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.

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

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

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 $5\frac{17}{26} \times 9\frac{7}{18}$ .

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

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

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

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

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

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

= $\frac{112}{9}\times \frac{1}{14}$

= $\frac{112}{126}=\frac{112\div 14}{126\div 14}$

= $\frac{8}{9}$

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

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

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

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

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

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

Solution : $\frac{3}{4}=\frac{3 \times 25}{4\times 25}=\frac{75}{100}$ = 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) $5.9 \div 10 =5.9 \times \frac{1}{10} =\frac{5.9}{10}$

= $\frac{5.9 \times 10}{10 \times 10}=\frac{59}{100}$

= 0.59

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

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

= 0.059

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

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

= 0.0059

Example 12. Divide 0.0042 $\div$ 7 .

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

= $\frac{6}{1000}$

=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 : $fractions and decimals class7$

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

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

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

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

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

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

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

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

(viii) 6.29- 3.78 = ………..

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

(x) $4.7 \div 100$ = …………

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

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

(xiii) $7.7 \div \, \square \, =0.0077$

(xiv) $1.8 \times 0.01\times 0.2$ = …………

(xv) 0.7432 $\times \, \square \, =74.32$

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 = $\mathrm{\frac{total\, \, length }{length\, \, of\, \, each \, piece }}$

= $\frac{27}{5}\div \frac{3}{5}$

= $\frac{27}{5}\times \frac{5}{3}$ = 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.