S.chand class 6 Mathematics Chapter 5 Exercise 5F

 Exercise 5F

Question 1

1. What fraction of $1 \mathrm{~kg}$ is $650 \mathrm{~g}$ ?

2. Find the value of $1 \frac{2}{3}$ of 1 minute 15 seconds in seconds.

3. What is the cost of a dress, if $\frac{8}{9}$ of the cost of the dress equals $₹ 2400 ?$

4. Vibha's height is $4 \frac{4}{5}$ feet. She bought a yo-yo with a string that was $\frac{5}{8}$ of her height. How long was the string on Vibha's yo-yo?

5. Deepa makes handbags from $1 \frac{1}{5} \mathrm{~m}$ of fabric each. She has enough fabric to make $12 \frac{3}{4}$ handbags. What is the least amount of fabric that Deepa should have?

6. Menka and Shalu ran a 100 metre race. Menka took $18 \frac{1}{5}$ seconds and Shalu took $21 \frac{3}{4}$ seconds. How much longer time did Shalu take?

7. Mohan did $\frac{1}{2}$ of the work on Monday and $\frac{1}{3}$ of the work on Tuesday. How much work will he have to do on Wednesday to complete the remaining work?

8. Archana practices her violin $7 \frac{1}{2}$ hours each week. If she practices $1 \frac{1}{4}$ hours each day, how many days does she practice each week?

9. In a library, $\frac{1}{5}$ are Maths books, $\frac{1}{8}$ are Science books, $\frac{1}{12}$ are Hindi books and the rest are Evs books. If the number of EVS books is 142, find the total number of books in the library.

10. Raman works for $6 \frac{1}{2}$ hours a day. If he works for $\frac{2}{5}$ of the total time in the morning, for how many hours is he working in the afternoon?

Multiple Choice Questions (MCQs)

Tick (✔) the correct option.

11. Vinita spent $6 \frac{3}{5}$ hours making ceramic potteries. During that time, she took a $\frac{1}{2}$ hour break and another $1 \frac{1}{4}$ hour break for lunch. How many total hours did Vinita spend on the pottery.

(a) $5 \frac{17}{20}$ hours

(b) $4 \frac{17}{20}$ hours

(c) $7 \frac{7}{20}$ hours

(d) $4 \frac{3}{20}$ hours

12. Mr Singh has a board that is $12 \frac{3}{5}$ feet long. If he builds steps that are $3 \frac{1}{4}$ feet across, how many steps can he make with the board?

(a) 3

(b) 4

(c) 2

(d) 5

S.chand class 6 Mathematics Chapter 5 Exercise 5E

 Exercise 5E

Question 1

Simplify:

1. $\frac{3}{4}-\frac{5}{6} \times \frac{6}{7}$

2. $\frac{2}{3}$ of $\frac{3}{4} \div \frac{4}{5}$

3. $\frac{2}{3} \times \frac{3}{4}+\frac{5}{6} \div \frac{7}{12}$

4. $\frac{2}{3} \times\left(\frac{3}{4}-\frac{1}{8}\right) \div \frac{3}{4}$

5. $\frac{4}{5}$ of $\left(\frac{4}{9}+\frac{2}{3}\right) \div 2 \frac{2}{3}$

6. $\frac{1}{2} \div \frac{1}{6} \times \frac{1}{2}-\frac{1}{2}$

7. $\left(\frac{1}{2}+\frac{1}{3}\right) \div 1 \frac{5}{6} \times 11-3 \frac{1}{2}$

8. $1+1 \div\left\{1+1 \div\left(1+\frac{1}{3}\right)\right\}$

S.chand class 6 Mathematics Chapter 5 Exercise 5D

 Exercise 5D

Question 1

1. Multiply as indicated and reduce the product to its lowest terms:

(i) $9 \times \frac{2}{3}$

(ii) $16 \times \frac{7}{16}$

(iii) $\frac{7}{9} \times \frac{3}{14}$

(iv) $\frac{8}{12} \times \frac{9}{10}$

(v) $\frac{3}{5} \times \frac{4}{7} \times \frac{5}{16}$

(vi) $\frac{5}{6} \times \frac{3}{4} \times \frac{8}{25}$

(vii) $2 \frac{3}{10} \times \frac{3}{5}$

(viii) $2 \frac{1}{7} \times \frac{7}{22} \times 2 \frac{4}{9}$

Question 2

Find the value of

(i) one-fourth of 1 minute

(ii) $\frac{4}{50}$ of $1 \mathrm{~kg}$

(iii) $\frac{5}{6}$ of a leap year

(iv) $\frac{7}{8}$ of 1 day

3. Find the reciprocal of

(i) $\frac{4}{5}$

(ii) 7

(iii) $3 \frac{2}{7}$

(iv) $3 \frac{1}{2}+1 \frac{5}{8}$

4. Divide:

(i) $35 \div \frac{1}{5}$

(ii) $24 \div \frac{3}{4}$

(iii) $\frac{8}{12}+\frac{5}{18}$

(iv) $12 \div 2 \frac{1}{3}$

(v) $1 \frac{3}{4} \div 2 \frac{3}{16}$

(vi) $8 \frac{1}{4} \div 1 \frac{5}{6}$

(vii) $5 \frac{1}{4} \div 1 \frac{1}{8}$

(viii) $5 \frac{5}{8} \div 6 \frac{1}{4}$

5.Simplify:

(i) $1 \frac{1}{24} \times 2 \frac{1}{4}+1 \frac{1}{14}$

(ii) $1 \frac{1}{8} \div 2 \frac{1}{4} \times 4 \frac{1}{3}$

(iii) $1 \frac{13}{27} \times 2 \frac{11}{12} \div 3 \frac{1}{9}$

(iv) $\frac{5}{3}$ of $\frac{6}{10} \div 1 \frac{3}{5}$

6. The product of two fractions is $10 \frac{5}{7}$. If one of the fraction is $1 \frac{5}{7}$, find the other fraction.

7. Simplify:

(i) $\frac{\frac{3}{5}}{\frac{1}{5}}$

(ii) $\frac{\frac{6}{21}}{\frac{3}{28}}$

(iii) $\frac{12}{\frac{4}{9}}$

(iv) $\frac{\frac{4}{5}-\frac{1}{4}}{1 \frac{9}{20}+1 \frac{3}{10}}$

8.Manu said that $\frac{4}{5}+\frac{7}{10}$ is equal to $\frac{5}{4} \times \frac{10}{7}$. Is this correct? If no, explain the mistake and give the correct answer?

Multiple Choice Questions (MCQs)

Tick (✔) the correct option.

9.Which one is true?

(a) $1 \frac{3}{5} \times 1 \frac{4}{9}=2 \frac{1}{4}$

(b) $2 \frac{7}{12} \times 1 \frac{3}{10}=6 \frac{10}{22}$

(c) $5 \frac{1}{3} \times 1 \frac{5}{8}=6 \frac{7}{10}$

(d) $3 \frac{1}{6} \times 1 \frac{3}{15}=3 \frac{4}{5}$

10. Anita lives $5 \frac{5}{8} \mathrm{~km}$ from her school. Sanya lives $1 \frac{5}{9}$ times as far as Anita. How far does Sanya live from the school?

(a) $5 \frac{3}{16} \mathrm{~km}$

(b) $6 \mathrm{~km}$

(c) $8 \frac{3}{4} \mathrm{~km}$

(d) $5 \frac{25}{72} \mathrm{~km}$

11. Which of the following is not equal to the expression $3 \frac{3}{4}+\frac{1}{2}$ ?

(a) $18 \div 2 \frac{2}{5}$

(b) $1 \frac{7}{8} \div \frac{1}{4}$

(c) $3 \frac{3}{7} \div 1 \frac{1}{3}$

(d) $1 \frac{1}{9}+\frac{4}{27}$

12. A candle burns for $2 \frac{2}{5}$ hours. How many candles would you need to give light for 24 hours?

(a) $10 \frac{1}{2}$

(b) 10

(c) 8

(d) $11 \frac{3}{4}$

S.chand class 6 Mathematics Chapter 5 Exercise 5C

 Exercise 5C

Question 1

1. Add or Subtract:

(i) $\frac{1}{5}+\frac{2}{5}$

(ii) $\frac{3}{11}+\frac{4}{11}$

(iii) $\frac{1}{16}+\frac{7}{16}$

(iv) $\frac{15}{23}-\frac{9}{23}$

(v) $\frac{10}{37}+\frac{19}{37}$

(vi) $\frac{21}{43}-\frac{19}{43}$

(vii) $1-\frac{9}{10}$

(viii) $\frac{26}{75}-\frac{24}{75}$

(ix) $\frac{200}{517}+\frac{317}{517}$

(x) $\frac{1}{19}+\frac{5}{19}+\frac{10}{19}$

(xi) $\frac{11}{25}+\frac{2}{25}+\frac{7}{25}$

2. (i) $2 \frac{1}{5}+1 \frac{3}{5}$

(ii) $9 \frac{9}{14}-5 \frac{3}{14}$

(iii) $37 \frac{13}{18}-24 \frac{7}{18}$

(iv) $101 \frac{11}{31}+99 \frac{10}{31}$

Question 2

2. (i) $2 \frac{1}{5}+1 \frac{3}{5}$

(ii) $9 \frac{9}{14}-5 \frac{3}{14}$

(iii) $37 \frac{13}{18}-24 \frac{7}{18}$

(iv) $101 \frac{11}{31}+99 \frac{10}{31}$

3. Solve the following.

(i) $\frac{1}{7}+\frac{3}{14}$

(ii) $\frac{1}{6}+\frac{5}{12}$

(iii) $\frac{1}{6}+\frac{7}{9}$

(iv) $\frac{5}{6}+\frac{3}{4}$

(v) $\frac{7}{8}-\frac{2}{3}$

(vi) $\frac{7}{12}-\frac{1}{4}$

(vii) $\frac{5}{14}-\frac{5}{21}$

(viii) $\frac{7}{12}-\frac{1}{2}$

4. Simplify:

(i) $7 \frac{1}{12}+3 \frac{1}{3}$

(ii) $17 \frac{1}{6}+12 \frac{1}{4}$

(iii) $8 \frac{5}{6}-2 \frac{3}{4}$

(iv) $36 \frac{5}{8}-24 \frac{5}{12}$

5. Simplify:

(i) $\frac{7}{10}+\frac{8}{9}+\frac{16}{15}$

(ii) $\left(\frac{1}{8}+\frac{3}{10}\right)-\frac{1}{4}$

(iii) $\frac{17}{12}-\left(\frac{1}{6}+\frac{5}{18}\right)$

6. Simplify:

(i) $7 \frac{2}{3}+1 \frac{5}{9}+4 \frac{7}{12}$

(ii) $3 \frac{7}{10}+9 \frac{21}{100}+1 \frac{3}{5}$

(iii) $6 \frac{3}{4}-4 \frac{2}{3}+1 \frac{7}{12}$

(iv) $7+5 \frac{1}{8}-3 \frac{1}{4}$

7. Of $5 \frac{2}{3}$ and $3 \frac{3}{4}$, which is greater and by how much?

8. What should be added to $8 \frac{3}{7}$ to get $11 \frac{11}{14}$ ?

9. What must be subtracted from $5 \frac{1}{6}$ to get $2 \frac{11}{18}$ ?

Multiple Choice Questions (MCQs) 

Tick (✔) the correct option.

10. Which expression does not have a sum of $6 \frac{3}{10}$ ?

(a) $1 \frac{1}{20}+5 \frac{1}{4}$

(b) $3 \frac{1}{5}+3 \frac{1}{10}$

(c) $3 \frac{2}{5}+3 \frac{1}{15}$

(d) $4 \frac{3}{20}+2 \frac{3}{20}$

11. What fraction should be filled in the blank circle given in the adjacent figure, so that the sum of fractions on each-side of the triangle is same?

<image to be added>

(a) $\frac{7}{13}$

(b) $\frac{2}{13}$

(c) $\frac{5}{13}$

(d) $\frac{6}{13}$

12. Priya is baking a cake for which she requires $\frac{3}{4}$ cup of sugar and nuts. If she has $\frac{2}{5}$ cup of this mixture, how much more does she need?

(a) $\frac{7}{20}$

(b) $\frac{1}{5}$

(c) $\frac{9}{20}$

(d) $\frac{1}{4}$

SChand New Learning Composite Mathematics Class 6 Chapter 3 Playing With Numbers Exercise 3F

Exercise 3F

Question 1

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SChand New Learning Composite Mathematics Class 6 Chapter 3 Playing With Numbers Exercise 3E

Exercise 3E

Question 1

(a) 24=3×2×2×2

=3×2³

(b) 36=2×2×3×3

=2²×3²

(c) 210=2×3×5×7

(d) 180=2×2×3×3×5

=2²×3²×5

(e) 300=2²×3×5²

Question 2

(a) 32 =2⁵

(b) 48= 2⁴ x3

(c) 66= 2x 3x 11

(d) 72= 2³ x 3²

(e) 84= 2² x 3x 7

(f) 100= 2² x5²

(g) 840= 2³x 2 x 5 x 7

(h) 504 = 2³ x 3² x7

(i) 2904= 2³ x 3 x 11²

(j) 13845= 3⁴ x 5x 7²

Question 3

343= 7³

Question 4

(a) When all the factors are prime and their product is the original number.

(b) Prime factors of a number are all prime numbers where the factors of a number do not have to be prime.

SChand New Learning Composite Mathematics Class 6 Chapter 3 Playing With Numbers Exercise 3D

Exercise 3D

Question 1

(a)12= 5+7

(b) 30= 11+19

(c) 68= 31+37

(d) 72= 31+41

Question 2

(a) 12= 5+7

(b) 30= 13+17

(c) 78= 37+41

(d) 90= 47+53

Question 3

(a) 15 = 3+5+7

(b) 23= 5+7+11

(c) 35= 5+7+23

(d) 55= 13+19+23

Question 4

The five pairs of prime numbers less than 20, whose sum is divisible by 5 —

(2,3) , (3,7), (2,13), (3,17) and (13,17).

Question 5

(a) 151 is divisible by 1 and 151 , so it is a prime number.

(b) 69 is divisible by 1, 3, 2, 69 ,so, it is not a prime number.

(c) 241 is divisible by 1 and 241 so, it is a prime number.

(d) 265 is divisible by 1, 5, 53, 265 so it is not a prime number.

Question 6

The tree prime numbers are 5, 7 and 11

5x7x11= 385

Question 7

F

SChand New Learning Composite Mathematics Class 6 Chapter 3 Playing With Numbers Exercise 3C

Exercise 3C

Question 1

SChand New Learning Composite Mathematics Class 6 Chapter 3 Playing With Numbers Exercise 3B

Exercise 3B

Question 1

260, 7018, 20008, 148

Question 2

48, 594, 3096, 609513

Question 3

524, 71316, 8001008

Question 4

365, 7290, 21340, 845

Question 5

516, 7038, 800712

Question 6

464, 4176, 87544, 900392

Question 7

639, 29304, 38457

Question 8

670, 90020, 57390

Question 9

418, 7909, 17743, 10000001

Question 10

Divisible by 2 and 5 only.

Question 11

Divisible by 6, 8, 10 only.

Question 12

(a) Yes, it is also divisible by its factors because 6 & 9 are not co-prime.

(b) No, it is not divisible by their product because 6 & 9 are not co –prime.

Question 13

705 2 4 is divisible by 3.

Question 14

9 3 2760 is divisible by 9.

Question 15

(a) Yes

(b) Yes

(c) Yes

(d) Yes

(e) Yes

(f) Yes

(g) No

(h) Yes

(i) No

Question 16

984 and 1736 are divisible by 8

Sum of 984 and 1736 = 2720, divisible by 8 differences of 1736 and 384= 752, divisible by 8.

SChand New Learning Composite Mathematics Class 6 Chapter 3 Playing With Numbers Exercise 3A

Exercise 3A

Question 1

(a) 1, 2, 3, 4, 6, 12

(b) 1, 2, 7, 14

(c) 1, 19

(d) 1, 3, 7, 21

(e) 1, 2, 3, 4, 6, 8, 12, 24

(f) 1, 23

(g) 1, 2, 3, 6, 7, 14, 21, 42

(h) 1, 5, 17, 85

(i) 1, 73

(j) 1, 2, 4, 23, 46, 92

Question 2

(a) 2, 4, 6, 8, 10

(b) 4, 8, 12, 16, 20

(c) 6, 12, 18, 24, 30

(d) 9, 18, 27, 36, 45

(e) 10, 20, 30, 40, 50

Question 4

List of the multiples of 7 between 1 and 75 – 7, 14, 21, 28, 35, 42, 49, 56, 63, 70

Question 4

The all multiples of 9 up to 100 – 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99

Question 5

(a) The ninth multiple of 75-9 × 75

= 675

(b) The multiples of 10 between 150 and 200 – 160, 170, 180, 190

Question 6

Addition Facts

Even + Even = Even, Example – 2+6=8

Odd + Odd = Even, Example – 3+5=8

Even + Odd = Odd, Example – 4+3=7

Multiplication Facts

Even  Even = Even, Example – 24=8

Odd  Odd = Odd, Example – 35=15

Even  Odd = Even, Example – 25=10 

SChand New Learning Composite Mathematics Class 6 Chapter 2 Whole Numbers Exercise 2E

Exercise 2E

Question 1

(a) 8, 13, 18, 23, 28, 33, 38, 43

∴ Increase each term by 5.

(b) 56, 54, 52, 50, 48, 46

∴ Decrease each term by 2.

(c) 7, 14, 28, 56, 112, 224

∴ Multiply the previous number by 2.

(d) 25, 24, 23, 22, 21, 20

∴ Each term decreases by 1.

(e) 5, 10, 15, 20, 25, 30

∴ Each term increasing by 5.

(f) 100, 94, 88, 82, 76, 70

∴ Each term decreases by 6.

(g) 15 ml, 25 ml, 35 ml, 45 ml, 55 ml, 65 ml

∴ Increases each term by 10 ml.

(h) 1, 4, 9, 16, 25, 36, 49

∴ The are square numbers of consecutive natural number.

(j) 0, 1, 3, 6, 10, 15, 21, 28, 36, 45

∴ First term increased by 1, 2^nd term by 2, 3^rd term by 3 and so on.

(k) 0, 3, 8, 15, 24, 35, 48, 63

∴ First term increased by 3, 2^nd term by 5, 3^rd term by 7, 4^th term by 9, and so on.

(l) 1, 3, 9, 27, 81, 243, 729

∴ Multiply the previous number by 3.

(m) 101, 202, 303, 404, 505, 606

∴ Each term increases by 101

(n) 10:20 P.M, 10:10 P.M, 10:00 PM, 9:50 PM, 9:40 PM

∴ Each term decreases by 10 minutes.

(o) 14, 28, 42, 56, 70, 84

∴ Each term increases by 14

(p) 18, 36, 72, 144, 288, 576

∴ Multiply the previous term by 2.

(q) 90, 81, 72, 63, 54, 45

∴ Each term decreases by 9.

Question 2

(a)

$2\xrightarrow{+7}9\xrightarrow{-2}7\xrightarrow{+7}14\xrightarrow{-2}12\xrightarrow{+7}19\xrightarrow{-2}17$

∴Add 7 to one term and then subtract 2 from the next term.

(b)

$50\xrightarrow{-10}40\xrightarrow{+3}43\xrightarrow{-10}33\xrightarrow{+3}36\xrightarrow{-10}26\xrightarrow{+3}29$

∴Subtract 10 from one term and then add 3 to the next term.

(c)

$60\xrightarrow{-4}56\xrightarrow{+5}61\xrightarrow{-4}57\xrightarrow{+5}62\xrightarrow{-4}58\xrightarrow{+5}63\xrightarrow{-4}59\xrightarrow{+5}64$

∴Subtract 4 from one term and then add 5 to next term.

(d)

$100\xrightarrow{÷2}50\xrightarrow{×4}200\xrightarrow{÷2}100\xrightarrow{×4}400\xrightarrow{÷2}200$

∴Divide by 2 from one term and then multiply by 4 to the next term.

(e)

$2\xrightarrow{×3}6\xrightarrow{-1}5\xrightarrow{×3}15\xrightarrow{-1}14\xrightarrow{×3}42\xrightarrow{-1}41\xrightarrow{×3}123$

∴Multiplying by 3 to the one term then decrease 1 from the next term

(f)

$80\xrightarrow{÷10}8\xrightarrow{×5}40\xrightarrow{÷10}4\xrightarrow{×5}20\xrightarrow{÷10}2\xrightarrow{×5}10\xrightarrow{÷10}1$

∴Divide by 10 to the one term then multiplying 2 to the next term.

Question 3

1×9+1=10

12×9+2=110

123×9+3=110

1234×9+4=11110

12345×9+5=111110

SChand New Learning Composite Mathematics Class 6 Chapter 2 Whole Numbers Exercise 2D

Exercise 2D

Question 1

(a) Parentheses

(b) Parentheses

(c) Multiplication

(d) Addition

(e) Division

(f) Parentheses

Question 2

(a) 27 – 11 + 4

= 16 + 4

= 20

(b) (28 – 8) ÷ 4

= 20 ÷ 4

= 5

(c) 136 – 100 ÷ 5

= 136 – 20

= 116

(d) 80 – 35 x 2

= 80 – 70

= 10

(e) 20 + 15 ÷ 3 – 8

= 20 + 5 – 8

= 17

(f) 14 x (17 – 7) + 5

= 14 x 10 + 5

= 140 + 5

= 145

(g) 54 ÷ 9 + 3 x 5

= 6 + 3 x 5

= 6 + 15

= 21

(h) 60 – 8 x 12 ÷ 3

= 60 – 8 x 4

= 60 – 32

= 28

(i) 15 ÷ 3 x 5

= 5 x 5

= 25

(j) 18 ÷ (6 ÷ 3)

= 18 ÷ 2

= 9

(k) (20 ÷ 4) ÷ 5

= 5 ÷ 5

= 1

(l) 4 x 5 + 8 – 7

= 20 + 4 – 7

= 24 – 7

= 17

(m) 19 – 15 ÷ 5 – 16

= 19 – 3 – 16

= 16 – 16

= 0

(n) 8 x (7 – 2) ÷ 5 – 8

= 8 x 5 ÷ 5 – 8

= 8 x 1 – 8

= 8 – 8

= 0

(o) 72 ÷ (9 + 0 x 8) ÷ 8

= 72 ÷ (9 + 0) ÷ 8

= 72 ÷ 9 ÷ 8

= 8 ÷ 8

= 1

Question 3

(a) 24 – (8 ÷ 4 x 2) = 20

(b) 24 – 8 ÷ (4 x 2) = 23

(c) (24 – 8) ÷ 4 x 2 = 8

(d) (24 – 8 ÷ 4) x 2 = 44

(e) (7 + 2) x 6 – (4 -3) = 53

(f) 16 x (3 -2) ÷ 4 = 4

(g) 8 x (0 + 4) – 5 = 27

(h) 26 ÷ (5 + 8) x 7 = 14

Question 4

(a) 7 x 4 – 3

= 28 – 3

= 25

7 x (4 – 3)

= 7 x 1

= 7

7 x 4 – 3 > 7 x (4 – 3)

(b) 60 ÷ 5 x 4

= 12 x 4

= 48

60 ÷ (5 x 4)

= 60 ÷ 20

= 3

60 ÷ 5 x 4 > 60 ÷ (5 x 4)

(c) (8 + 12) ÷ 4

= 20 ÷ 4

= 50

8 + 12 ÷ 4

= 8 + 3

= 11

(8 + 12) ÷ 4 < 8 + 12 ÷ 4

(d) 23 – 18 + 7

= 5 + 7

= 12

15 ÷ 3 + 7

= 5 + 7

= 12

23 – 18  + 7 = 15 ÷ 3 + 7

Question 5

(a) (1025 ÷ 25) ÷ (205 ÷ 5)

= 41 ÷ 41

= 1

(b) (1500 ÷ 1500) x (165 ÷ 165)

= 1 x 1

= 1

SChand New Learning Composite Mathematics Class 6 Chapter 2 Whole Numbers Exercise 2C

 Exercise 2C

Question 1

SChand New Learning Composite Mathematics Class 6 Chapter 2 Whole Numbers Exercise 2B

 Exercise 2B

Question 1

(a) 8396 x 1 = 8396

(b) 64937 x 0 = 0

(c) 45 x 7 = 7 x 45

(d) (7 x 4) x 3= 7 x (4 x 3)

(e) 194 x 23 = 194 x (20 + 3)

(f) 89 x 302 = 89 x 300 + 89 x 2

(g) 57 x 29 = 57 x 20 + 57 x 5 + 57 x 4

(h) 12(8 – 5) = (12 x 8) – (12 x 5)

Question 2

(a) Identity property

(b) Property of zero

(c) Commutative Property

(d) Commutative Property

(e) Distributive Over Addition

(f) Associative Property.

Question 3

(a) 50 x 27 x 2

= (50 x 2) x 27 [Associative Property]

= 100 x 27

= 2700

(b ) 4 x (9 x 25)

= 4 x 225

= 900

(c) 25 x 39 x 8

= (25 x 8) x 39 [Associative Property]

= 200 x 39

= 7800

(d) 625 x 20 x 8 x 50

= (625 x 20) x (8 x 50) [Group the factor to make calculation easy]

= 12500  x 400

= 50,00,000

(e) 16 x 250 x 125 x 2

= (16 x 250) x (125 x 2) [Group the factor to make calculation easy]

= 4000 x 250

= 1,0,00,000

Question 4

(a) 79328 x 93 + 7 x 79328

= 79328 x (93 +7) [ Distributive Property over addition]

= 79328 x 100

= 7932800

(b) 8057 x 59 + 8057 x 25 + 8057 x 16

= 8057 x (59 + 25 + 16) [Distributive Property over addition]

= 8057 x 100

= 805700

Question 5

(a) 9 x 15

= (10 – 1) x 15

= (10 x 15) – (1 x 15)

= 150 – 15

= 135

(b) 82 x 103

= 82 x (100 + 3)

= (82 x 100) + (82 x 3)

= 8200 + 246

= 8446

(c) 7 x 124

= 7 x (100 + 24)

= (7 x 100) + (7 x 24)

= 700 + 168

= 868

(d) 3807 x 8

= (3800 + 7) x 8

= (3800 x 8) + (7 x 8)

= 30400 + 56

= 30456

(e) 258 x 1008

= 258 x (1000 + 8)

= (258 x 1000) + (258 x 8)

= 258000 + 2064

= 260064

(f) 869 x 10005

= 869 x (10000 + 5)

= (869 x 10000) + (869 x 5)

= 8690000 + 4345

= 8694345