Acme Mathematics-4 1019. 67896 people were in a district. If 38930 were women, how many were men?10. A man bought mobile sets for Rs 44321. If he gave Rs 41500. How much money was less to pay the bill?11. Solve the following problems.(a) The sum of two numbers is 700. If one of them is 200, find the other number.(b) The total of money that Sita and Nita have is Rs 7000, if Nita has Rs 400, how much money does Sita have?(c) What is the difference between the smallest and the largest 5-digit numbers?(d) What must be added to 200 to make 800?(e) What must be added to 5534 to make 6000?(f) What must be subtracted from 7654 to get 5555?(g) What must be subtracted from 8888 to get 1999?12. If A = 67890, B = 28907, C = 19888 find(a) A – B (b) B – C (c) A – C
102 Acme Mathematics-410 × 72 × 5 5 × 147 × 10 35 × 2704 × 102 × 20 8 × 53 × 9 4 × 7 405 × 302 × 40 4 × 2010 × 8 5 × 40804 × 53 × 9 2 × 105 × 4 1 × 20201 × 5010 × 5 2 × 84 × 3 2 × 25501 × 902 × 45 2 × 203 × 30 5 × 18906 × 55 × 6 4 × 82 × 15 3 × 10301 × 603 × 20 2 × 62 × 30 3 × 9602 × 504 × 25 5 × 201 × 100 50 × 2100Colour the answer yellow, correct petal red and leaf green.MultiplicationActivity-1
Acme Mathematics-4 103Colour the peacock according to the following colour code.8 × 28 × 28 × 28 × 2 8 × 28 × 28 × 28 × 28 × 98 × 58 × 48 × 28 × 28 × 68 × 68 × 68 × 68 × 68 × 68 × 68 × 68 × 6 8 × 48 × 48 × 48 × 48 × 48 × 48 × 48 × 48 × 8 8 × 48 × 88 × 88 × 88 × 88 × 88 × 88 × 88 × 7 8 × 88 × 38 × 78 × 38 × 38 × 78 × 38 × 78 × 38 × 78 × 1016 24 32 40 48 56 64 72 80Activity-2
104 Acme Mathematics-4A. Multiplication tableStudy the given multiplication table carefully.Multiplication Tables (0 – 12) × 0 1 2 3 4 5 6 7 8 9 100 0 0 0 0 0 0 0 0 0 0 01 0 1 2 3 4 5 6 7 8 9 102 0 2 4 6 8 10 12 14 16 18 203 0 3 6 9 12 15 18 21 24 27 304 0 4 8 12 16 20 24 28 32 36 405 0 5 10 15 20 25 30 35 40 45 506 0 6 12 18 24 30 36 42 48 54 607 0 7 14 21 28 35 42 49 56 63 708 0 8 16 24 32 40 48 56 64 72 809 0 9 18 27 36 45 54 63 72 81 9010 0 10 20 30 40 50 60 70 80 90 10011 0 11 22 33 44 55 66 77 88 99 11012 0 12 24 36 48 60 72 84 96 108 120B. Multiplication as repeated addition4 + 4 + 4 = 123 times 4 oranges3 × 4 = 123× 412We can use multiplication in place of repeated addition. Do you remember multiplication tables?Multiplication is repeated addition.
Acme Mathematics-4 105Classwork1. Fill in the blanks:(a) 2 + 2 + 2 + 2 + 2 (b) 3 + 3 + 3 + 3 = 5 × ........ = ........ = 4 × ........ = ........ (c) 4 + 4 + 4 + 4 + 4 + 4 (d) 5 + 5 + 5 + 5 + 5= 6 × ........ = ........ = 5 × ........ = .........(e) 6 + 6 + 6 + 6 + 6 + 6 (f) 7 + 7 + 7 + 7= 6 × ........ = ........ = ........ × ........ = ........ (g) 8 + 8 + 8 + 8 + 8 (h) 9 + 9 + 9 + 9 + 9 + 9= ........ × ........ = ........ = ........ × ........ = ........(i) 10 + 10 + 10 + 10 (j) 11 + 11 + 11 + 11 + 11= ........ × ........ = ........ = ........ × ........ = ........Exercise 2.161. Fill in the blanks:(a) 3 × 3 = ........ (b) 4 × 4 = ........ (c) 10 × 3 = ........(d) 3 × 4 = ........ (e) 4 × 5 = ........ (f) 7 × 9 = ........(g) 8 × 5 = ........ (h) 3 × 7 = ........ (i) 6 × 9 = ........(j) 8 × 4 = ........ (k) 7 × 4 = ........ (l) 6 × 7 = ........(m) 2 × 8 = ........ (n) 7 × 7 = ........ (o) 2 × 9 = ........(p) 9 × 6 = ........ (q) 5 × 4 = ........ (r) 5 × 7 = ........(s) 9 × 5 = ........ (t) 6 × 8 = ........ (u) 8 × 8 = ........2. Multiply:(a) 4 3× 5(b) 2 2× 7(c) 2 4× 7(d) 4 2× 6
106 Acme Mathematics-4(e) 6 8× 4(f) 8 5× 5(g) 9 4× 6(h) 8 9× 2(i) 7 4× 6(j) 9 2× 5(k) 9 0× 9(l) 4 9× 83. Multiply:(a) 32 by 4 (b) 48 by 7 (c) 85 by 5 (d) 76 by 6(e) 29 by 5 (f) 99 by 4 (g) 98 by 2 (h) 76 by 3(i) 55 by 64. Write a multiplication equation to find the number of shapes.× =× =× =× =× =× =
Acme Mathematics-4 107C. Multiplying 3-digit number by 1-digit number 1. Multiply 231 by 3.H T O2 3 1× 36 9 3Multiply each place in turn. Start with ones place.Step I 1 × 3 = 3 Ones. Write 3 in Ones columnStep II 3 × 3 = 9 Tens. Write 9 in Tens columnsStep III 2 × 3 = 6 Hundreds. Write 6 in Hundreds column.The product = 6932. Multiply 654 by 4.H T O2 16 5 4× 42 6 1 6Step I 4 × 4 = 16 Ones. Write 6 in Ones column and carry 1 to the tens columnStep II 5 × 4 = 20 Tens + 1 Ten (carry) = 21 Tens. Write 1 in Tens column and carry 2 to the Hundreds column.Step III 6 × 4 = 24 Hundreds 24 + 2 = 26 hundredsWrite 6 in Hundreds column and take 2 to the Thousand column.The product = 2616D. Multiplying by 10, 20, 30,........, 901. Multiplying by 104 × 10 = 405 × 10 = 506 × 10 = 607 × 10 = 70You know how we multiply 2-digit number by 1-digit number. In the same way we can multiply 3-digit number by 1 digit number.Is there anything common?To multiply a number by 10 we simply put a zero to the right of the number.
108 Acme Mathematics-42. Multiplying by 20, 30, 40, ........, 904 × 10 = 404 × 20 = 804 × 30 = 1204 × 40 = 1604 × 50 = 2004 × 60 = 2404 × 70 = 2804 × 80 = 3204 × 90 = 3603. Multiply: 42 × 20.42 × 20 = 42 × 2 tens= 42 × 2 × 10= 84 × 10= 840 Classwork1. Multiply:(a) 4 3 2× 2(b) 3 1 0× 2(c) 3 0 1× 3(d)5 1 3× 4(e)6 4 1× 4(f)3 1 4× 52. Fill in the blanks:(a) 12 × 10 = ........ (b) 8 × 20 = ........To multiply a number by 20, 30, 40, ......., 90, we multiply the given number by 2, 3, 4, ....., 9 and put one zero to the right of the product.
Acme Mathematics-4 109(c) 24 × 100 = ........ (d) ........ × 30 = 3000(e) ........ × 33 = 330 (f) ........ × 41 = 410(g) 55 × ........ = 550 (h) 67 × ........ = 67000(i) 78 × ........ = 7800 (j) 100 × ........ = 2300(k) 105 × ........ = 1050Exercise 2.171. Multiply:(a)3 1 5× 6(b)6 1 0× 6(c)1 1 4× 7(d)2 0 9× 8(e)7 0 4× 8(f)3 0 5× 92. Multiply:(a) 333 by 2 (b) 732 by 3 (c) 324 by 4 (d) 652 by 5(e) 246 by 6 (f) 557 by 7 (g) 123 by 8 (h) 128 by 93. Multiply each of the following by 10:(a) 78 (b) 85 (c) 92 (d) 1004. Find the product:(a) 52 × 30 (b) 43 × 40 (c) 62 × 50(d) 58 × 60 (e) 49 × 10 (f) 75 × 205. Multiply:(a) 7 by 400 (b) 8 by 300 (c) 9 by 200(d) 11 by 500 (e) 12 by 700 (f) 15 by 600
110 Acme Mathematics-4E. Multiplying 3-digit numbers by 2-digit numbersExample 1 : Multiply 74 by 23.Solution :Example 2 : Multiply 456 by 34.Solution :F. Multiplying by 10, 100, 1000Study the following example.1. Multiplication by 104 × 10 = 405 × 10 = 506 × 10 = 607 × 10 = 702. Multiplication by 10014 × 100 = 140015 × 100 = 150016 × 100 = 160045 × 100 = 4500T O7 4× 2 32 2 2+ 1 4 8 01 7 0 2Step I Arrange the number as shown.Step II Multiply 74 by 3 ones74 × 3 = 222 onesStep III Multiply 74 by 2 tens74 × 20 = 1480Step IV Add both the products222 + 1480 = 1702H T O4 5 6× 3 41 8 2 4+ 1 3 6 8 01 5 5 0 4Step I Arrange the number as shown .Step II Multiply 456 by 4 ones456 × 4 = 1824 onesStep III Multiply 456 by 3 tens456 × 3 tens = 1368 tens = 13680Step IV Add both the products1824 + 13680 = 15504Is there anything common?To multiply a number by 10, we simply put a zero to the right of the numberTo multiply a number by 100, we multiply the given number by 1 and put two zeros to the right of the product.
Acme Mathematics-4 1113. Multiplication by 10001 × 1000 = 10002 × 1000 = 20003 × 1000 = 30004 × 1000 = 40005 × 1000 = 50004. Multiplication by 20, 30, 50, etc.7 × 20 = 7 × 2 × 10 = 1408 × 30 = 8 × 3 × 10 = 24025 × 50 = 25 × 5 × 10 = 1250G. Multiplying 3-digit numbers by 3-digit numbersMultiply 789 by 1231. Arrange the numbers.2. Multiply by the ones.3. Multiply by the tens.4. Multiply by the hundreds.5. Add the products.Classwork1. Multiply:(a) 4 8× 2 3+(b) 5 7× 2 5+(c) 4 9× 2 6+To multiply a number by 20, we multiply the given number by 2 and put one zero (0) to the right of the product.Th H T O7 8 9 Arrangement× 1 2 32 3 6 7 Product of Ones1 5 7 8 0 Product of Tens + 7 8 9 0 0 Product of Hundred9 7 0 4 7 Sum of 3 products
112 Acme Mathematics-4(d) 5 2 3× 2 1+(e) 7 5 2× 2 4+(f) 5 1 8× 3 5+2. Fill in the blanks:(a) 6 × 20 = ..................... (b) 9 × 30 = ....................(c) 8 × .................... = 240 (d) 50 × .................... = 150(e) 600 × 7 = .................... (f) 14 × 300 = ................(g) 400 × .............. = 5600 (h) ............ × 33 = 33000(i) 3 × 1 = .................... (j) 19 × .................... = 19(k) 14 × 0 = .................... (l) 0 × 66 = ......................(m) 55 × 0 = .................... (n) 0 × 123 = ....................(o) 1 × 200 = .................... (p) 900 × 1 = ....................Exercise 2.181. Multiply the following:(a) 4 3 2× 1 2+(b) 9 6 7× 2 2+(c) 8 5 3× 3 4+(d) 4 3 8× 4 1+(e) 6 8 5× 4 5+(f) 5 3 2× 4 9+
Acme Mathematics-4 113(g) 3 4 2× 3 3+(h) 4 6 7× 4 4+(i) 8 4 2× 5 5+2. Multiply each of the following numbers by 10:(a) 176 (b) 895 (c) 972 (d) 3453. Find the product:(a) 452 × 100 (b) 443 × 100 (c) 642 × 100(d) 578 × 100 (e) 489 × 100 (f) 795 × 1004. Multiply by 1000:(a) 675 (b) 834 (c) 957(d) 915 (e) 729 (f) 8565. Multiply:(a) 127 by 400 (b) 834 by 300 (c) 129 by 200(d) 161 by 500 (e) 912 by 700 (f) 955 by 6006. Multiplying the following:(a) 5 4 3× 2 3 4+(b) 6 7 8× 3 4 5+(c) 8 4 3× 4 3 2+(d) 4 9 8× 2 1 3+(e) 9 8 7× 2 1 0+(f) 1 2 3× 9 1 8+
114 Acme Mathematics-4(g) 4 5 6× 9 2 9+(h) 7 8 9× 3 4 6+(i) 6 3 4× 8 8 6+7. Multiply:(a) 128 by 161 (b) 509 by 152 (c) 235 by 122(d) 615 by 321 (e) 332 by 213 (f) 716 by 262(g) 464 by 251 (h) 865 by 223 (i) 999 by 333Key Words Used in Multiplication's Word Problemsmultiplied bytimestablegroupsoflots ofmultiplytimesproduct
Acme Mathematics-4 115Word problems on multiplicationStudy the given examples:Example 1 : In a library there are 237 books in one place, if there are 75 such places. Find the number of books in the library.Solution: This problem is related to multiplication.So,There are 17775 books in the library.Example 2 : The cost of a teddy bear is Rs.755. Find the cost of 98 such teddy bear.Solution:The cost of 98 teddy bear is Rs. 73990.Classwork1. Fill in the blanks:(a) 1 chocolate cost Rs. 10. 5 chocolates cost ............ rupees.(b) 1 cow gives 20 litre of milk. 5 cows give ................ milk.(c) 1 dog eat 5 kg. 8 dogs eat ................ kg.(d) 1 book cost Rs. 100. 6 books cost ................ rupees.(e) 1 radio cost Rs. 200. 5 radios cost ................ rupees. 2 3 7 × 7 5 1 1 8 5 1 6 5 9 0 1 7 7 7 5755× 9860406795073990
116 Acme Mathematics-42. Do the following word problems carefully.(a) There are 42 chairs in a hall. How many chairs are there in 7 such halls?(b) An ice-cream factory produces 125 ice-creams in a day. How many ice– creams does it produce in 9 days?(c) Roshan spends Rs. 210 in a month on transportation. How much does he spend in 9 months ?(d) A book has 126 pages. Find the number of a pages in 6 such books.(e) There are 504 questions in a textbook. How many questions are there in 3 such text books?Exercise 2.191. There are 123 books in each class. How many books are there in 78 such classes?2. There are 264 packets of noodles in one carton. How many packets of noodles will be there in 400 such cartons?3. The cost of one t-shirt set is 900 rupees. How much money is needed to buy 234 such t-shirt?4. There are 321 flowers in one garden. How many flowers are there in 625 such gardens?
Acme Mathematics-4 1175. There are 714 marbles in one box. How many marbles are there in 705 such boxes?6. There are 312 grapes in one grape-vine. How many grapes are there in 210 such grape-vines?7. There are 515 students in one school. How many students are there in 142 such schools?8. The cost of one dinner plate is 450 rupees. What will be the cost of 250 such dinner plates?9. There are 123 pens in one box. How many pens are there in 120 such boxes?10. There are 3 triangles, 3 stars, 10 rectangles and 5 pentagons. How many vertices are there altogether?PROJECT WORKIn the table, monthly consumption of foods and their price are given. Calculate the total expenditure of Jaykrishna' family.Items Quantity Price (Rs.) Total Cost (Rs.)1. Rice2. Oil3. Sugar4. Daal5. Salt6. Milk50 kg5 liter2 kg4 kg2 kg60 liter90/kg380/ltr120/kg125/kg20/kg100/ltr..................................................................................................................................................................TotalIn Words : ................................................................................................................
118 Acme Mathematics-4DivisionA. Division as repeated subtractionStudy the following:How many times 25 can be subtracted from 100?25 can be subtracted 4 times from 100.It can also be written as 100 ÷ 25 = 4Hence, division is the repeatedsubtraction of the same number.Remember The number to be divided is called dividend. The number which divides is called divisor. The number you get is the quotient. The number left over is called the remainder.Let's see the example.Here, Quotient = 4Remainder = 0Oh!4 timesSubtraction 1 0 0 – 2 5 7 5 – 2 5 5 0 – 2 5 2 5 – 2 5 01 time2 times3 times4 times100 ÷ 25 is adivisionproblem÷ is the sign for division 25) 1 0 0 (4 – 10 0 × 15) 6 0 (4 – 6 0 0DivisorDividendQuotientRemainder60 ÷ 15
Acme Mathematics-4 119Remember: When a number is divided by 1, the quotient is the number itself.Examples: 5 ÷ 1 = 5, 10 ÷ 1 = 10 525 ÷ 1 = 525 When a number is divided by itself the quotient is always 1.Examples: 5 ÷ 5 = 1 10 ÷ 10 = 1 525 ÷ 525 = 1 When 0 is divided by any number (except 0) the quotient is always 0.Examples: 0 ÷ 5 = 0 0 ÷ 10 = 0 0 ÷ 525 = 0 We can not divide a number by zero (0). Dividend = divisor × quotient + remainderExample 1 : Divide 37 by 3.Solution: Here, 37 ÷ 3Hence, 37 = 3 × 12 + 1Dividend QuotientDivisorRemainderZero at the end and divisionStudy the following examples:770 ÷ 70 = 77 ÷ 7 = 111100 ÷ 1100 = 11 ÷ 11 = 11500 ÷ 500 = 15 ÷ 5 = 32000 ÷ 400 = 20 ÷ 4 = 53050 ÷ 50 = 305 ÷ 5 = 61Zeros at the end of dividend and divisor makes the division easy.Interesting 7 ÷ 0is not possible1 2× 33 6+ 13 7CheckQuotientRemainderDivisorDividend 3) 3 7 (12 – 30 7 – 61We can cancel the equal number of zeros from the end of dividend and divisor.
120 Acme Mathematics-4Classwork1. Fill in the blanks.(a) 12 – 2 – 2 – 2 – 2 – 2 – 2 12 ÷ 2 6(b) 25 – 5 – 5 – 5 – 5 – 5 ........... ...........(c) ....................................... 20 ÷ 4 ...........(d) 30 – 10 – 10 – 10 ........... ...........(e) ......................................... 45 ÷ 9 ...........2. Complete the table.Dividend Divisor Quotient Remainder(a) 14 ÷ 2(b) 20 ÷ 5(c) 28 4 7 0(d) 6 4 2(e) 49 6Exercise 2.201. Fill in the blanks.(a) 18 ÷ 1 = ...................... (b) 50 ÷ 1 = ....................(c) 19 ÷ ..................... = 19 (d) 44 ÷ 1 = ...................(e) ..................... ÷ 1 = 30 (f) .................. ÷ 1 = 40(g) 0 ÷ 9 = ....................... (h) 0 ÷ 19 = .....................2. Is 21 ÷ 0 possible?3. Divide and write the quotient in the box.(a) 20 ÷ 10 = (b) 50 ÷ 10 = (c) 100 ÷ 100 = (d) 300 ÷100 = (e) 500 ÷ 10 = (f) 700 ÷ 10 = (g) 100 ÷ 50 = (h) 150 ÷ 30 = (i) 140 ÷ 70 = (j) 280 ÷ 40 =
Acme Mathematics-4 121(k) 200 ÷ 100 = (l) 800 ÷ 200 = 4. Divide and write the quotient and the remainder.(a) 324 ÷ 10 (b) 462 ÷ 20 (c) 209 ÷ 20 (d) 887 ÷ 40(e) 666 ÷ 30 (f) 789 ÷ 70 (g) 550 ÷ 20 (h) 880 ÷ 60[Remember! Dividend = Divisor × Quotient + Remainder]C. Dividing 3-digit numbers by 1-digit numberLet us divide 246 by 2.2 2 4 6–20 4– 40 6– 601 2 3H T O Step I Divide 2 Hundreds by 2.2 ÷ 2 =1Write 1 in the hundred place of the quotient.Step II Divide 4 Tens by 2.4 ÷ 2 = 2. Write 2 in tens place of the quotient.Step III Divide 6 ones by 2.6 ÷ 2 = 3. Write 3 in ones place of the quotient.So, 246 ÷ 2 = 123Let us divide 804 by 4.4 8 0 4–80 0– 00 4– 402 0 1H T OStep I Divide 8 hundreds by 4.8 ÷ 4 = 2Step II Divide 0 tens by 4.0 ÷ 4 = 0Step III Divide 4 Ones by 4.4 ÷ 4 = 1So, 804 ÷ 4 = 201
122 Acme Mathematics-4Let us divide 693 by 3.3 6 9 3–60 9– 90 3– 302 3 1H T O Step I Divide 6 hundreds by 3.6 ÷ 3 = 2 Step IIDivide 9 tens by 3.9 ÷ 3 = 3Step III Divide 3 Ones by 3.3 ÷ 3 = 1So, 693 ÷ 3 = 231Let us divide 800 by 2.2 8 0 0–80 0– 00 0– 004 0 0H T O Step I Divide 8 hundreds by 2.8 ÷ 2 = 4Step IIDivide 0 tens by 2.0 ÷ 2 = 0Step III Divide 0 Ones by 2.0 ÷ 2 = 0So, 800 ÷ 2 = 400You may verify your answers. Remember ! Dividend = Divisor × Quotient + RemainderVerificationDivisor × Quotient + Remainder = Dividend2 × 400 + 0 = 800800 + 0 = 800800 = 800It is verified.
Acme Mathematics-4 123Classwork1. Divide using repeated subtraction method:(a) 12 by 3 (b) 21 by 7 (c) 40 by 8(d) 20 by 4 (e) 16 by 4 (f) 36 by 6.2. Divide using long division method:(a) 64 by 2 (b) 48 by 4 (c) 86 by 2(d) 30 by 5 (e) 63 by 3 (f) 45 by 5(g) 36 by 3 (h) 48 by 6 (i) 54 by 9Exercise 2.211. Find the quotient and verify the answer:(a) 286 ÷ 2 (b) 402 ÷ 2 (c) 440 ÷ 2 (d) 482 ÷ 2(e) 662 ÷ 2 (f) 808 ÷ 2 (g) 333 ÷ 3 (h) 339 ÷ 3(i) 963 ÷ 3 (j) 600 ÷ 3 (k) 666 ÷ 3 (l) 480 ÷ 4(m) 880 ÷ 4 (n) 800 ÷ 4 (o) 500 ÷ 5 (p) 550 ÷ 5D. Division with remainderLet us divide 98 by 3Start with tens9 ÷ 3 = 39 – 9 = 0 nothing is leftBring down 8 ones8 ÷ 3 = 2 and 2 is left.8 – 6 = 2So, 2 is the remainder.3 9 8–90 8– 623 2RemainderNow divide 697 by 3
124 Acme Mathematics-43 6 9 7–60 9– 00 7– 612 3 2 Step I Divide 6 hundred by 36 ÷ 3 = 2Step II Divide 9 tens by 3.9 ÷ 3 = 3Step III Divide 7 ones by 3.3 × 1 = 33 × 2 = 63 × 3 = 9 (9 is bigger than 7 ones)So write 2 in the quotient.7 – 6 = 1, remainder.Quotient = 232 and Remainder = 1Divide 4849 by 4Step II Divide 4 hundred by 4.4 ÷ 4 = 1Step III Divide 8 tens by 4.4 ÷ 8 = 2Step IV Divide 7 ones by 4.4 × 1 = 44 × 2 = 8 (8 is bigger than 7 ones ). So, write 1 in the quotient.7 – 4 = 3, remainderQuotient = 121 and Remainder = 34 4 8 7–40 8– 80 7– 431 2 1ClassworkDo the following division and find out quotients and remainders:(a) 25 ÷ 4 (b) 39 ÷ 4 (c) 37 ÷ 5 (d) 43 ÷ 6(e) 43 ÷ 5 (f) 50 ÷ 6 (g) 59 ÷ 7 (h) 44 ÷ 7Exercise 2.22Do the following division and find out quotients and remainders:(a) 664 ÷ 3 (b) 6395 ÷ 3 (c) 445 ÷ 4 (d) 8406 ÷ 4(e) 557 ÷ 5 (f) 5505 ÷ 5 (g) 668 ÷ 6 (h) 2469 ÷ 6(i) 359 ÷ 7 (j) 4978 ÷ 7 (k) 569 ÷ 8 (l) 6489 ÷ 8(m) 457 ÷ 9 (n) 9997 ÷ 9 (o) 2465 ÷ 2 (p) 8876 ÷ 9Division is not as hard as I had thought!
Acme Mathematics-4 125F. Division with regroupingLet us divide 685 by 9.9 6 8 5– 6 30 5 5– 5 417 6 Step I Start with hundred6 is less than the divisor 9.So we take the hundred and tens together.Step II Now, 68 is the dividend68 ÷ 9,9 × 7 = 63 is less than 689 × 8 = 72 is greater than 68So, we take 9 × 7 = 6368 ÷ 9 = 7 (write 7 in the quotient)Remainder = 5Step III Bring down 5 from ones place.55 is the new dividend.55 ÷ 9 = 6 (write 6 in the quotient)Remainder = 1Let us divide 763 by 3.3 7 6 3– 61 6– 1 51 3– 1 212 5 4 Step I Start with hundreds7 ÷ 3 = 2, Remainder = 1Step IIBring down 6 from tens place.16 is the new dividend. 16 ÷ 3 = 5, Remainder = 1Step III Bring down 3 from ones place.13 is the new dividend. 13 ÷ 3 = 4Remainder = 1So, 763 ÷ 3 = 254, remainder = 1
126 Acme Mathematics-4VerificationDividend = Divisor × Quotient + Remainder763 = (3 × 254) + 1763 = 762 + 1763 = 763 it is verified.Can we verify our division?G. Division by 10Let us divide 83 by 10.10 8 3– 8 038Quotient = 8Remainder = 3Now, divide 678 by 10.10 6 7 8– 6 07 8– 7 086 7Quotient = 67Remainder = 8Quotient Remainder 63 ÷ 10 963 ÷ 106 963 3Classwork1. Divide and find the quotient and remainder:(a) 60 ÷ 7 (b) 71 ÷ 8 (c) 346 ÷ 9(d) 564 ÷ 8 (e) 506 ÷ 7 (f) 608 ÷ 9Remember ! Digit in ones place is the remainder and digit in tens place is the quotient.When we divide 678 by 10,digit in ones place is the remainder and other digits of the number make quotient.
Acme Mathematics-4 1272. Find the quotient and remainder:(a) 85 ÷ 10 (b) 99 ÷ 10 (c) 205 ÷ 10(d) 215 ÷ 10 (e) 368 ÷ 10 (f) 440 ÷ 10Exercise 2.231. Divide and find the quotient and remainder:(a) 726 ÷ 5 (b) 345 ÷ 6 (c) 242 ÷ 7(d) 454 ÷ 8 (e) 500 ÷ 9 (f) 568 ÷ 52. Find the quotient and remainder:(a) 510 ÷ 10 (b) 650 ÷ 10 (c) 785 ÷ 10(d) 888 ÷ 10 (e) 980 ÷ 10 (f) 999 ÷ 10H. Dividing 3-digit numbers by 2-digit numbersDivide 487 by 1515 4 8 7– 4 53 7– 3 073 2 Step I The first digit from the left is 4, which is less than 15Step II We consider the next digit beside it which is 8. We take 48Step III 48 tens ÷ 15 = 3 tens and 3 tens remainderStep IV Bring down the ones digit.37 ones ÷ 15 = 2 ones and 7 ones remainderSo, 487 ÷ 15 = 32, remainder = 7You may verify your answers. So Remember!Dividend = Divisor × Quotient + RemainderI'm getting smarter day by day!VerificationDivisor × Quotient + Remainder = Dividend15 × 32 + 7 = 487480 + 7 = 487487 = 487It is verified.
128 Acme Mathematics-4Classwork1. (a) 18 – 6 – 6 – 6 can be written as,(i) 12 (ii) 18 ÷ 6 (iii) 36 (iv) 18666(b) In 37 ÷ 4, 4 is called,(i) Dividend (ii) Quotient (iii) Divisor (iv) number(c) When 870 is divided by 10, the quotient is:(i) 8700 (ii) 87 (iii) 870 × 10 (iv) 870 ÷ 102. (a) Divide and find the quotient: 130 ÷ 50(b) Divide: 999 ÷ 253. Fill in the blanks.(a) Divisor × quotient + ......................... = Dividend.(b) Dividend = Divisor + .........................(c) In 36 ÷ 4 = 9, (i) 36 in called ....................... .(ii) 4 is called ....................... .(iii) 9 is called .......................(d) If divisor is 4, quotient 2 and remainder is 3 them dividend is ............. .Exercise 2.24Find the quotients and remainders and verify the answers:(a) 149 ÷ 10 (b) 163 ÷ 11 (c) 829 ÷ 11 (d) 649 ÷ 12(e) 453 ÷ 12 (f) 685 ÷ 13 (g) 798 ÷ 13 (h) 281 ÷ 14(i) 397 ÷ 15 (j) 285 ÷ 16 (k) 581 ÷ 17 (l) 120 ÷ 18(m) 496 ÷ 18 (n) 873 ÷ 19 (o) 128 ÷ 20 (p) 135 ÷ 20(q) 610 ÷ 25 (r) 818 ÷ 30 (s) 999 ÷ 36 (t) 800 ÷ 40
Acme Mathematics-4 129I. Word problemThere were 684 stickers to be shared among 6 children. How many did each get?Total stickers = 684Number of children = 6Each of child got 684 ÷ 6 stickersNow,Each child got 114 stickers.Classwork1. Rohini brought in 36 pizza rolls for the 6 girls at the party. How many pieces did each girl receive?2. Kali Prasad had 84 sheets of music to pass out. Each musician received 4 sheets. How many students did he have in his chor?3. Eight children were invited to Indira's party. She made 49 cookies to share with her friends.(a) How many cookies did each of her friends receive?(b) How many cookies were left over?4. 852 balloons needed to be filled with water. The coach asked that each student fill 6 ballons. How many students helped fill them?5. Sumi has 974 gold stickers. She wants to give equal number to 9 students.(a) How many stickers will each student receive?(b) How many stickers are left?Remember multiplication tables. You'll need them for division. 6 6 8 4– 60 8– 62 4– 2 40 01 1 4
130 Acme Mathematics-4Exercise 2.25Solve the following division problems:1. There were 550 sweets in a packet. If there were 5 students, how many sweets did each get?2. There were 432 eggs. If there were 12 baskets, how many eggs were there in each basket?3. There were 690 ice-creams. If there were 15 families, how many ice-creams did each family get?4. Rs. 240 was to be shared by 80 people. How much did each person get?5. There are 480 students in a school. If there are 12 classes, how many students are there in each class?6. There are 400 children who want to learn computer. If there are 25 children in 1 group, how many groups are there?7. 12 video games cost Rs. 792. Find the cost of 1 video game.8. There are 980 birds in a zoo. If there are 35 cages, how many birds are there in each cage?9. Some ice-creams cost Rs. 885. If each ice-cream costs Rs. 5, how many ice-creams were there?10. Sarthak spent Rs. 990 on two trouser. What was the cost of each suit?
Acme Mathematics-4 13111. There were 160 kg of rice in some bags. If each bag had 5 kg, how many bags were there?12. There are 994 sheets of paper. If I want to make 7 bundles, how many sheets of paper will there be in each bundle?13. In class - 4, there are 41 students and there are 500 copies to distribute them equal. (a) How many copies each student get?(b) How many copies are left there?(c) How many copies should be added to distribute them equal so that each get 13 copies?14. The cost of 1 chocopan is Rs. 13. (a) How much chocopan can Esha buy from Rs. 169.(b) If she gave Rs.200 to shopkeeper, how much rupees she got return back?15. A crate can hold 30 eggs. A farmer has 999 eggs. (a) How many crates does farmer need?(b) How many eggs are left?(c) How many eggs should be added to fill one crate more?J. Relation between multiplication and division9 × 8 = 728 × 9 = 72Factor × Factor = ProductDivisor × Quotient = DividendMultiplication Facts Division Facts6 × 7 = 42 42 ÷ 6 = 77 × 6 = 42 42 ÷ 7 = 6Divisor DividendQuotient9 728Multiplication and Division are inverse operations. For every multiplication fact we have two division facts.
132 Acme Mathematics-4Exercise 2.26Check your answers by multiplication fact:(a) 60 ÷ 5 = 12, 5 × 12 = 60 , 60 ÷ 12 = 5(b) 50 ÷ 10 = 5, = , 50 ÷ 5 = 10(c) 72 ÷ 9 = 8, = , ÷ 8 = 9(d) 49 ÷ 7 = 7, = , ÷ 7 = 7(e) 84 ÷ 12 = 7, = , ÷ 7 = 12(f) 55 ÷ 11 = 5, = , ÷ 5 = 11(g) 90 ÷ 5 = 18, = , ÷ 18 = 5SimplificationAdd first then subtract.Put the same sign together.(a) Simplify : 12 + 13 – 17Here, 12 + 13 – 17= 25 – 17= 8(b) Simplify : 20 – 8 + 7Here, 20 + 7 – 8= 27 – 8= 19Exercise 2.271. Tick the correct result:(a) 5 + 7 – 2 = 10 (b) 6 + 13 – 4 = 3 (c) 15 + 5 – 6= 14(d) 8 + 10 – 7 = 11 (e) 1 + 20 – 7 -=12 (f) 2 + 30 – 10 = 22(g) 20 – 8 + 2 = 16 (h) 30 – 10 + 7 = 28 (i) 15 – 5 + 7 = 17
Acme Mathematics-4 1332. Simplify: (add first)(a) 16 + 4 – 2 (b) 5 + 16 – 4 (c) 19 + 50 – 5(d) 10 + 10 – 10 (e) 8 + 14 – 7 (f) 20 – 15 – 3(g) 24 – 4 – 2 (h) 25 – 8 – 23. Simplify:(a) 18 – 12 + 15 (b) 12 + 15 – 3 (c) 115 + 114 – 50(d) 111 + 112 – 113 (e) 128 – 412 + 516 (f) 234 + 507 – 6124. Simplify:(a) 2896 – 3874 + 4444 (b) 7893 – 2580 – 3876(c) 9999 + 8463 – 7892 (d) 10000 + 67891 – 56789(e) 78934 – 25803 – 38668 (f) 82963 – 54783 + 222225. (a) A mobile phone costs Rs.15875. It is Rs.1898 cheaper than Guitar. What is the cost of a Guitar?(b) Soni had a total of 100 candies. She gave 3 candies to each of her 10 griends. She again purchased 45 more candies.(i) Convert the above verbal statement into mathematical statement.(ii) Simplify the statement?(iii) How many candies she has now?(c) Amara had Rs.300. Her father gave her Rs.450. She bought a diary of Rs.175.(i) Convert the above verbal statement into mathematical statement.(ii) Simplify the statement?(iii) How much money is left with Amara?(d) 150 is subtracted from the sum of 200 and 7. (i) Convert the above verbal statement into mathematical statement.(ii) Simplify the statement?(iii) Is answer 50?6. Can you solve this puzzle? Write the numbers 11, 12, 13, 14, 15 and 16 in the circles, so that the sum of the numbers on each side is 22.Sum22
134 Acme Mathematics-4Project Work1. Objective : To identify the quotient, divisor and dividend.2. Materials required : A number grid Colours Pencil3. Activity : Find 3 number and colour them such that one is divisor, the other is dividend and the third is quotient. 8 2 4 9 1 10 7 3 212 4 4 0 2 5 6 30 316 8 16 6 1 50 42 1 71 0 4 6 7 2 14 30 020 2 48 36 9 100 0 8 08 24 1 18 1 2 3 6 182 24 48 1 9 5 7 48 016 2 32 18 1 10 2 20 0For example: 42 ÷ 6 = 742 is called dividend.6 is called divisor.7 is called quotient4. Now, make 10 such examples.
Acme Mathematics-4 1351. A rice mill sold 95,345 sacks of rice in Baishakh, 78,842 in Jeshta and 9702 in Asar.(a) Find the total sacks of rice in three months.(b) Round off the given numbers to the nearest 10 and 100.Number Nearest 10 Nearest 10095,34578,8822. Ram gave 'thirteen lakhs fifty six thousand and two' rupees for his sister.(a) Write in the number(b) Write the place value of 3(c) Write in the expanded form3. Sita bought a car for Rs. 45,60,506. (a) Insert the given number by making place-value chart. (b) Write in words the cost of car.(c) Fill in the blank: 35,289 + ................. = 1,50,2504. Consider the numeral : 24823(a) Write the given Hindu-Arabic number into Devnagari number.(b) Write the given numeral in words in Devnagari number system.(c) Show the given numeral in place value table.5. The population of a town in 8347256. Answer the following questions.(a) Rewrite the numeral after using comma (,) and then in words.(b) What is the place value of 3 in the numeral?(c) Write the given numeral in expanded form and power of 10 form.6. Solve the following:(a) 72345 + 2632.(b) In a school, out of 25785 students 19987 are the girls. Find the number of boys.(c) Perform 275 ÷ 6 and verify that : Divisor × Quotient + Remainder = DividendMixed Exercise
136 Acme Mathematics-47. Write the number into word and word into number.(a) 36,03,123(b) Fifty one lakhs eighty seven thousand four hundred and seventy two.(c) Round off the given number.(i) 53 (in ten) (ii) 270 (in hundred)8. (a) Add : (b) 34 + 18(c) In 4,56,213 where does 6 lie?(i) Ten's place (ii) Hundred's place (iii) Thousand's place9. (a) Subtract : (b) 811 – 511(c) Which is the number, if 16 is rounded off to the nearest ten?(i) 20 (ii) 30 (iii) 1010. (a) Multiply : (b)(c) What is the product of 5 and 4?(i) 20 (ii) 9 (iii) 3011. (a) Divide : 3)504( (b) 30)150((c) What is obtained when 8 is added to the product of 4 and 3?(i) 15 (ii) 20 (iii) 9012. (a) Simplify : 15 – 6 + 3 (b) (15 – 5) + 5 – 2(c) Which sign is use first in simplify?(i) + (ii) – (iii) both13. Tick () the correct answers.(a) The smallest 5 digit number is ............ .(i) 10000 (ii) 99999 (iii) 11111(b) The sum of two number 347829 and 895751 is ............ .(i) 1243580 (ii) 1253580 (iii) 1253590(c) Multiply : 43461+ 3208152271– 312923256× 42456× 357890× 53
Acme Mathematics-4 13714. (a) Divide : 14) 476 ((b) Write 3929057 in the expanded form.(c) Round off the following to the nearest 10.(i) 21 (ii) 422 (iii) 816715. The number 7653412 is given:(a) Write the following numerals in the place value chart (b) Write their number name is Hindu-Arabic number system.16. Observe the price of the given bike and answer the following.(a) Write the price using comma.(b) Write the price of the bike in words.(c) Show its price in abacus.17. The number 9876054 is given.(a) Rewrite and use commas according to our Number system of given number.(b) Write the expanded form of the given number.(c) Put the international place value chart and write in words of the given number.18. (a) Subtract and verify the answer by using inverse operation. 350 – 41.(b) The sum of two numbers is 98720, the smaller number is 31841. Find the larger one.(c) Round off 846i. to the nearest ten. ii. to the nearest hundred.19. Kedar wants to plant cauliflower in his land. He has Rs 12,263. He need Rs 15,000 more for cultivate the land. He took loan Rs 18000 from his friend Prem.(a) How much money do Kedar has?(b) He bought 2000 cauliflower seedling for Rs 10000. How much money is left with him?(c) If he needs fertilizer for Rs 5000, how much money is needed to him?Rs 560000
138 Acme Mathematics-4EvaluationTime: 50 minutes Full Marks: 211. A book has 220 pages.(a) How many pages are there in 20 such books ? [2] (b) By how much the total number of pages is less than 5000 ? [2] (c) The cost of a book is Rs. 360. Ram buy 20 such books, find the amount of change that Ram received if he gave the shopkeeper Rs. 10,000. [2] 2. (a) Simplify M 16 ÷ 4 + 3 × 2- 5 [2] (b) Multiply [2] 367 ×45 (c) Subtract : 8742– 4653 [1] 3. Sabin has Rs. 34,250 and planned to goat farming in his village. From municipality the gain Rs. 60,750 agriculture grant for his planning. (a) Find out the total money does Sabin have including agriculture grant from municipality ? [1](b) If Sabin spend Rs. 35,850 for goat kids and Rs. 45,250 for built goat pen then, (i) How much money does he spend ? [1] (ii) How much money does he have left ? [1]4. The cost of one book is Rs. 245 (a) Rounding off the amount Rs 245 in nearest ten. [1](b) Find the cost of 32 books. [2](c) Divide: 245 ÷ 5 [2] (d) Simplify: 9 × 2 + 7–12 [2]
Acme Mathematics-4 139Colour 14 Colour 25Colour 13 Colour 15Colour 24 Colour 34Colour 23 Colour 45Colour 35 Colour 122.3 FractionDo the following activities.Activity
140 Acme Mathematics-4A. IntroductionThe figure alongside is a pizza. It is circular and divided into three equal parts. Each part is written as 13and read as one by three. It is called one-third of the whole pizza.The figure alongside is a rectangle. It is divided into two equal parts. One part of it is shaded. It is written as 12and read as one-half.23 is shaded, two-third shaded.14 is shaded, one-fourth is shaded.16 is shaded , one-sixth is shaded.34 is shaded, three-fourth is shaded.Fraction means part of a whole, that is less than one. Each part represents the fractional number.12, 13, 23, 16, 34, etc. are all fractions.B. Numerator and denominatorIn 34 the number 3 is called the numeratorand 4 is called the denominator.34 is read as 3 by 4 or 3upon 4. 34 is shaded. 34NumeratorDenominator12 12
Acme Mathematics-4 141Total parts = 5Shaded parts = 3Three-fifth is shaded.Total parts = 8Shaded parts = 5Five-eighths is shaded.1. Match the following:1427232645342. Study the following figure and circle the correct fraction.(a) 12 56 16 16 65 Classwork
142 Acme Mathematics-41. Write the numerator in the following fractions:(a) 13(b) 25(c) 56(d) 46(e) 710(f) 37(b)(c)(d)(e)(f)(g)(h)(i)12 16 38 17 68 13 12 36 15 14 46 46 57 16 35 13 12 14 15 21 12 56 34 14 43 16 33 23 13 25 35 54 34 46 45 14 36 34 13 15 Exercise 2.28
Acme Mathematics-4 1432. Tick () the fractions with 7 as denominator:(a) 37(b) 79(c) 17(d) 47(e) 78(f) 273. Write the fractions with:(a) 1 as numerator and 2 as denominator(b) 4 as denominator and 3 as numerator(c) 7 as denominator and 4 as numerator(d) 5 as numerator and 8 as denominator4. Write the fractions for each of the following:(a) Two-fifth 25 (b) Seven-tenth(c) One-third (d) Three-eighth(e) Three-fourth (f) Two-third(g) Eight-tenth (h) Nine-tenth5. Write the name for each fraction:(a) 14 One-fourth (b)37(c) 48 (d)13(e) 57 (f)7106. Shade the parts as shown in each fraction:(a) 14 (b) 35(c) 48 (d) 13(e) 57 (f) 710
144 Acme Mathematics-47. Study the given fraction and choose the correct shaded fraction notation in the box.3945135936344833891105712
Acme Mathematics-4 145C. Unit FractionA unit fraction is any fraction with 1 as its numerator (top number) and a whole number for the denominator (bottom number).Examples of unit fractions are given below:1213181511011212011 971614D. Like FractionsStudy the given fractions carefully.15 One - fifth25 Two - fifth35 Three - fifth45 Four - fifth15, 25, 35 and 45are the parts of the same whole as their denominator is the same. These are like fractions as their denominator are the same.25, 12, 37 and 46are fractions having different denominators. So, they are unlike fractions.Read these fractions.
146 Acme Mathematics-4E. Ordering of Fractions121314 > >342414 > >Study the figure1121314151617181 > 12 > 13 > 14 > 15 > 16 > 17 > 18F. Fraction on the Number Line2 310 3 12 43 410 4 1Let's see which fraction is greater?When the numerator is same then the fraction that has smaller denominator is greater.When the denominator is same then the fraction that has greater numerator is greater.
Acme Mathematics-4 147Classwork1. Choose the like fractions:(a) 12, 34, 14, 24, 13, 27 (b) 23, 57, 17, 12, 47, 37 (c) 16, 25, 18, 36, 17, 56(d) 49, 27, 59, 19, 59, 38 (e) 57, 27, 39, 38, 67, 17 (f) 16, 17, 18, 19, 382. Compare the following using given comparison symbol; <, >, = .110 13 14 13 19 17 12 12 18 14 12 12 15 15 15 12 18 110 3. Put the sign (<, = or >) : 15184. Tick () the unit fraction : 37 , 18 , 29 , 1125. Complete the number line:0 15 35
148 Acme Mathematics-42. Compare the shaded fractions in the shapes by using <, > or =.1. Choose the unlike fractions:(a) 57, 34, 12, 24, 13, 27 (b) 23, 14, 17, 12, 47, 37 (c) 16, 67, 27, 36, 17, 56(d) 49, 27, 59, 19, 59, 38 (e) 57, 27, 39, 38, 18, 17Exercise 2.29
Acme Mathematics-4 1493. Write >, < or = in the circle:(a) 15 >18 (b) 210210 (c) 38310(d) 4749 (e) 110 19 (f) 5757(g) 3515 (h) 510610 (i) 7999(j) 2878 (k) 4767 (l) 14144. Arrange the following fractions in increasing order:(a) 15,18, 17, 110, 13 (b) 25,26, 27, 28, 29(c) 19,69, 59, 39, 79 (d) 27,37, 17, 57, 675. Arrange the following fractions in descending order:(a) 18, 14, 13, 16, 110 (b) 47, 42, 45, 410, 48(c) 17, 37, 47, 27, 57 (d) 29, 69, 19, 89, 396. Can you add the missing factions?18 84860 1424 0 12640 11530 5 1
150 Acme Mathematics-47. Fill in the missing fraction numbers on each number line.0 15 35 45 111 311 411 611 1011 18 48 28 58 88 0413 813 1113 8. What fraction do the letters on each number line represent?19 29 49 59 89 99 W V UW = ......... V = ......... U = .........210 610 310 710 410 810 1010 0 B A CA = ......... B = ......... C = .........66 46 16 0 X Y ZX = ......... Y = ......... Z = .........414 714 514 914 1014 0 P Q R R SP = ......... Q = ......... R = ......... S = .........