Fractions — NCERT Solutions, AI Tutor & Practice

When a whole is divided into 5 equal parts, each part is $\frac{1}{5}$.

Taking 3 such parts gives: $3 \times \frac{1}{5} = \frac{3}{5}$

On the number line between 0 and 1, divide the gap into 5 equal segments. Count 3 segments from 0:

$0 \;\; \frac{1}{5} \;\; \frac{2}{5} \;\; \boxed{\frac{3}{5}} \;\; \frac{4}{5} \;\; 1$

So the required fraction is $\frac{3}{5}$.

Total number of equal parts = 8 (denominator).

Number of shaded parts = 5 (numerator).

So the shaded fraction is: $\frac{5}{8}$

Since the numerator $5$ is less than the denominator $8$, this is a proper fraction.

To get equivalent fractions, multiply both numerator and denominator by the same non-zero number.

Multiply by 2: $\frac{2 \times 2}{3 \times 2} = \frac{4}{6}$

Multiply by 3: $\frac{2 \times 3}{3 \times 3} = \frac{6}{9}$

Multiply by 4: $\frac{2 \times 4}{3 \times 4} = \frac{8}{12}$

So three equivalent fractions are $\frac{4}{6},\ \frac{6}{9},\ \frac{8}{12}$.

Divide the numerator by the denominator: $17 \div 5 = 3 \text{ remainder } 2$

Here:

• Quotient = 3 (whole number part)
• Remainder = 2 (new numerator)
• Denominator = 5 (stays the same)

So: $\frac{17}{5} = 3\frac{2}{5}$

Use the rule: (whole number $\times$ denominator) $+$ numerator, over the same denominator.

$4\frac{3}{7} = \frac{(4 \times 7) + 3}{7}$

$= \frac{28 + 3}{7} = \frac{31}{7}$

Find the HCF of 24 and 36.

• Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
• Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

The highest common factor is $12$.

Divide numerator and denominator by 12: $\frac{24 \div 12}{36 \div 12} = \frac{2}{3}$

Since 2 and 3 have no common factor other than 1, $\frac{2}{3}$ is the simplest form.

The denominators are 4 and 7. Take the LCM of 4 and 7, which is $28$.

Convert both fractions: $\frac{3}{4} = \frac{3 \times 7}{4 \times 7} = \frac{21}{28}$ $\frac{5}{7} = \frac{5 \times 4}{7 \times 4} = \frac{20}{28}$

Now compare the numerators: $21 > 20$.

Therefore: $\frac{3}{4} > \frac{5}{7}$

The denominators are the same (both 9), so add the numerators and keep the denominator: $\frac{2}{9} + \frac{4}{9} = \frac{2+4}{9} = \frac{6}{9}$

Now simplify. The HCF of 6 and 9 is 3: $\frac{6 \div 3}{9 \div 3} = \frac{2}{3}$

So the answer is $\frac{2}{3}$.

The denominators are 6 and 4. Their LCM is $12$.

Convert each fraction: $\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}$ $\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$

Now subtract: $\frac{10}{12} - \frac{3}{12} = \frac{10-3}{12} = \frac{7}{12}$

Since 7 and 12 have no common factor other than 1, the answer is $\frac{7}{12}$.

We need $\frac{3}{5} + \frac{7}{10}$.

The LCM of 5 and 10 is $10$.

Convert the first fraction: $\frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10}$

Now add: $\frac{6}{10} + \frac{7}{10} = \frac{13}{10}$

Since this is improper, write it as a mixed number: $\frac{13}{10} = 1\frac{3}{10}$

So the total milk is $1\frac{3}{10}$ litres.

The denominators are 2, 3, 6, 4. The LCM is $12$.

Convert each fraction to twelfths: $\frac{1}{2} = \frac{6}{12}, \quad \frac{2}{3} = \frac{8}{12}, \quad \frac{5}{6} = \frac{10}{12}, \quad \frac{3}{4} = \frac{9}{12}$

Now order the numerators: $6 < 8 < 9 < 10$.

So in ascending order: $\frac{1}{2} < \frac{2}{3} < \frac{3}{4} < \frac{5}{6}$

Number who play chess: $\frac{2}{5} \text{ of } 30 = \frac{2}{5} \times 30 = \frac{2 \times 30}{5} = \frac{60}{5} = 12$

So 12 students play chess.

Fraction who do NOT play chess: The whole is $1 = \frac{5}{5}$, so: $1 - \frac{2}{5} = \frac{5}{5} - \frac{2}{5} = \frac{3}{5}$

So $\frac{3}{5}$ of the students do not play chess (which is $\frac{3}{5} \times 30 = 18$ students).