Fractions — Mental Maths

Fill in the blanks :

(i) $\dfrac{7}{11}$ ............... $\dfrac{5}{8}$

(ii) $\dfrac{3}{7}$ ............... $\dfrac{3}{5}$

(iii) $\dfrac{4}{9}$ ............... $\dfrac{4}{7}$

(iv) $\dfrac{15}{4} \times$ ............... = $\dfrac{3}{2}$

(v) $\dfrac{14}{15}$ ÷ ............... = $\dfrac{2}{3}$

(vi) Reciprocal of $2\dfrac{3}{4}$ is ...............

Answer

(i) $\dfrac{7}{11}$ ............... $\dfrac{5}{8}$

Cross multiply; 7 x 8 and 5 x 11

⇒ 56 and 55

Now, comparing both numbers;

⇒ 56 > 55

Hence, $\dfrac{7}{11}$ ${\boxed{\gt}}$ $\dfrac{5}{8}$

(ii) $\dfrac{3}{7}$ ............... $\dfrac{3}{5}$

Cross multiply; 3 x 5 and 3 x 7

⇒ 15 and 35

Now, comparing both numbers;

⇒ 15 < 35

Hence, $\dfrac{3}{7}$ ${\boxed{\lt}}$ $\dfrac{3}{5}$

(iii) $\dfrac{4}{9}$ ............... $\dfrac{4}{7}$

Cross multiply; 4 x 7 and 4 x 9

⇒ 28 and 36

Now, comparing both numbers;

⇒ 28 < 36

Hence, $\dfrac{4}{9}$ ${\boxed{\lt}}$ $\dfrac{4}{7}$

(iv) $\dfrac{15}{4} \times$ ............... = $\dfrac{3}{2}$

Let $\dfrac{15}{4} \times x = \dfrac{3}{2}$

Solving,

$\Rightarrow x = \dfrac{3}{2} ÷ \dfrac{15}{4}\\[1em] \Rightarrow x = \dfrac{3}{2} \times \dfrac{4}{15}\\[1em] \Rightarrow x = \dfrac{3 \times 4}{2 \times 15}\\[1em] \Rightarrow x = \dfrac{12}{30}\\[1em] \Rightarrow x = \dfrac{2}{5}$

Hence, $\dfrac{15}{4} \times \dfrac{2}{5} = \dfrac{3}{2}$

(v) $\dfrac{14}{15}$ ÷ ............... = $\dfrac{2}{3}$

Let $\dfrac{14}{15} \div x = \dfrac{2}{3}$

Solving,

$\Rightarrow \dfrac{14}{15} ÷ x = \dfrac{2}{3}\\[1em] \Rightarrow x = \dfrac{14}{15} ÷ \dfrac{2}{3} \\[1em] \Rightarrow x = \dfrac{14}{15} \times \dfrac{3}{2} \\[1em] \Rightarrow x = \dfrac{14 \times 3}{15 \times 2}\\[1em] \Rightarrow x = \dfrac{42}{30}\\[1em] \Rightarrow x = \dfrac{7}{5}.$

Hence, $\dfrac{14}{15} ÷ \dfrac{7}{5} = \dfrac{2}{3}$

(vi) Reciprocal of $2\dfrac{3}{4}$ is ...............

Reciprocal of $2\dfrac{3}{4} = \dfrac{11}{4}$ is $\dfrac{4}{11}$

Hence, reciprocal of $2\dfrac{3}{4}$ is $\dfrac{4}{11}$.

Fill in the blanks :

(i) $\dfrac{8}{5}$ ÷ 1 = ...............

(ii) $1\dfrac{3}{8}$ of $\dfrac{4}{5}$ = ...............

(iii) $\Big(\dfrac{5}{6} \text{ of 1 hour}\Big)$ = ............... minutes

(iv) $\Big(\dfrac{3}{8} \text{ of 1 km}\Big)$ = ............... metre

(v) $\Big(\dfrac{3}{5} \text{ of ₹ 1}\Big)$ = ............... paise

Answer

(i) $\dfrac{8}{5}$ ÷ 1 = ...............

$\Rightarrow \dfrac{8}{5} ÷ 1\\[1em] \Rightarrow \dfrac{8}{5} \times \dfrac{1}{1}\\[1em] \Rightarrow \dfrac{8 \times 1}{5 \times 1}\\[1em] \Rightarrow \dfrac{8}{5}\\[1em] \Rightarrow 1\dfrac{3}{5}$

Hence, $\dfrac{8}{5} ÷ 1 = 1\dfrac{3}{5}$.

(ii) $1\dfrac{3}{8}$ of $\dfrac{4}{5}$ ...............

$\Rightarrow 1\dfrac{3}{8} \times \dfrac{4}{5}\\[1em] \Rightarrow \dfrac{11}{8} \times \dfrac{4}{5}\\[1em] \Rightarrow \dfrac{11 \times 4}{8 \times 5}\\[1em] \Rightarrow \dfrac{44}{40}\\[1em] \Rightarrow \dfrac{11}{10}\\[1em] \Rightarrow 1\dfrac{1}{10}\\[1em]$

Hence, $1\dfrac{3}{8}$ of $\dfrac{4}{5} = \dfrac{11}{10}$.

(iii) $\Big(\dfrac{5}{6} \text{ of 1 hour}\Big)$ = ............... minutes

$\Rightarrow \dfrac{5}{6} \text{ of 1 hour}\\[1em] \Rightarrow \dfrac{5}{6} \text{ of 60 minutes}\\[1em] \Rightarrow \dfrac{5}{6} \times 60 \\[1em] \Rightarrow \dfrac{5 \times 60}{6} \\[1em] \Rightarrow \dfrac{300}{6} \\[1em] \Rightarrow 50$

Hence, $\Big(\dfrac{5}{6} \text{ of 1 hour}\Big)$ = 50 minutes.

(iv) $\Big(\dfrac{3}{8} \text{ of 1 km}\Big)$ = ............... metre

$\Rightarrow \dfrac{3}{8} \text{ of 1 km}\\[1em] \Rightarrow \dfrac{3}{8} \text{ of 1,000 m}\\[1em] \Rightarrow \dfrac{3}{8} \times 1,000\\[1em] \Rightarrow \dfrac{3 \times 1,000}{8}\\[1em] \Rightarrow \dfrac{3,000}{8}\\[1em] \Rightarrow 375$

Hence, $\Big(\dfrac{3}{8} \text{ of 1 km}\Big)$ = 375 metres.

(v) $\Big(\dfrac{3}{5} \text{ of ₹ 1}\Big)$ = ............... paise

$\Rightarrow \Big(\dfrac{3}{5} \text{ of ₹ 1}\Big)\\[1em] \Rightarrow \Big(\dfrac{3}{5} \text{ of 100 paise}\Big)\\[1em] \Rightarrow \dfrac{3}{5} \times 100 \\[1em] \Rightarrow \dfrac{3 \times 100}{5}\\[1em] \Rightarrow \dfrac{300}{5}\\[1em] \Rightarrow 60$

Hence, $\Big(\dfrac{3}{5} \text{ of ₹ 1}\Big)$ = 60 paise.

Write T for true and F for false statement :

1 ÷ $\dfrac{3}{2}$ = $\dfrac{2}{3}$.

Answer

True

Reason

Given, 1 ÷ $\dfrac{3}{2}$ = $\dfrac{2}{3}$.

Taking L.H.S.

$\Rightarrow 1 ÷ \dfrac{3}{2}\\[1em] \Rightarrow 1 \times \dfrac{2}{3}\\[1em] \Rightarrow \dfrac{1 \times 2}{3}\\[1em] \Rightarrow \dfrac{2}{3}$

Taking R.H.S. = $\dfrac{2}{3}$.

Since, L.H.S. = R.H.S.

Write T for true and F for false statement :

$1\dfrac{2}{3}$ ÷ $\dfrac{3}{4}$ = $1\dfrac{1}{2}$.

Answer

False

Reason

Given, $1\dfrac{2}{3}$ ÷ $\dfrac{3}{4}$ = $1\dfrac{1}{2}$.

Taking L.H.S.

$\Rightarrow 1\dfrac{2}{3} ÷ \dfrac{3}{4}\\[1em] \Rightarrow \dfrac{5}{3} ÷ \dfrac{3}{4}\\[1em] \Rightarrow \dfrac{5}{3} \times \dfrac{4}{3}\\[1em] \Rightarrow \dfrac{5 \times 4}{3 \times 3}\\[1em] \Rightarrow \dfrac{20}{9}\\[1em] \Rightarrow 2\dfrac{2}{9}\\[1em]$

Taking R.H.S. = $1\dfrac{1}{2}$

Since, L.H.S. ≠ R.H.S.

Write T for true and F for false statement :

$\dfrac{3}{5}$ of 1 kg = 600 g.

Answer

True

Reason

Given, $\dfrac{3}{5}$ of 1 kg = 600 g.

Taking L.H.S.

$\Rightarrow \dfrac{3}{5} \text{ of 1 kg}\\[1em] \Rightarrow \dfrac{3}{5} \text{ of 1000 g}\\[1em] \Rightarrow \dfrac{3}{5} \times 1000\\[1em] \Rightarrow \dfrac{3 \times 1000}{5}\\[1em] \Rightarrow \dfrac{3000}{5}\\[1em] \Rightarrow 600$

Taking R.H.S. = 600 g

Since, L.H.S. = R.H.S.

Write T for true and F for false statement :

$\dfrac{3}{4}$ of ₹ 1 = 65 paise.

Answer

False

Reason

Given, $\dfrac{3}{4}$ of ₹ 1 = 65 paise.

Taking L.H.S.

$\Rightarrow \dfrac{3}{4} \text{ of ₹ 1}\\[1em] \Rightarrow \dfrac{3}{4} \text{ of 100 paise}\\[1em] \Rightarrow \dfrac{3 \times 100}{4} \\[1em] \Rightarrow \dfrac{300}{4} \\[1em] \Rightarrow 75$

Taking R.H.S. = 65 paise

Since, L.H.S. ≠ R.H.S.

Write T for true and F for false statement :

$\dfrac{7}{10}$ of 1 hour = 42 minutes.

Answer

True

Reason

Given, $\dfrac{7}{10}$ of 1 hour = 42 minutes.

Taking L.H.S.

$\Rightarrow \dfrac{7}{10} \text{ of 1 hour}\\[1em] \Rightarrow \dfrac{7}{10} \text{ of 60 minutes}\\[1em] \Rightarrow \dfrac{7}{10} \times 60 \\[1em] \Rightarrow \dfrac{7 \times 60}{10}\\[1em] \Rightarrow \dfrac{420}{10}\\[1em] \Rightarrow 42$

Taking R.H.S. = 42 minutes

Since, L.H.S. = R.H.S.

Write T for true and F for false statement :

$\dfrac{5}{6}$ and $\dfrac{5}{7}$ are like fractions.

Answer

False

Reason

Given, $\dfrac{5}{6}$ and $\dfrac{5}{7}$

Since denominator of both fractions are different. So, these are unlike fractions.

Write T for true and F for false statement :

$\dfrac{1}{4}$ and $\dfrac{1}{5}$ are unlike fractions.

Answer

True

Reason

Given, $\dfrac{1}{4}$ and $\dfrac{1}{5}$

Since denominator of both fractions are different. So, these are unlike fraction.