Acme Mathematics-3 201A. Subtraction of 3-digit numbers (without borrowing)Answer : 113Subtract:Step 1 : Subtract the ones.5 ones – 2 ones = 3 onesWrite 3 in the ones column.Step 2 : Subtract the tens.7 tens – 6 tens = 1 tenWrite 1 in the tens column.Step 3 : Subtract the hundreds.4 hundreds – 3 hundreds =1 hundred.Write 1 in the hundreds column. H T O4 7 5– 3 6 21 1 3Exercise 6.3Subtract the following:H T O7 8 4– 3 4 3H T O6 9 8– 5 6 7H T O5 8 4– 2 7 2H T O9 7 9+ 3 5 7H T O5 7 9– 4 3 5H T O9 6 8– 7 6 2H T O6 8 9– 4 3 7H T O7 8 9– 6 3 5H T O5 6 8– 3 3 4H T O4 9 2– 3 6 0H T O3 4 3– 2 2 0H T O7 8 6– 5 7 3
202 Acme Mathematics-3B. Subtraction of 3-digit numbers (with borrowing)Answer : 325Subtract:Step 1 : Subtract the ones.You cannot take away 7 ones from 2 ones. So, change 1 ten for 10 ones. Now, you have 12 ones. 12 – 7 = 5 Write 5 in the ones column.Step 2 : Subtract the tens.You have 7 tens left. 7 – 5 = 2Write 2 in the tens column.Step 3 : Subtract the hundreds.7 – 4 = 3.Write 3 in the hundreds column.H T O7 8 2– 4 5 73 2 5Exercise 6.4Subtract the following:H T O5 9 4– 2 4 3H T O4 8 4– 1 7 5H T O6 5 1– 3 2 6H T O6 6 3– 1 5 6H T O6 7 2– 3 5 5H T O4 9 7– 2 8 8H T O8 8 4– 7 6 6H T O6 8 6– 1 4 9H T O7 6 7– 1 4 9H T O5 7 1– 2 3 2H T O6 1 8– 1 0 9H T O9 6 3– 5 5 4
Acme Mathematics-3 203C. Subtract the following (with borrowing)Answer : 264Subtract:Step 1 : Subtract the ones, 9 – 5 = 4Write 4 in the ones column.Step 2 : Subtract the tens. You cannot take away 7 tens from 3 tens. So change 1 hundred for 10 tens. Now, you have 13 tens. 13 – 7 = 6Write 6 in the tens column.Step 3 : Subtract the hundreds. You have 3 hundreds left.3 hundreds – 1 hundred = 2 hundreds .Write 2 in the hundreds column.H T O4 3 9– 1 7 52 6 4Classwork1. Subtract the following:H T O8 2 4– 2 3 0H T O8 0 8– 1 8 7H T O9 3 8– 5 4 6H T O9 2 5– 4 9 7H T O6 3 9– 2 4 4H T O6 7 0– 2 9 0H T O7 1 5– 1 8 4H T O5 0 8– 2 7 2H T O3 8 7– 1 9 6H T O4 4 6– 2 8 4H T O5 1 2– 2 9 0H T O5 5 8– 3 8 5
204 Acme Mathematics-3Exercise 6.51. Subtract the following:5 5 8– 3 8 55 8 5– 2 7 67 3 5– 3 1 97 8 2– 5 4 59 1 2– 6 4 59 6 5– 6 8 75 3 2– 2 6 33 2 1– 2 4 76 2 3– 2 3 96 6 5– 4 8 87 3 8– 2 6 95 4 5– 2 8 65 6 5– 3 9 96 2 6– 2 8 77 8 3– 3 8 89 5 7– 5 9 82. Solve the following subtraction problems:Karuna has 327 stamps. She pasted 119 stamps in her album. How many stamps are left to be pasted?Total 3 2 7 stampsPasted – 1 1 9 stamps2 0 8 s t a m p s are left to paste.There were 745 kites in a shop. During the kite festival 567 kites were sold. How many kites were left in the shop?Total 7 4 5 kitesPasted – 5 6 7 kiteskites are left in the shop.There are 863 students in a school. On a rainy day 374 students were absent. How many students were present?
Acme Mathematics-3 205Varun sold 365 mobile phones and Lalit sold 168 mobile phones. Who sold more mobile phones and by how many?565 children of a school had ice creams. 278 students had vanilla ice-cream. The rest had chocolate ice-cream. How many had chocolate ice-creams?The students of class 2 and class 3 put up 213 arts in an exhibition. If class 2 students made 139 arts, how many arts did class 3 students make?3. There were 931 cows on a farm. If 683 of them have died, how many are left?4. There were 678 apples in a store. 123 apples were sold. How many were left?5. There were 643 people in a village. 247 of them were children. How many of them were adults?6. There were 632 red and green marbles in a shop. If 397 were red, how many were green?7. A man bought a TV doll for Rs. 350. If he has paid only Rs. 267, how much has he still left to pay?8. Tom had 780 stamps. He gave 578 away. How many were left with him.9. A man bought a mobile set for Rs. 3421. He gave Rs. 500 note, how much was returned to him?
206 Acme Mathematics-3Study the following addition and subtraction:20 + 30 = 5050 – 20 = 3050 – 30 = 20 Sum is always greater than its addend. Difference is always less than its minuend. Addition is opposite to subtraction and vice-versa.Exercise 6.61. Fill in the blanks.(a) 100 + 80 = 180 – 100 = 80 – 80 = 100(b) 60 + 140 = – 60 = 140 – 140 = 60(c) 70 + 80 = – 70 = 80150 – = 70(d) 120 + 120 = – 120 = 120240 – = 120(e) 200 + 100 = 300 – = 200 – 200 = (f) 500 + 400 = 900 – = 400 – 400 = 500(g) 700 + = 900900 – = 200 – 200 = 700(h) + = – = – = 20 + 30 = 50addend addend sum50 – 30 = 20minuend subtrahend differenceRelation between addition and 6.4 subtraction
Acme Mathematics-3 2079 × 1 = 9 × 2 = 9 × 3 = 9 × 4 = 9 × 5 = 9 × 6 = 9 × 7 = 9 × 8 = 9 × 9 = 9 × 10 = Complete the table given below. Colour the apples 'red' that are equal to the numbersFill the circles.84902036457235799186339548127762412 36120Activity-16.5 Multiplication
208 Acme Mathematics-3Complete the multiplication problem and colour the picture.3 × 4 = 3 × 9 = 4 × 2 = 4 × 5 = 8 × 0 = 6 × 3 = 8 × 6 = 6 × 7 = 4 × 2 = 8 × 2 = 9 × 0 = 7 × 9 = 7 × 5 = 5 × 4 = 6 × 4 = 8 × 3 = 5 × 7 = 9 × 7 = 9 × 5 = 7 × 7 = 3 × 6 = 8 × 6 = 7 × 4 = 9 × 8 = 8 × 4 = 4 × 6 = 7 × 10 = 7 × 2 = 7 × 3 = 3 × 8 = 5 × 6 = 9 × 2 = 5 × 3 = 6 × 9 = 8 × 5 = 6 × 10 = 8 × 7= 5 × 8 = 6 × 5 = 9 × 6 = Activity-2
Acme Mathematics-3 209A. Multiplication tableStudy the given multiplication table carefully.Multiplication Tables (0 – 10) × 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 100B. 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.
210 Acme Mathematics-3Classwork1. 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 6.71. 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 = ........
Acme Mathematics-3 2112. Multiply:(a) 4 3× 5(b) 2 2× 7(c) 2 4× 7(d) 4 2× 6(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 6C. Multiplying 3-digit number by 1-digit number You know how we multiply 2-digit number by 1-digit number. In the same way we can multiply 3-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 = 693
212 Acme Mathematics-32. 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 (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 = 2616Exercise 6.81. 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× 5(g)3 1 5× 6(h)6 1 0× 6(i)1 1 4× 7(j)2 0 9× 8(k)7 0 4× 8(l)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 9
Acme Mathematics-3 213Is there anything common?To multiply a number by 10 we simply put a zero to the right of the number.D. Multiplying by 10, 20, 30,........, 901. Multiplying by 104 × 10 = 405 × 10 = 506 × 10 = 607 × 10 = 702. Multiplying by 10, 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 = 840 Exercise 6.91. Multiply each of the following by 10:(a) 78 (b) 85 (c) 92 (d) 1002. Find the product:(a) 52 × 30 (b) 43 × 40 (c) 62 × 50(d) 58 × 60 (e) 49 × 10 (f) 75 × 20To 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.
214 Acme Mathematics-33. Multiply:(a) 7 by 400 (b) 8 by 300 (c) 9 by 200(d) 11 by 500 (e) 12 by 700 (f) 15 by 6004. Fill in the blanks:(a) 12 × 10 = ........ (b) 8 × 20 = ........(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 × ........ = 1050E. Multiplying 3-digit numbers by 2-digit numbers1. Multiply 74 by 23.T O7 4× 2 32 2 2+ 1 4 8 01 7 0 2Step I Arrange the number as shown in the left side.Step II Multiply 74 by 3 ones74 × 3 = 222 onesStep III Multiply 74 by 2 tens74 × 20 = 1480Step IV Add both the products222 + 1480 = 17022. Multiply 456 by 34.H T O4 5 6× 3 41 8 2 4+ 1 3 6 8 01 5 5 0 4Step I Arrange the number as shown in the left side.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 = 15504
Acme Mathematics-3 215Exercise 6.101. Multiply:(a) 4 8× 2 3+(b) 5 7× 2 5+(c) 4 9× 2 6+(d) 5 2 3× 2 1+(e) 7 5 2× 2 4+(f) 5 1 8× 3 5+2. 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+(g) 3 4 2× 6 9+(h) 4 6 7× 7 5+(i) 8 4 2× 8 6+
216 Acme Mathematics-3F. Word problemsExample: 1 There are 42 classrooms in a school. 30 students sit in each class. How many students are there in the school?Solution : Number of classrooms = 42Number of students in each class = 304 2× 3 00 01 2 61 2 6 0ClassroomsStudents1260 students are there in the school.Example 2: One book has 175 pages. How many pages are there in 16 such books?Solution : Number of pages in one book = 175Number of books = 161 7 5 Pages× 1 6 Books1 0 5 01 7 5 02 8 0 0+2800 pages are there in 16 books.Exercise 6.111. There are 10 books in each class. How many books are there in 160 such classes?2. There are 24 packets of noodles in one cartoon. How many packets of noodles will be there in 40 such cartoons?Multiplication is very simple. Just remember the value of one thing × number of things.
Acme Mathematics-3 2173. The cost of one T – shirt is 415 rupees. How much money is needed to buy 9 such T– shirts?4. There are 215 flowers in one garden. How many flowers are there in 25 such gardens?5. There are 144 pencils in one box. How many pencils are there in 90 such boxes?6. There are 312 grapes in one bunch. How many grapes are there in 80 such bunches?7. There are 150 students in one class. How many students are there in 42 such classes?8. The cost of one bag is 450 rupees. What will be the cost of 25 such bags?9. There are 20 oranges in one box. How many oranges are there in 120 such boxes?10. There are 62 pens in one box. How many pens are there in 111 such boxes?11. There are 35 benches in one room. How many benches are there in 213 such rooms?12. The cost of one watch is 650 rupees. What will be the cost of 99 such watches?
218 Acme Mathematics-3Project Work1. Objective: To know the multiplication facts.2. Materials required: A-4 Size paper Colours Scale3. Activity: Take any multiplication problem.4. An example is given below:3 × 5 = 15Multiplication follow the commutative property.Multiplication as group:5 group of 3. 3 group of 5.Multiplication as repeated addition.Multiplication as regroup5 × 3 = 153 × 5 = 153 + 3 + 3 + 3 + 3 = 155 + 5 + 5 = 15
Acme Mathematics-3 219Complete the multiplication and colour the answer with different colour in the box given below.38 × 5 = 47 × 5 = 26 × 5 = 59 × 5 = 28 × 6 = 19 × 6 = 37 × 6 = 46 × 6 = 47 × 7 = 38 × 7 = 59 × 7 = 26 × 7 = 56 × 8 = 27 × 8 = 19 × 8 = 38 × 8 = 19 × 9 = 56 × 9 = 48 × 9 = 27 × 9 = 180615448152216115182304400101333413540171504202266101333115432542242329414150190180202242243615101276180115235202180222202130615325114555295400354333168242325STARTEXITProject Work
220 Acme Mathematics-3A. Division as repeated subtraction10 apples 10 apples 10 apples 10 applesThere are 40 apples on this tree. Put them equally in 4 baskets.40 – 10 – 10 – 10 – 10 = 0Remember : Division is repeated subtraction40 apples in 4 baskets.10 apples in each basket.4 40– 4010Division using repeated subtraction methodLook at the following examples:20 ÷ 520 – 5 = 15 –––––––– 1 time15 – 5 = 10 –––––––– 2 times10 – 5 = 5 –––––––– 3 times5 – 5 = 0 –––––––– 4 times5 can be subtracted 4 times from 20,20 ÷ 5 = 430 ÷ 630 – 6 = 24 –––––––– 1 time24 – 6 = 18 –––––––– 2 times18 – 6 = 12 –––––––– 3 times12 – 6 = 6 –––––––– 4 times6 – 6 = 0 –––––––– 5 times6 can be subtracted 5 times from 30,30 ÷ 6 = 56.6 Division
Acme Mathematics-3 221B. Dividing 2-digit number by 1-digit number (long division method)Let us divide 82 by 2.2 8 2– 80 2– 204 1T O Dividend = 82 (8 tens 2 Ones)Step I : Divide 8 Tens by 28 ÷ 2 = 4Write 4 in the Tens place of the Quotient and write Product 8 below the dividend in the Tens place.8 – 8 = 0Step II : Bring down 22 ÷ 2 = 1Write 1 in the Ones place in the Quotient and write 2 below the dividend in Ones place.2 – 2 = 0The Quotient is 41.Remember:2 is called divisor.82 is called divided0 is called remainder41 is called quotientExercise 6.121. 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 9
222 Acme Mathematics-3C. Dividing 3-digit number 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 = 201Let 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 II Divide 9 tens by 3.9 ÷ 3 = 3Step III Divide 3 Ones by 3.3 ÷ 3 = 1So, 693 ÷ 3 = 231
Acme Mathematics-3 223Let 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 II Divide 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.Exercise 6.131. 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 ÷ 5
224 Acme Mathematics-3D. Division with remaindera. Solve the following division problems and find the remainder.Himalaya had 9 books. He reads 2 books every day. How many days did he take to read all the books ?9 – 2 – 2 – 2 – 2 = 10 1 2 3 4 5 6 7remainder8 94 3 2 119 ÷ 2 = 4 and 1 is remainder.b. Divide 98 by 3.Let 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 33 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 = 1Himalaya read all the books in 4 days.
Acme Mathematics-3 225Exercise 6.141. Divide on the number line:0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1515 ÷ 2 = 7 and 1 remainder 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1514 ÷ 3 = and remainder0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1512 ÷ 5 = and remainder0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1515 ÷ 6 = and remainder2. Do the following division and find out quotients and remainders:(a) 25 ÷ 4 (b) 43 ÷ 6 (c) 37 ÷ 5(d) 59 ÷ 7 (e) 39 ÷ 4 (f) 44 ÷ 7(g) 43 ÷ 5 (h) 50 ÷ 6 (i) 695 ÷ 3(j) 445 ÷ 4 (k) 664 ÷ 3 (l) 806 ÷ 4(m) 505 ÷ 5 (n) 359 ÷ 7 (o) 668 ÷ 6(p) 557 ÷ 5 (q) 569 ÷ 8 (r) 648 ÷ 8(s) 478 ÷ 7 (t) 469 ÷ 6 (u) 997 ÷ 9(v) 465 ÷ 2 (w) 457 ÷ 9 (x) 876 ÷ 9
226 Acme Mathematics-3E. 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 = 1VerificationDividend = Divisor × Quotient + Remainder685 = (9 × 76) +12685 = 684 + 1685 = 685 it is verified.Can we verify our division?You may verify your answers. So Remember!Dividend = Divisor × Quotient + RemainderExercise 6.15Divide and find the quotient and remainder:(a) 60 ÷ 7 (b) 71 ÷ 8 (c) 346 ÷ 9 (d) 564 ÷ 8(e) 506 ÷ 7 (f) 608 ÷ 9 (g) 765 ÷ 5 (h) 745 ÷ 6(i) 422 ÷ 7 (j) 449 ÷ 8 (k) 565 ÷ 9 (l) 568 ÷ 5
Acme Mathematics-3 227F. 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 3Exercise 6.16Find the quotient and remainder:(a) 85 ÷ 10 (b) 99 ÷ 10 (c) 205 ÷ 10(d) 215 ÷ 10 (e) 368 ÷ 10 (f) 440 ÷ 10(g) 510 ÷ 10 (h) 650 ÷ 10 (i) 785 ÷ 10(j) 888 ÷ 10 (k) 980 ÷ 10 (l) 999 ÷ 10Remember ! 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.
228 Acme Mathematics-3G. 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 sticker.Exercise 6.17Solve 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 9 baskets, how many eggs were there in each basket?3. There were 690 ice-creams. If they were divided among 10 families, how many ice-creams did each family get?4. Rs. 240 was to be shared by 5 people. How much did each person get?Remember multiplication tables. You'll need them for division. 6 6 8 4– 60 8– 62 4– 2 40 01 1 4
Acme Mathematics-3 2295. There are 480 students in a school. If there are 8 classes, how many students are there in each class?6. There are 406 children who want to learn computer. If there are 7 children in 1 group, how many groups are there?7. 3 video games cost Rs. 180. Find the cost of 1 video game.8. There are 210 birds in a zoo. If they are kept in 7 cages, how many birds are there in each cage?9. Some ice-creams cost Rs. 105. If each icecream costs Rs. 5, how many ice-creams are there?10. A man spent Rs. 550 on two suits. What was the cost of each suit?11. There were 160 kg rice in some bags. If each bag had 5 kg, how many bags were there?12. There are 350 sheets of paper. If I want to divide them in 7 bundles, how many sheets of paper will there be in each bundle?
230 Acme Mathematics-3H. 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.Exercise 6.18Check 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) 63 ÷ 9 = 7, = , ÷ 7 = 9(f) 54 ÷ 6 = 9, = , ÷ 9 = 6(g) 90 ÷ 5 = 18, = , ÷ 18 = 5
Acme Mathematics-3 2318 ÷ 2 = 4Division is not commutative 8 ÷ 2 is not same asDivision as groups:4 groups of 2.Division as repeated subtractionDivision as array:2 ÷ 88 – 2 = 66 – 2 = 44 – 2 = 22 – 2 = 0subtracted 4 times.4 is quotient.22224 rowsProject Work1. Objective: To know the division facts.2. Materials required: A-4 Size paper Colours Scale3. Activity: Take any Division problem.4. An example is given below:
232 Acme Mathematics-3Project Work1. Objective : To identify the quotient, divisor and dividend.2. Materials required : A number grid Colours Pencil3. Activity : Find 3 numbers such that one is divisor, another is dividend and third is quotient. 8 2 4 9 2 10 7 3 213 4 4 16 2 5 6 30 524 16 1 6 1 50 42 1 41 0 4 0 7 2 14 30 2020 2 4 36 9 100 0 8 08 24 1 18 1 2 3 6 182 24 48 12 4 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, find 10 such examples.
Acme Mathematics-3 2331. Match the following.30 + 40 30150 – 50 10sum of 14 and 6 80difference of 100 and 70 639×7 7010×8 10050 ÷ 5 202. Add: H T U4 3 7+ 2 3 24. Divide : 4 2 85. Calculate the total cost of all goods.Rs. 750 Rs. 150 Rs. 100Total cost is Rs. .................6. How much money is left?– = .............Rs. 7503. SubtractH T U5 6 7– 4 3 2Mixed Exercise
234 Acme Mathematics-37. Add:8. Subtract:-9. Count the bottom of a shirt and calculate the total bottom of 124 such shirts.10. Find the remainder: 9 8 911. Add:3 5 6 72 2 2 2+ 2 4 1 413. Find the quotient: 4 9 7 6.........................................14. Divide Rs. 320 among 6 students. How many rupees will each student get?15. How many students can the given bus carry?Number of students per seat = 3Number of seats = 4816. Express in multiplication and division from addition form676+2961435–82612. Multiply:693×563 + 3 + 3 + 3 + 3 + 3 + 3 = 217 + 7 + 7 = 21..............................................................
Acme Mathematics-3 235MEASUREMENT THEME7 - Area of an object by counting square roomWeightage: 3
236 Acme Mathematics-3Area of an object by counting square roomIn the figure four plots A, B, C and D are given.A B C DA is Hari's land.B is Juna's land. C is Ronit's land. D is Jagir's land. Who has more land? How we can say the land is more or less?The area of land help us to compare the size of land.We say that the area of square of side 1 cm is 1 square centimeter. (or 1 sq.cm)We measure area of a closed figure by seeing how many such squares can fit into it. It has 20 square cm room.Therefore, its area is 20 sq. cm.The area of the shaded figure is half square cm.2 coloured triangles together in the given figures make 1 square cm.The area of the given figure is 4 square cm.1 cm1 cm1 cm 1 cmIt's area is 1 square cm.1cm1cm2 coloured triangles together in the given figure make 1 square cm.
Acme Mathematics-3 237ClassworkMake different shapes on the given graph and colour them.1 sq. cmExercise 71. Colour the figures and tick () the figure with larger area:(a)(b)
238 Acme Mathematics-3(c)(d)2. Write the area of coloured figures by counting the small squares:1 sq. cm(a) (b) (c)(d) (e) (f)
Acme Mathematics-3 239(g) (h) (i)(a) square cm (b) square cm (c) square cm(d) square cm (e) square cm (f) square cm(g) square cm (h) square cm (i) square cm3. What is the area of each shape?[Note : Each small square room represents 1 square cm.](a) (b) (c)Area = Sq.cm Area = Sq.cm Area = Sq.cm(d) (e) (f)Area = Sq.cm Area = Sq.cm Area = Sq.cm(g) (h)Area = Sq.cm Area = Sq.cm
240 Acme Mathematics-34. Find the area of each shape.[Note :Each small square room represents 1 square cm.](a) (b) (c)(d) (e) (f)(g) (h) (i)5. Join the dot and find the area of each shape.[Note :Each small square room represents 1 square cm.](a) (b) (c)
Acme Mathematics-3 2412 cm3 cm3 cm3 cm1 cm2 cm2 cm3 cm3 cm3 cm2 cm2 cm(d) (e) (f)(g) (h) (i)6. By counting the square room find the area of the following figures.
242 Acme Mathematics-37. Join the dots and count the square rooms then calculate the area of the given figure.[Note :Each small square room represents 1 square cm.]8. Divide the given figure into square cm and find the area of them. 4 cm7 cm 4 cm4 cmArea of the rectangle is ......... sq. cm. Area of the square is ......... sq. cm.
Acme Mathematics-3 243Project Work1. Objective: To find the area of square and rectangles by counting square rooms.2. Materials required:Pencil ScalesColours Grid paper3. Activity: Join the dots and make different squares and rectangles. 4. An example is given below: (1 room = 1 square cm)ABArea of rectangle A is 20 sq. cmArea of square B is 9 sq. cm
244 Acme Mathematics-31. Count the square rooms. ......... square rooms ......... square rooms2. Calculate the area of given rectangle.Area = .......... sq. cm7 cm5 cmarea = ............. sq. cm2 cm3 cm3. Make square rooms and calculate the area of given rectangle. (Each room is 1 cm2.)Area = ................... cm24. Make square rooms and calculate the area of given square.Area = .............. sq cm.4 cm4 cmMixed Exercise
Acme Mathematics-3 2451. Read and write the length of given the object. [1]0 cm0 inch 6 5 4 3 2 11 2 3 4 5 6 7 8 9 10 11 12 13 14 15............... cm2. Join the dots and make a line [1]BA3. Tick the rectangular surface objects. [1]book matches box circle cube 4. Match the following. [1]10001005. Fill in the blank. [1]10 tens = .................. ones.6. Tick () if it is correct and cross () if it is wrong. [1]1000 is the smallest four-digit number.7. Write in devanagari. [1]5620 = ......................................................................................................TEST YOURSELFTime : 2 hrs. F.M. : 50
246 Acme Mathematics-38. Write in fraction. [1]One-half = ....................9. Fill in the blanks: 3 cm = ....................... mm. [1]10. Count the square rooms. [1] ......... square rooms11. Write true or false. [1]Three-fourth is written as 34. ..............12. Guess the length of given Mathematics book. [1]It is ...................... cm long.13. Draw a line segment 6 cm long and name it ........................ is a line segment. [1]14. Colour the greater angle. [1]AB CDE F................................. is greater angle.15. Count the blocks and write the number. [1]= ............
Acme Mathematics-3 24716. Complete the abacus: 6500 [1]TH H T O17. Write the number name. [1]4009 = ..........................18. Write in number. [1]Thirty thousand, six hundred and forty-five = .........................19. Write number name in Devanagari and Hindu-Arabic number system:5432 [1]..........................................................................................................................................................................................................................20. Write the place value of circled digits. [1]9 7 8 621. How much money is left? [1]– = .............Rs. 75022. Calculate the total cost of all goods. [1]Rs. 750 Rs. 150 Rs. 100Total cost is Rs. .................
248 Acme Mathematics-323. Count the buttons of a shirt and calculate the total buttons of 124 such shirts. [1]24. Find the remainder: 9 8 9 [1]25. Measure the length of the given object. [1] It is ....................... long26. Colour the given fractions. [1]12 14 27. Calculate the area of the given rectangle. [1]Area = .................. sq. cm 2 cm3 cm28. Fill in the blanks: [1]12 cm = ...................... mm400 mm = ...................... cm29. Divide the circle into one-third and colour it. [1]30. Guess the area of these rectangular objects. [1].................... sq. cm .................... sq. cm
Acme Mathematics-3 24931. Name sides, vertices and the name of the triangle. [2]KP Asides : ........., ..........., ............vertices : ........., ..........., ............Name of triangle : ∆ ................32. Using the given numbers, 9, 1, 7, and 5 make 4 digit numbers and write them in increasing and decreasing order. [2]33. Add: [2]3 5 6 72 2 2 2+ 2 4 1 434. Multiply: [2]693×5635. Study the place value chart and complete the following. [2]Thousand UnitsOnes Hundred Tens Ones4 3 2 1In word :Place of digits Place value of digit431........................................................................
250 Acme Mathematics-336. Divide Rs. 320 among 6 students. How many rupees will each get?[2]37. Norbu has 1000 liter water in his tank. He uses 325 liter on Sunday and 200 liter on Monday. How much water is left now? [2]38. Change into centimeter. [2](a) 3 meter(b) 4 meter 30 cm.39. Make square rooms and calculate the area of the given rectangle. [2] Area = ................... cm240. Study the given pictograph. [2] represents 5 students.Class Pictograph123Answer the following questions.(a) How many students are there in class two?(b) In which class are there least number of students?(c) How many students are there altogether?