CBSE Class 7 Maths NCERT Solutions: Chapter 2 - Fractions and Decimals

To solve this problem, we first convert the mixed fraction $5\frac{1}{5}$ into an improper fraction. The formula for converting a mixed number $a\frac{b}{c}$ to an improper fraction is $\frac{(a \times c) + b}{c}$.

$$5\backslash frac\{1\}\{5\}\; =\; \backslash frac\{(5\; \backslash times\; 5)\; +\; 1\}\{5\}\; =\; \backslash frac\{25\; +\; 1\}\{5\}\; =\; \backslash frac\{26\}\{5\}$$

Now, we multiply the fraction $\frac{2}{5}$ by the improper fraction $\frac{26}{5}$.

$$\backslash frac\{2\}\{5\}\; \backslash times\; \backslash frac\{26\}\{5\}\; =\; \backslash frac\{2\; \backslash times\; 26\}\{5\; \backslash times\; 5\}$$

$$=\; \backslash frac\{52\}\{25\}$$

Therefore, $\frac{2}{5} \times 5\frac{1}{5}$ is equal to $\frac{52}{25}$. The correct option is (b).

First, we convert the mixed number $3\frac{3}{4}$ into an improper fraction. Using the formula $\frac{(a \times c) + b}{c}$ for $a\frac{b}{c}$:

3\frac{3}{4} = \frac{(3 \times 4) + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4}

Now, we need to divide $\frac{15}{4}$ by $\frac{3}{4}$. Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of $\frac{3}{4}$ is $\frac{4}{3}$.

\frac{15}{4} \div \frac{3}{4} = \frac{15}{4} \times \frac{4}{3}

We can cancel out the common factor of 4 in the numerator and denominator:

= \frac{15}{\cancel{4}} \times \frac{\cancel{4}}{3} = \frac{15}{3}

Finally, we simplify the fraction: = 5 Thus, $3\frac{3}{4} \div \frac{3}{4}$ is equal to 5. The correct option is (c).

To find the number of pieces, we need to divide the total length of the ribbon by the length of each small piece.

Total length of the ribbon = $5\frac{1}{4}$ m

Length of each piece = $\frac{3}{4}$ m

First, convert the total length from a mixed number to an improper fraction:

5\frac{1}{4} = \frac{(5 \times 4) + 1}{4} = \frac{20 + 1}{4} = \frac{21}{4}

Now, divide the total length by the length of each piece:

Number of pieces = Total length $\div$ Length of one piece

= \frac{21}{4} \div \frac{3}{4}

To divide by a fraction, we multiply by its reciprocal:

= \frac{21}{4} \times \frac{4}{3}

We can cancel the common factor of 4 in the numerator and denominator, and also simplify 21 and 3:

= \frac{21}{\cancel{4}} \times \frac{\cancel{4}}{3} = \frac{21}{3} = 7 Therefore, there will be 7 pieces. The correct option is (c).

To arrange the fractions $\frac{2}{3}$, $\frac{6}{7}$, and $\frac{13}{21}$ in ascending order, we need to find a common denominator. The denominators are 3, 7, and 21. The Least Common Multiple (LCM) of 3, 7, and 21 is 21.

Now, we convert each fraction to an equivalent fraction with a denominator of 21:

For $\frac{2}{3}$:

$$\backslash frac\{2\}\{3\}\; =\; \backslash frac\{2\; \backslash times\; 7\}\{3\; \backslash times\; 7\}\; =\; \backslash frac\{14\}\{21\}$$

For $\frac{6}{7}$:

$$\backslash frac\{6\}\{7\}\; =\; \backslash frac\{6\; \backslash times\; 3\}\{7\; \backslash times\; 3\}\; =\; \backslash frac\{18\}\{21\}$$

For $\frac{13}{21}$:

$$\backslash frac\{13\}\{21\}\; =\; \backslash frac\{13\; \backslash times\; 1\}\{21\; \backslash times\; 1\}\; =\; \backslash frac\{13\}\{21\}$$

Now we compare the numerators of these equivalent fractions: 13, 14, and 18. Since $13 < 14 < 18$, the fractions in ascending order are $\frac{13}{21}$, $\frac{14}{21}$, and $\frac{18}{21}$.

Substituting back the original fractions, the ascending arrangement is $\frac{13}{21}, \frac{2}{3}, \frac{6}{7}$. The correct option is (b).

The reciprocal of a fraction is obtained by interchanging its numerator and its denominator. If a fraction is represented as $\frac{p}{q}$, its reciprocal is $\frac{q}{p}$.

For the fraction $\frac{2}{3}$, the numerator is 2 and the denominator is 3.

Interchanging the numerator and the denominator, we get $\frac{3}{2}$.

Therefore, the reciprocal of the fraction $\frac{2}{3}$ is $\frac{3}{2}$. The correct option is (d).