tenths 8 2 1 1 y Activit Subtract the following. 6 7 . 8 – 2 3 . 4 4 4 . 4 a. Tens Ones Tenths 5 8 . 9 – 2 4 . 3 3 4 . 6 b. Tens Ones Tenths 6 3 . 4 – 2 5 . 6 3 7 . 8 c. Tens Ones Tenths 9 2 . 3 – 2 7 . 7 6 4 . 6 d. Tens Ones Tenths 6 3 . 8 – 2 3 . 6 4 0 . 2 e. Tens Ones Tenths 7 7 . 7 – 4 5 . 9 3 1 . 8 f. Tens Ones Tenths 8 6 . 5 – 5 7 . 8 2 8 . 7 g. Tens Ones Tenths 3 8 . 6 – 3 2 . 4 0 6 . 2 h. Tens Ones Tenths
35 Exercise 1. Write the shaded part as fraction. a. d. b. c. 2. Write the shaded part as a decimal fraction. a. d. b. c. 3. Write the place value of circled digits. a. 3 1 6 . 7 = ________ b. 2 3 4 . 5 = ________ c. 1 2 4 . 8 = ________ d. 2 0 9 . 1 = ________ e. 6 7 8 . 4 = ________ f. 7 8 5 . 4 = ________ g. 4 0 5 . 5 = ________ h. 8 8 1 . 1 = ________ i. 9 9 7 . 7 = ________ j. 8 5 0 . 9 = ________ k. 1 0 7 . 8 = ________ l. 9 7 0 . 5 = ________ m. 7 8 7 . 7 = ________ n. 9 6 0 . 8 = ________ 0.3 0.5 0.6 0.4 5 10 4 10 3 10 7 10 7 Tenths 8 Tenths 4 Tenths 5 Ones 9 Tens 1 Hundreds 7 Ones 3 tens 2 Hundreds 7 Hundreds 8 Tens 8 Hundreds 7 Tens 8 Tenths
36 4. Shade the given fraction. a. 7 10 8 10 6 10 b. c. d. 5 10 5. Add the following decimal fraction. 3 3 . 6 + 2 2 . 2 5 5 . 8 a. 1 4 . 3 + 1 1 . 4 2 5 . 7 b. 1 8 . 4 + 4 1 . 3 5 9 . 7 c. 1 4 . 5 + 1 5 . 6 3 0 . 1 d. 2 4 . 7 + 2 6 . 8 5 1 . 5 e. 6 7 . 7 + 2 4 . 8 9 2 . 5 f. 2 3 . 4 + 2 6 . 6 5 0 . 0 g. 3 5 . 8 + 3 4 . 8 7 0 . 6 h. 3 7 . 9 + 8 2 . 3 1 2 0 . 2 i. 6. Subtract the following decimal fraction. 4 2 . 7 – 2 4 . 8 1 7 . 9 a. 2 4 . 5 – 1 1 . 2 1 3 . 3 b. 3 9 . 8 – 2 4 . 7 1 5 . 1 c. 3 8 . 9 – 2 6 . 8 1 2 . 1 d. 4 1 . 3 – 2 4 . 5 1 6 . 8 e.
37 7. Subtract, add and then check your answer, whether they are equal or not equal. 6 7 . 6 – 3 8 . 7 2 8 . 9 f. 8 7 . 0 – 3 9 . 8 4 7 . 2 g. 6 4 . 3 – 3 9 . 9 2 4 . 4 h. Equal Not Equal Add a. b. c. d. e. f. Subtract 8 2 . 7 – 3 2 . 4 5 0 . 3 3 2 . 4 + 5 0 . 3 8 2 . 7 6 3 . 8 – 2 0 . 6 4 3 . 2 2 3 . 2 + 2 0 . 2 4 3 . 4 8 0 . 1 – 3 7 . 1 4 3 . 0 4 3 . 0 + 3 7 . 1 8 0 . 1 8 7 . 8 – 3 9 . 7 4 8 . 1 2 0 . 8 + 2 7 . 3 4 8 . 1 9 0 . 3 – 3 8 . 9 5 1 . 4 1 8 . 7 + 3 2 . 7 5 1 . 4 7 1 . 1 – 2 4 . 7 4 6 . 4 2 0 . 6 + 2 4 . 8 4 5 . 4 P P P P P P
38 Roman Numbers We use digits in our daily life. They start from 0,1,2,3,................. and never ends. These digits are called arabic numbers. Before Arabs, Roman’s used their own numbers. Actually these were symbols of their alphabet. First, 20 Roman numbers and their equivalent numbers are given below. Student’s Learning Outcomes: After studying this unit, students will be able to: read and write Roman numbers. convert Roman numbers in Arabic numbers. convert Arabic numbers in Roman numbers. add and subtract Roman numbers. Unit 5 Arabic Numbers Roman Numbers Arabic Numbers Roman Numbers 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 I II III IV V VI VII VIII IX X XI XII XIII XIV XV XVI XVII XVIII XIX XX
39 y Activit 1 Write the Roman equivalent of given Arabic numbers. y Activit 2 Write the Arabic equivalent of given Roman numbers. i Basic Rules for Writing Roman Numbers VIII IX VI XI III V XVII XIX 5 7 10 12 14 18 20 16 Romans did not have equivalent for 0. So there is no substitute of 0 in Roman numbers. They used total 7 alphabets of their language for representing digits and they are: 1 = I 50 = L 5 = V 100 = C 10 = X 500 = D 40 = XL 1000 = M a. 8 = _____________ b. 3 = _____________ c. 9 = _____________ d. 5 = _____________ e. 6 = _____________ f. 17 = _____________ g. 11 = _____________ h. 19 = _____________ a. V = ___________ b. XIV = ___________ c. VII = ___________ d. XVIII = ___________ e. X = ___________ f. XX = ___________ g. XII = ___________ h. XVI = ___________ A symbol cannot be written more than three times. For example: II = 1 + 1 = 2 III = 1 + 1 + 1 = 3 VI = 5 + 1 = 6 VII = 5 + 1 + 1 = 7 VIII = 5 + 1 + 1 + 1 = 8
40 ii iii Challenge! Write Roman numbers from 21 to 30. How to Read and Wr ead and Wr ead and Write Bigger Number e Bigger Number e Bigger Numbers We use previous rules to read and write bigger numbers. Example 1: Write 35 in Roman numbers. Solution: 35 = 30 + 5 = (10 + 10 + 10) + 5 = XXXV Example 2: Write 68 in Roman numbers. Solution: 68 = 60 + 5 + 3 = (50 + 10) + 5 + (1 + 1 +1) = LXVIII When a smaller number is written at right side of a great number, it is added in previous number. For example: VI = 5 + 1 = 6 XI = 10 + 1 = 11 XV = 10 + 5 = 15 XVI = 10 + 5 + 1 = 16 XVIII = 10 + 5 + 1 + 1 + 1 = 18 When a smaller number is written at left side of a number, it is subtracted from its next number. For example: IV = 5 – 1 = 4 IX = 10 – 1 = 9 XXI XXII XXIII XXIV XXV XXVI XXVII XXVIII XXIX XXX
41 Note: Convert numbers to their equivalent Roman numbers. (symbols) I, V, C, L , C, D, M. Example 3: Write 126 in roman numbers. Solution: 126 = 100 + 20 + 6 = 100 + (10 + 10) + (5 + 1) = CXXVI y Activit 1 Convert Arabic numbers into Roman numbers using table I. y Activit 2 Complete the sequence. a. 3 b. 6 c. 8 d. 10 e. 15 f. 20 g. 25 h. 31 i. 19 j. 46 k. 24 l. 17 21 __________ 22 __________ 23 __________ 24 __________ 25 __________ 26 __________ 27 __________ 28 __________ 29 __________ 30 __________ Arabic Roman Arabic Roman Arabic Roman 31 __________ 32 __________ 33 __________ 34 __________ 35 __________ 36 __________ 37 __________ 38 __________ 39 __________ 40 __________ 41 __________ 42 __________ 43 __________ 44 __________ 45 __________ 46 __________ 47 __________ 48 __________ 49 __________ 50 __________ III XIX XV VI XLVI XX VIII XXIV XXV X XVII XXXI XXI XXII XXIII XXIV XXV XXVI XXVII XXVIII XXIX XXX XXXI XXXII XXXIII XXXIV XXXV XXXVI XXXVII XXXVIII XXXIX XL XLI XLII XLIII XLIV XLV XLVI XLVII XLVIII XLIX L
42 How to Convert Roman Number oman Numbers to Arabic Numbers How to Convert Roman Numbers to Arabic Numbers We have seen that VII = 7 It is because smaller number comes after bigger numbers, i.e, 1 is smaller number and V is bigger number, so we add them. Hence, VII means 5 + 1+ 1 = 7 Example 1: What is the equivalent of XIV. Solution: Here two symbols are used X and IV. X is larger number and IV is smaller number so we add smaller number in larger number. Hence, XIV = X IV = 10 + 4 = 14 Example 2: What is equivalent of IV and IX? Solution: IV smaller number (I) is at left side of larger number (V). So, we subtract smaller number from larger number. So, IV = 5 – 1 = 4 Smaller number (I) is at left side of bigger number (X). So, we subtract smaller number from larger number. So , IX = 10 – 1 = 9 y Activit Write Arabic equivalent of these Roman numbers. a. XV e. C b. XXI f. XXIV c. XVII g. XL d. XIX h. XXIX 15 100 21 24 17 19 40 29
43 1. Write Arabic and Roman number from 1 to 20. 2. Write Roman numbers from XV to XXX. 3. Write in Arabic numbers. Exercise a. XII b. VII c. XVI d. XIV e. XIX f. XXI g. XXXV h. XXXIV i. XXXIX j. XL k. XXV l. XXXI m. XIX n. XXI o. XLV p. XXVII q. XXXIX r. XLII 12 19 39 19 27 7 21 40 21 39 16 35 25 45 42 14 34 31 1 I 6 11 16 VI XI XVI 2 II 3 III 4 IV 5 V 7 8 9 10 12 13 14 15 17 18 19 20 VII VIII IX X XII XIII XIV XV XVII XVIII XIX XX XVI XVII XVIII XIX XX XXI XXVI XXII XXVII XXIII XXVIII XXIV XXIX XXV XXX
44 a. 17 b. 19 c. 21 d. 25 e. 28 f. 34 g. 47 h. 48 i. 52 j. 60 k. 35 l. 47 4. Write in Roman numbers. 5. Add these and convert your answer in Roman number. (One is done for you) + 4 2 1 2 5 4 a. 1 2 2 4 3 6 + b. 2 0 3 0 5 0 + c. 1 7 1 7 3 4 + d. 2 0 4 0 6 0 + e. 1 7 3 3 5 0 + f. 2 5 1 3 3 8 + g. 1 4 2 9 4 3 + h. 3 1 1 8 4 9 + i. 2 4 1 7 4 1 + j. 1 9 1 9 3 8 + k. XVII XXVIII LII XIX XXI XXV XXXIV XLVII XLVIII LX XXXV XLVII L I V X X X V I L X X X I V L X L XXXVIII X L I I I X L I X X L I XXXVIII
45 Unitary Method Student’s Learning Outcomes: After studying this unit, students will be able to: understand basic concept of unitary method. solve questions related to unitary method. understand the situation in which this method is used. differentiate between unitary method and other. Unit 6 Often while shopping we have to calculate if price of one thing is this, than what will be the price of more things. If price of one dozen things is this, what will be the price of one thing. While doing so, we are using unitary method. The method which helps us to find value of a single item or more items is called unitary method. Example 1: If price of 10 pencils is Rs. 70. What is the price of one pencil? Solution: Price of 10 pencils = Rs. 70 Price of 1 pencil = = = Rs. 7 70 10 10 70 70 0 7 _ Price of 10 pencils total pencils Unitary Method Rough Work 10 70 70 0 7 _
46 Example2: If the price of one dozen oranges is Rs.108. What will be the price of one orange? Solution: Price of one dozen oranges = Rs. 108 (remember a dozen means 12) Price of one orange = = = Rs. 9 We can also find price of more items with the help of this method. Example 3: If the price of 5 chairs is Rs.655. What will be the price of such 10 chairs. Solution: First we find the price of one chair by division process and then find the price of 10 chairs by multiplication process. Price of 5 chairs = Rs. 655 Price of 1 chair = = = Rs. 131 Price of 10 chairs = Price of one chair x 10 = Rs. 131 x 10 = Rs. 1310 Price of 5 chairs Total chairs 655 5 5 655 5 15 15 5 5 x 131 _ _ _ 1 3 1 x 1 0 0 0 0 1 3 1 x 1 3 1 0 Price of 12 oranges total oranges 108 12 12 108 108 0 9 Rough Work Rough Work
47 y Activit 1 Find the price of 8 toys if the price of one toy is Rs. 15. y Activit 2 Find the price of one ball if the price of 3 balls is Rs. 210. y Activit 3 Find the price of 12 geometry boxes if the price of 5 geometry boxes is Rs. 275. y Activit 4 Find the price of 1 notebook if the price of 10 notebooks is Rs. 800. I know the Answer! ? ? Price of one toy = Rs.15 Price of eight toys = 15 x 8 = Rs.120 1 5 x 8 1 2 0 Price of 3 balls = Rs.210 Price of one ball = = =Rs.70 Price of balls Total balls 210 3 3 210 210 0 70 Price of 5 geometry boxes = Rs.275 Price of 1 geometry boxes = = 55 Price of 12 g. boxes =Price of 1 g. box x 12 = 55 x12 = Rs.660 275 5 5 275 25 25 25 0 55 Price of 10 notebooks = Rs.800 Price of 1 notebook = = Rs.80 800 10 10 800 800 0 80 5 5 x 1 2 1 1 0 5 5 0 6 6 0
48 Exercise 1. Price of one racket is Rs. 75. Find the cost of such 4 rackets. 2. Price of one school bag is Rs. 345. What will be the cost of such 12 school bags? 3. Price of 11 shirts is Rs.1320. Find the price of such one shirt. 4. Price of 15 balls is Rs. 645. Find the price of one ball. 5. A car can travel 448 km in 14 litres of petrol. What distance will it cover in one litre of petrol? 7 5 x 4 3 0 0 Price of one racket = Rs.75 Price of four rackets = 75 x 4 = Rs.300 3 4 5 x 1 2 6 9 0 3 4 5 0 4 1 4 0 Price of one school bag = Rs.345 Price of 12 school bags = 345 x 12 = Rs.4140 15 645 60 45 45 0 43 Price of 11 shirts = Rs.1320 Price of one shirt = = Rs.120 1320 11 Price of 15 balls = Rs.645 Price of one ball = = Rs.43 645 15 Travel in 14 litres petrol = 448 km Travel in one litres petrol = = 32 km 448 14 11 1320 11 220 220 0 120 14 448 42 28 28 0 32
49 6. Cost of 8 books is Rs.568. What is the cost of such 12 books? 7. Cost of 5 burgers is Rs. 625. What will be the cost of 15 burgers? 8. Cost of 3 pizzas is Rs.750. What will be the price of 8 pizzas? 9. A man earns Rs. 48000 in four months. How much will he earn in one year? 10 If the cost of 5 shoes is Rs. 2000 then complete the given table: Price of 5 shoes = Rs. 2000 Price of 1 shoe = = 400 Price of 2 shoes = 400 x 20 = 800 Price of 10 shoes = 400 x 10 = 4000 Price of one dozen shoes = 400 x 12 = Rs.4800 8 568 56 8 8 0 Cost o 71 f 8 books = Rs.568 Cost of one books = = 71 Cost of 12 books = 71 x 12 = Rs.852 568 8 8 625 5 12 10 25 25 0 125 Cost of 5 burgers = Rs.625 Cost of one burgers = = 125 Cost of 15 burger = 125 x 15 = Rs.1875 625 5 Cost of 3 pizzas = Rs.750 Cost of one pizza = = 250 Cost of 8 pizzas = 250 x 8 = Rs.2000 625 5 3 750 6 150 150 0 250 Earn in four months = Rs.48000 Earn in one month = = 12000 Earn in 12 months (1 year) = 12000 x 12 = Rs.144000 48000 4 4 48000 4 8000 8000 0 12000 2000 5 7 1 x 1 2 1 4 2 7 1 0 8 5 2 1 2 5 x 1 5 6 2 5 1 2 5 0 1 8 7 5 2 5 0 x 8 2 0 0 0 1 2 0 0 0 x 1 2 2 4 0 0 0 1 2 0 0 0 0 1 4 4 0 0 0 5 2000 200 0 0 400
50 Time We use watches and clocks to read the time. But there is more confusion, when we look a clock in the morning and it is showing 7’O clock and in the evening it is again showing 7’O clock. Then what is the difference between these two times? Remember a whole day has 24 hours, but a clock and a watch have numbers from 1 to 12. So, time is divided into two parts ‘a.m.’ and ‘p.m.’ ‘p.m.’ is the time duration from 12:00’O clock noon to 12:00’O clock at night and ‘a.m.’ is the time duration from 12:00’O at night to 12:00’O clock at noon. Student’s Learning Outcomes: After studying this unit, students will be able to: understand concept of a.m and p.m. convert 12-hours format to 24-hours format. convert 24-hours format to 12-hours format. add and subtract time. Unit 7 a.m. p.m. 12 6 1 7 2 8 9 3 4 10 5 11 Super Clock Company 12:00 12:00 midnight noon 12:00 12:00 noon midnight a.m. stands for antemeridiem p.m. stands for postmeridiem 12 6 1 7 2 8 9 3 4 10 5 11 Super Clock Company