Question

Pls help me with step by step explanation

Answer 1

Question 1 :

$\sf\:\frac{2}{5} \times 5\frac{1}{5}$ is equal to :

Options :

(a) $\sf\:\frac{26}{25}$

(b) $\sf\:\frac{52}{25}$ $\sf\color{red}{\checkmark}$

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

(d) $\sf\:6$

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Solution :

$\sf\:\frac{2}{5} \times 5\frac{1}{5}$

Multiplying the numbers

$\sf\longrightarrow\:\frac{2}{5} \times \frac{26}{5}$

$\small{\underline{\boxed{\mathrm{\longrightarrow\:\frac{52}{25}}}}}$ $\sf\color{cyan}{⋆}$

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Question 2 :‎

$\sf\:3\frac{3}{4} \div \frac{3}{4}$ is equal to :

Options :

(a) $\sf\:3$

(b) $\sf\:4$

(c) $\sf\:5$ $\sf\color{red}{\checkmark}$

(d) $\sf\:\frac{45}{16}$

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Solution :

$\sf\:3\frac{3}{4} \div \frac{3}{4}$

Multiplying the terms

$\sf\longrightarrow\:\frac{15}{4} \div \frac{3}{4}$

Converting ÷ into ×

$\sf\longrightarrow\:\frac{15}{4} \times \frac{4}{3}$

Multiplying

$\sf\longrightarrow\:\frac{60}{12}$

Reducing the fraction to lower terms

$\sf\longrightarrow\:\cancel{\frac{60}{12}}$

$\small{\underline{\boxed{\mathrm{\longrightarrow\:5}}}}$ $\sf\color{cyan}{⋆}$

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Question 3 :‎

A ribbon of length $\sf\:5\frac{1}{4}$ m is cut into small pieces each of length $\sf\:\frac{3}{4}$ m. Number of pieces will be :

Options :

(a) 5

(b) 6

(c) 7 $\sf\color{red}{\checkmark}$

(d) 8

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Solution :

Given -

• Total length of ribbon = $\sf\:5\frac{1}{4}$ m

• Length of each ribbon pieces = $\sf\:\frac{3}{4}$ m

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So,

The number of pieces would be -

$\sf\:\frac{Total~length~of~ribbon}{Length~of~each~pieces~of~ribbon}$

Substituting the values

$\sf\longrightarrow\:5\frac{1}{4} \div \frac{3}{4}$

$\sf\longrightarrow\:\frac{21}{4} \div \frac{3}{4}$

Converting ÷ into ×

$\sf\longrightarrow\:\frac{21}{4} \times \frac{4}{3}$

$\sf\longrightarrow\:\frac{84}{12}$

Reducing the fraction to lower terms

$\sf\longrightarrow\:\cancel{\frac{84}{12}}$

$\small{\underline{\boxed{\mathrm{\longrightarrow\:7}}}}$ $\sf\color{cyan}{⋆}$

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Question 4 :‎

The ascending arrangement of $\sf\:\frac{2}{3}$ , $\sf\:\frac{6}{7}$ , $\sf\:\frac{13}{21}$ is :

Options :

(a) $\sf\:\frac{6}{7}$ , $\sf\:\frac{2}{3}$ , $\sf\:\frac{13}{21}$

(b) $\sf\:\frac{13}{21}$ , $\sf\:\frac{2}{3}$ , $\sf\:\frac{6}{7}$ $\sf\color{red}{\checkmark}$

(c) $\sf\:\frac{6}{7}$ , $\sf\:\frac{13}{21}$ , $\sf\:\frac{2}{3}$

(d) $\sf\:\frac{2}{3}$ , $\sf\:\frac{6}{7}$ , $\sf\:\frac{13}{21}$

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Solution :

Given - $\sf\:\frac{2}{3}$ , $\sf\:\frac{6}{7}$ , $\sf\:\frac{13}{21}$

So calculating the LCM of 3 , 7 and 21 we get 21

Now changing each of the fraction into an equivalent fraction having 21 as the denominator.

• $\sf\:\frac{2}{3} \times \frac{7}{7} = \frac{14}{21}$

• $\sf\:\frac{6}{7} \times \frac{3}{3} = \frac{18}{21}$

• $\sf\:\frac{13}{21} \times \frac{1}{1} = \frac{13}{21}$

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Clearly $\sf\:\frac{13}{21}$ < $\sf\:\frac{14}{21}$ < $\sf\:\frac{18}{21}$

Hence,

$\bf\:\frac{13}{21}$ < $\bf\:\frac{2}{3}$ < $\bf\:\frac{6}{7}$ $\sf\color{cyan}{⋆}$

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Question 5 :

Reciprocal of the fraction $\sf\:\frac{2}{3}$ is :

Options :

(a) $\sf\:2$

(b) $\sf\:3$

(c) $\sf\:\frac{2}{3}$

(d) $\sf\:\frac{3}{2}$ $\sf\color{red}{\checkmark}$

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Solution :

While finding the reciprocal of a fraction we just exchange the numerator and denominator. In simple words numerator becomes denominator and denominator becomes numerator.

So the reciprocal of the fraction $\sf\:\frac{2}{3}$ is $\sf\:\frac{3}{2}$ $\sf\color{cyan}{⋆}$

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Question 6 :

The product of $\sf\:\frac{11}{13}$ and 4 is :

Options :

(a) $\sf\:3\frac{5}{13}$ $\sf\color{red}{\checkmark}$

(b) $\sf\:5\frac{3}{13}$

(c) $\sf\:13\frac{3}{5}$

(d) $\sf\:13\frac{5}{3}$

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Solution :

$\sf\:\frac{11}{13} \times 4$

Multiplying the numbers

$\sf\:\longrightarrow\frac{44}{13}$

Converting the fraction into mixed term

$\small{\underline{\boxed{\mathrm{\longrightarrow\:3\frac{5}{13}}}}}$ $\sf\color{cyan}{⋆}$

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