RS Aggarwal 2019,2020 solution class 7 chapter 2 Fractions Exercise 2D

Exercise 2D

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Question 4:

Mark (✓) against the correct answer
$\frac{2}{3},\frac{4}{6},\frac{6}{9},\frac{8}{12}$ are
(a) like fractions
(b) irreducible fractions
(c) equivalent fractions
(d) none of these

Answer 4:

(c) equivalent fractions

Equivalent fractions are those which are the same but look different.

Thus, $\frac{2}{3}, \frac{4}{6}=\frac{2}{3}, \frac{6}{9}=\frac{2}{3}, \frac{8}{12}=\frac{2}{3}$ are equivalent fractions.

Question 5:

Mark (✓) against the correct answer
Which of the following statements is true?

(a) $\frac{9}{16}=\frac{13}{24}$
(b) $\frac{9}{16}<\frac{13}{24}$
(c) $\frac{9}{16}>\frac{13}{24}$
(d) none of these

Answer 5:

(c) $\frac{9}{16}$ > $\frac{13}{24}$
The two fraction are $\frac{9}{16}$ and $\frac{13}{24}$.
By cross multiplication, we have:
9 $\times$ 24 = 216 and 13 $\times$ 16 = 208
However, 216 > 208
∴ $\frac{9}{16}$ > $\frac{13}{24}$

Question 6:

Mark (✓) against the correct answer
Reciprocal of $1\frac{3}{4}$ is

(a) $1\frac{4}{3}$
(b) $4\frac{1}{3}$
(c) $3\frac{1}{4}$
(d) none of these

Answer 6:

(d) none of these
Reciprocal of $1\frac{3}{4}$ = Reciprocal of $\frac{7}{4}$ = $\frac{4}{7}$

Question 7:

Mark (✓) against the correct answer
$\left(\frac{3}{10}+\frac{8}{15}\right)=?$

(a) $\frac{11}{10}$
(b) $\frac{11}{15}$
(c) $\frac{5}{6}$
(d) none of these

Answer 7:

(c) $\frac{5}{6}$

$\left(\frac{3}{10}+\frac{8}{15}\right)=\left(\frac{9+16}{30}\right)$        [∵ LCM of 10 and 15 = 30]

               = $\frac{25}{30}=\frac{5}{6}$

Question 8:

Mark (✓) against the correct answer
$\left(3\frac{1}{4}-2\frac{1}{3}\right)=?$

(a) $1\frac{1}{12}$
(b) $\frac{1}{12}$
(c) $1\frac{1}{11}$
(d) $\frac{11}{12}$

Answer 8:

(d) $\frac{11}{12}$

$\left(3\frac{1}{4}-2\frac{1}{3}\right)$ = $\left(\frac{13}{4}-\frac{7}{3}\right)$
                = $\left(\frac{39-28}{12}\right)$            [∵ LCM of 4 and 3 = 12]
                = $\frac{11}{12}$

Question 9:

Mark (✓) against the correct answer
$36÷\frac{1}{4}=?$

(a) 9
(b) $\frac{1}{9}$
(c) $\frac{1}{144}$
(d) 144

Answer 9:

(d) 144

$36÷\frac{1}{4}=36\times 4$   [∵ Reciprocal of $\frac{1}{4}$= 4]
          = 144

Question 10:

Mark (✓) against the correct answer
By what number should $2\frac{3}{5}$ be multiplied to get $1\frac{6}{7}$ ?

(a) $1\frac{5}{7}$
(b) $\frac{5}{7}$
(c) $1\frac{1}{7}$
(d) $\frac{1}{7}$

Answer 10:

(b) $\frac{5}{7}$

Required number = $1\frac{6}{7}÷2\frac{3}{5}$

                             = $\frac{13}{7}÷\frac{13}{5}$

                             = $\frac{13}{7}\times \frac{5}{13}$    [∵ Reciprocal of $\frac{13}{5}$ = $\frac{5}{13}$]

                             = $\frac{5}{7}$

Question 11:

Mark (✓) against the correct answer
By what number should $1\frac{1}{2}$ be divided to get $\frac{2}{3}$ ?

(a) $2\frac{2}{3}$
(b) $1\frac{2}{3}$
(c) $\frac{4}{9}$
(d) $2\frac{1}{4}$

Answer 11:

(d) $2\frac{1}{4}$

Required number = $1\frac{1}{2}÷\frac{2}{3}$

                             = $\frac{3}{2}÷\frac{2}{3}$

                             = $\frac{3}{2}\times \frac{3}{2}$      [∵ Reciprocal of $\frac{2}{3}$ = $\frac{3}{2}$]

                             = $\frac{9}{4}=2\frac{1}{4}$

Question 12:

Mark (✓) against the correct answer
$1\frac{3}{5}÷\frac{2}{3}=?$

(a) $1\frac{1}{15}$
(b) $1\frac{9}{10}$
(c) $2\frac{2}{5}$
(d) none of these

Answer 12:

(c) $2\frac{2}{5}$

$1\frac{3}{5}÷\frac{2}{3}=\frac{8}{5}÷\frac{2}{3}$

           = $\frac{8}{5}\times \frac{3}{2}$        [∵ Reciprocal of $\frac{2}{3}$ = $\frac{3}{2}$]

           = $\left(\frac{4\times 3}{5}\right)=\frac{12}{5}=2\frac{2}{5}$

Question 13:

Mark (✓) against the correct answer
$2\frac{1}{5}÷1\frac{1}{5}=?$

(a) 1
(b) 2
(c) $1\frac{1}{5}$
(d) $1\frac{5}{6}$

Answer 13:

(d) $1\frac{5}{6}$

$2\frac{1}{5}÷1\frac{1}{5}=\frac{11}{5}÷\frac{6}{5}$

             = $\frac{11}{5}\times \frac{5}{6}$         [∵ Reciprocal of $\frac{6}{5}$ = $\frac{5}{6}$]

              = $\frac{11}{6}=1\frac{5}{6}$

Question 14:

Mark (✓) against the correct answer
The reciprocal of $1\frac{2}{3}$ is
(a) $3\frac{1}{2}$
(b) $2\frac{1}{3}$
(c) $1\frac{1}{3}$
(d) $\frac{3}{5}$

Answer 14:

(d) $\frac{3}{5}$

Reciprocal of $1\frac{2}{3}$ = Reciprocal of $\frac{5}{3}$ = $\frac{3}{5}$

Question 15:

Mark (✓) against the correct answer
Which one of the following is the correct statement?

(a) $\frac{2}{3}<\frac{3}{5}<\frac{14}{15}$
(b) $\frac{3}{5}<\frac{2}{3}<\frac{14}{15}$
(c) $\frac{14}{15}<\frac{3}{5}<\frac{2}{3}$
(d) none of these

Answer 15:

(b) $\frac{3}{5}<\frac{2}{3}<\frac{14}{15}$

The given fractions are $\frac{3}{5}, \frac{2}{3} \mathrm{and}\frac{14}{15}.$

LCM of 5, 3 and 15 = 15

Now, we have:

$\frac{2}{3}\times \frac{5}{5}=\frac{10}{15}$, $\frac{3}{5}\times \frac{3}{3}=\frac{9}{15}$ and $\frac{14}{15}\times \frac{1}{1}=\frac{14}{15}$

Clearly, $\frac{9}{15 }<\frac{10}{15}<\frac{14}{15}$

∴ $\frac{3}{5}<\frac{2}{3}<\frac{14}{15}$

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Question 16:

Mark (✓) against the correct answer
A car runs 16 km using 1 litre of petrol. How much distance will it cover in $2\frac{3}{4}$ litres of petrol?
(a) 24 km
(b) 36 km
(c) 44 km
(d) $32\frac{3}{4}$ km

Answer 16:

(c) 44 km
Distance covered by the car on $2\frac{3}{4}$ L of petrol =$\left(16\times 2\frac{3}{4}\right)$ km

                                                                   = $\left(16\times \frac{11}{4}\right)$ km

                                                                   = (4 $\times$ 11) km = 44 km

Question 17:

Mark (✓) against the correct answer
Lalit reads a book for $1\frac{3}{4}$ hours evrey day and reads the entire book in 6 days. How many hours does he take to read the entire book?

(a) $10\frac{1}{2}$ hours
(b) $9\frac{1}{2}$ hours
(c) $7\frac{1}{2}$ hours
(d) $11\frac{1}{2}$ hours

Answer 17:

(a) $10\frac{1}{2}$ hours
Time taken by Lalit to read the entire book = $\left(6\times 1\frac{3}{4}\right)$ h

                                                                   = $\left(6\times \frac{7}{4}\right)$ h

                                                                     = $\left(\frac{21}{2}\right)$ h = $10\frac{1}{2}$ h