Fractions and Decimals questions for class 7

Fractions and decimals class 7

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 

\thereforenumber 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.

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

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

=(\frac{1}{5}\, \, \times \, \, \frac{15}{2}) kg

=\frac{3}{2} \mathrm{kg} = 1\frac{1}{2} kg

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

\frac{15}{2} kg – \frac{3}{2} kg 

\frac{15-3}{2} kg = \frac{12}{2} kg= 6\, 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 \frac{66}{7} = \frac{48}{5}\times \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 

Amount received by each cadet= Rs. 8.75

Number of cadets = \frac{560}{8.75}=\frac{560 \times 100}{8.75 \times 100}=\frac{56000}{875} =64

Hence, the number of cadets is 64.

Fractions and decimals  (worksheet)

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