December 9, 2022

# Fractions and decimals class 7| Fractions and Decimals questions for class 7

Fractions and decimals class 7

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# Fractions and decimals  class 7 ( Short  Answer type questions)

Question 1: If $\frac{5}{3}$

of a number is 15, find the number.

Solution: Let $x$ be the required number.

$\therefore&space;\,&space;\frac{5}{3}&space;\,&space;\,&space;of&space;\,&space;\,&space;x&space;=15&space;\Rightarrow&space;\frac{5}{3}&space;\times&space;x&space;=15$

$\Rightarrow&space;x=15$ ÷ $\frac{5}{3}$ $=15\times&space;\frac{3}{5}&space;=3&space;\times&space;3&space;=9$

Hence the required number is 9.

Question 2: Solve $20\frac{1}{2}+30\frac{1}{3}-15\frac{1}{6}$  .

Solution. $20\frac{1}{2}+30\frac{1}{3}-15\frac{1}{6}=\frac{41}{2}+\frac{91}{3}-\frac{91}{6}$

=  $\frac{123+182-91}{6}=\frac{214}{6}$

=$\frac{107}{3}=35\frac{2}{3}$

Hence  $20\frac{1}{2}+30\frac{1}{3}-15\frac{1}{6}$ = $35\frac{2}{3}$

Question 3: Multiply  $5\frac{17}{26}&space;\times&space;9\frac{7}{18}$ .

Solution. $5\frac{17}{26}&space;\times&space;9\frac{7}{18}=\frac{147}{26}&space;\times&space;\frac{169}{18}$

=$\frac{147&space;\times&space;169}{26&space;\times&space;18}=&space;\frac{24843}{468}$

= $\frac{24843\div&space;39}{468\div&space;39}$ =$\frac{637}{12}=53\frac{1}{12}$

Hence $5\frac{17}{26}&space;\times&space;9\frac{7}{18}$= $53\frac{1}{12}$

Question 4:  Solve  $12\frac{4}{9}\div&space;14$ .

Solution: $12\frac{4}{9}\div&space;14$ = $\frac{112}{9}\div&space;14$

=$\frac{112}{9}\times&space;\frac{1}{14}$

= $\frac{112}{126}=\frac{112\div&space;14}{126\div&space;14}$

=$\frac{8}{9}$

Question 5: which one is smaller ?      $\frac{7}{45}&space;\,&space;\mathrm{or}\,&space;\,&space;\frac{14}{89}$

Solution:  $\frac{7}{45}=\frac{7\times&space;2}{45\times&space;2}=\frac{14}{90}$

Now $\frac{14}{90}<\frac{14}{89}$  . So $\frac{7}{45}&space;<\frac{14}{89}$

Another Method :  7 x 89= 623   and  14 x 45 = 630

As 623 < 630 , therefore  $\frac{7}{45}&space;<\frac{14}{89}$ .

Question 6 :  Express $\frac{3}{4}$  as a decimal.

Solution : $\frac{3}{4}=\frac{3&space;\times&space;25}{4\times&space;25}=\frac{75}{100}$ = 0.75

Question 7 : Round off 86.953 to tenths place.
Solution: For rounding off to tenths place, we look at the hundredths place. Here the digit is 5.So, the digit at the tenths place (9)

will be increased by 1 (i.e., it will become 9 + 1). Hence, rounding off 86.953 to tenths place, we get 87.0

Question 8:  Arrange the following in ascending order

(i) 0.20 , 0.002,  0.02,  2.2 ,  2.02, 2.22

(ii) 9.99, 9.099, 99.9, 99.09 , 9.009

Solution : (i) 0.002 < 0.02< 0.20< 2.02< 2.2 < 2.22

(ii) 9.009< 9.099 <  9.99 < 99 .09 < 99.9

Question 9:  Which of the following fractions is the smallest?   (a)  $\frac{12}{9}$        (b) $\frac{12}{7}$      (c)  $\frac{12}{10}$      (d) $\frac{12}{6}$

Solution .  When the numerator of the fractions  are equal , the fraction with greater denominator  will be the smallest.  Hence the fraction $\frac{12}{10}$   is the smallest.

Question 10. Arrange the following in descending order.

(i) 9.45, 9.054,  9.504, 9.405,  9.54,  9.045

(ii) 77.7,  7.77, 0.777, 7.07,  0.707, 7.077

Solution. (i) 9.54 > 9.504 > 9.45 > 9.405> 9.054> 9.045

(ii) 77.7 > 7.77 > 7.077>  7.07> 0.777 > 0.707

Question 11: (i) 5.9 ÷ 10 = _____

(ii)  5.9 ÷ 100 = _____

(iii)  5.9 ÷ 1000 = _____

Solution: (i) $5.9&space;\div&space;10&space;=5.9&space;\times&space;\frac{1}{10}&space;=\frac{5.9}{10}$

=$\frac{5.9&space;\times&space;10}{10&space;\times&space;10}=\frac{59}{100}$

= 0.59

(ii) $5.9&space;\div&space;100&space;=5.9&space;\times&space;\frac{1}{100}&space;=\frac{5.9}{100}$

=$\frac{5.9&space;\times&space;10}{100&space;\times&space;10}=\frac{59}{1000}$

= 0.059

(iii)$5.9&space;\div&space;1000&space;=5.9&space;\times&space;\frac{1}{1000}&space;=\frac{5.9}{1000}$

=$\frac{5.9&space;\times&space;10}{1000&space;\times&space;10}=\frac{59}{10000}$

= 0.0059

Example 12. Divide 0.0042 $\div$ 7 .

Solution . $0.0042&space;\div&space;7&space;=&space;\frac{42}{10000}\div&space;7&space;=&space;\frac{42}{10000}\times&space;\frac{1}{7}$

=$\frac{6}{1000}$

=0.0006

Example 13. Find the average of 4.21, 3.82 and 7.63 .

Solution.  The average of 4.21, 3.82 and 7.63 is  =$\frac{4.21+3.82+7.63}{3}$

= $\frac{15.66}{3}$ =5.22

Example 14 : Divide (a) 0.5176  by 8             (b) 3.45  by 25

Solution :

## Fractions and decimals class 7  (Fill in the blanks type questions)

(i) $6\frac{7}{8}&space;\times&space;0&space;=\square$

(ii) $\square&space;\times&space;8\frac{2}{3}=8\frac{2}{3}$

(iii) $0\div&space;11\frac{6}{7}=\square$

(iv)$8\frac{2}{3}\times&space;\left&space;[&space;6\frac{1}{2}-3\frac{3}{7}&space;\right&space;]=\left&space;[&space;8\frac{2}{3}\times&space;6\frac{1}{2}&space;\right&space;]-\left&space;[8\frac{2}{3}\times&space;\square&space;\right&space;]$

(v) $9\frac{1}{4}\times&space;2\frac{5}{6}+&space;9\frac{1}{4}\times&space;4\frac{7}{11}=9\frac{1}{4}\times&space;\left&space;[&space;2\frac{5}{6}+\square&space;\right&space;]$

(vi) $12&space;\times&space;3\frac{2}{3}=\square&space;\times&space;12$

(vii) Decimal 8.125 is equal to the fraction ……………

(viii) 6.29- 3.78 =   ………..

(ix) Fill in the blanks using > or <  : $\frac{8}{45}\,&space;\square&space;\,&space;\frac{16}{89}$

(x) $4.7&space;\div&space;100$ = …………

(xi) The reciprocal of fraction more than  1 is always less than 1.

(xii) 230. 4 $\div$   $\square$ = 2.304

(xiii) $7.7&space;\div&space;\,&space;\square&space;\,&space;=0.0077$

(xiv)  $1.8&space;\times&space;0.01\times&space;0.2$ = …………

(xv) 0.7432 $\times&space;\,&space;\square&space;\,&space;=74.32$

Ans. (i) 0    (ii) 1      (iii) 0    (iv) $3\frac{3}{7}$    (v) $4\frac{7}{11}$   (vi) $3\frac{2}{3}$      (vii)  $8\frac{1}{8}$    (viii) 2 .51   (ix) <   (x) 0.047     (xi) True  (xii)100    (xiii) 1000   (xiv) 0.0036

(xv) 100

### Fractions and decimals   class 7 (Word problems)

Question 1: A ribbon of length $5\frac{2}{5}$ m is cut into small pieces each of length $\frac{3}{5}$ m.  Find the number of pieces that can be cut from the ribbon.

Solution. Total length of ribbon = $5\frac{2}{5}$ m= $\frac{27}{5}$ m

Length of each small piece=  $\frac{3}{5}$ m

$\therefore$number of pieces =$\mathrm{\frac{total\,&space;\,&space;length&space;}{length\,&space;\,&space;of\,&space;\,&space;each&space;\,&space;piece&space;}}$

=$\frac{27}{5}\div&space;\frac{3}{5}$

=$\frac{27}{5}\times&space;\frac{5}{3}$ = 9

Question 2: A car covers a distance of 99.1 km in 2.5 hours. What is the average distance covered by it in 1 hour?

Solution.  Distance covered by the car = 99.1 km.

Time required to cover this distance = 2. 5 hours.

So distance covered by it in 1 hour =$\frac{99.1}{2.5}$

= 39.64

Questions 3 : Tanvy bought $7\frac{1}{2}$ kg of apples. Later she found that  $\frac{1}{5}$ of them were rotten. Find the rotten apples and that of good ones.

Solution: Total weight of apples bought =$7\frac{1}{2}$  kg = $\frac{15}{2}$ kg

Weight of rotten apples =$\frac{1}{5}\,&space;\,&space;\mathrm{of}\,&space;\,&space;\frac{15}{2}$ kg

=$(\frac{1}{5}\,&space;\,&space;\times&space;\,&space;\,&space;\frac{15}{2})$ kg

=$\frac{3}{2}&space;\mathrm{kg}&space;=&space;1\frac{1}{2}&space;kg$

Weight of good apples =  total weight of apples – weight of rotten apples

$\frac{15}{2}$ kg – $\frac{3}{2}&space;kg$

$\frac{15-3}{2}$ kg = $\frac{12}{2}&space;kg=&space;6\,&space;kg$

Question 4: The product of two fractions is $9\frac{3}{5}$ .If one of the fraction  is $9\frac{3}{7}$ , find the other.

Solution: Product of two fractions = $9\frac{3}{5}$

One of the fractions =$9\frac{3}{7}$

The other fraction =  $9\frac{3}{5}$ $\div$  $9\frac{3}{7}$  = $\frac{48}{5}\div&space;\frac{66}{7}&space;=&space;\frac{48}{5}\times&space;\frac{7}{66}$

= $\frac{56}{55}=1\frac{1}{55}$ .

Hence , the other fraction is $1\frac{1}{55}$ .

Question 5: Mr. Amit distributed Rs. 560 among N.C.C. Cadets for refreshment . If each cadet receive Rs. 8.75 , How many cadets were there?

Solution: Total amount distributed = Rs. 560

Number of cadets = $\frac{560}{8.75}=\frac{560&space;\times&space;100}{8.75&space;\times&space;100}=\frac{56000}{875}&space;=64$

Hence, the number of cadets is 64.

#### Fractions and decimals  (worksheet)

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