Fractions

Q1: Fill in the blanks:

i. \(\frac{7}{11}\) ____ \(\frac{5}{8}\)

Step 1: To compare, cross multiply: \[ 7 \times 8 = 56 \\ 5 \times 11 = 55 \]Step 2: Since \(56 > 55\), \[ \frac{7}{11} > \frac{5}{8} \]Answer: \(\frac{7}{11} > \frac{5}{8}\)

ii. \(\frac{3}{7}\) ____ \(\frac{3}{5}\)

Step 1: Cross multiply: \[ 3 \times 5 = 15 \\ 3 \times 7 = 21 \]Step 2: Since \(15 < 21\), \[ \frac{3}{7} < \frac{3}{5} \]Answer: \(\frac{3}{7} < \frac{3}{5}\)

iii. \(\frac{4}{9}\) ____ \(\frac{4}{7}\)

Step 1: Cross multiply: \[ 4 \times 7 = 28 \\ 4 \times 9 = 36 \]Step 2: Since \(28 < 36\), \[ \frac{4}{9} < \frac{4}{7} \]Answer: \(\frac{4}{9} < \frac{4}{7}\)

iv. \(\frac{15}{4} \times\) ____ \(= \frac{3}{2}\)

Step 1: Let the blank be \(x\), \[ \frac{15}{4} \times x = \frac{3}{2} \]Step 2: Solve for \(x\): \[ x = \frac{3}{2} \div \frac{15}{4} = \frac{3}{2} \times \frac{4}{15} = \frac{12}{30} = \frac{2}{5} \]Answer: \(\frac{2}{5}\)

v. \(\frac{14}{15} \div\) ____ \(= \frac{2}{3}\)

Step 1: Let the blank be \(y\), \[ \frac{14}{15} \div y = \frac{2}{3} \]Step 2: Solve for \(y\): \[ y = \frac{14}{15} \div \frac{2}{3} = \frac{14}{15} \times \frac{3}{2} = \frac{42}{30} = \frac{7}{5} \]Answer: \(\frac{7}{5}\)

vi. Reciprocal of \(2\frac{3}{4}\) is _____

Step 1: Convert mixed fraction to improper fraction: \[ 2\frac{3}{4} = \frac{11}{4} \]Step 2: Reciprocal is: \[ \frac{4}{11} \]Answer: \(\frac{4}{11}\)

Q2: Fill in the blanks:

i. \(\frac{8}{5} \div 1 =\) ______

Step 1: Dividing any number by 1 gives the number itself: \[ \frac{8}{5} \div 1 = \frac{8}{5} \]Answer: \(\frac{8}{5}\)

ii. \(1\frac{3}{8}\ \text{of}\ \frac{4}{5} =\) ______

Step 1: Convert mixed fraction to improper fraction: \[ 1\frac{3}{8} = \frac{11}{8} \]Step 2: Multiply: \[ \frac{11}{8} \times \frac{4}{5} = \frac{44}{40} = \frac{11}{10} = 1\frac{1}{10} \]Answer: \(1\frac{1}{10}\)

iii. \(\left(\frac{5}{6}\ \text{of}\ 1\ \text{hour}\right) =\) ______ minutes

Step 1: 1 hour = 60 minutes
Step 2: Multiply: \[ \frac{5}{6} \times 60 = 50 \text{ minutes} \]Answer: 50 minutes

iv. \(\left(\frac{3}{8}\ \text{of}\ 1\ \text{km}\right) =\) ______ metres

Step 1: 1 km = 1000 metres
Step 2: Multiply: \[ \frac{3}{8} \times 1000 = 375 \text{ metres} \]Answer: 375 metres

v. \(\frac{3}{8}\ \text{of}\ ₹1 =\) ______ paise

Step 1: 1 rupee = 100 paise
Step 2: Multiply: \[ \frac{3}{8} \times 1 = \frac{3}{8} \text{ rupees} \\ = \frac{3}{8} \times 100 = 60 \text{ paise} \]Answer: 60 paise

Q3: Write T for true and F for false statement:

i. \(1 \div \frac{3}{2} = \frac{2}{3}\)

Step 1: Divide by a fraction = multiply by its reciprocal: \[ 1 \div \frac{3}{2} = 1 \times \frac{2}{3} = \frac{2}{3} \]Answer: T

ii. \(1\frac{2}{3} \div \frac{3}{4} = 1\frac{1}{2}\)

Step 1: Convert mixed fraction: \[ 1\frac{2}{3} = \frac{5}{3} \]Step 2: Divide by \(\frac{3}{4}\): \[ \frac{5}{3} \div \frac{3}{4} = \frac{5}{3} \times \frac{4}{3} = \frac{20}{9} = 2\frac{2}{9} \]Answer: F

iii. \(\frac{3}{5}\ \text{of}\ ₹1\ \text{kg} = 600g\)

Step 1: 1 kg = 1000 g
Step 2: Multiply: \[ \frac{3}{5} \times 1000 = 600 \text{ g} \]Answer: T

iv. \(\frac{3}{4} \ \text{of} \ ₹1 = 65\ \text{paise}\)

Step 1: 1 rupee = 100 paise
Step 2: Multiply: \[ \frac{3}{4} \times 100 = 75 \text{ paise} \]Answer: F

v. \(\frac{7}{10} \ \text{of} \ 1\ \text{hour} = 42\ \text{minutes}\)

Step 1: 1 hour = 60 minutes
Step 2: Multiply: \[ \frac{7}{10} \times 60 = 42 \text{ minutes} \]Answer: T

vi. \(\frac{5}{6}\ \text{and}\ \frac{5}{7}\ \text{are like fractions}\)

Step 1: Like fractions have the same denominator.
Step 2: Denominators here are 6 and 7, which are different.
Answer: F

vii. \(\frac{1}{4}\ \text{and}\ \frac{1}{5}\ \text{are unlike fractions}\)

Step 1: Unlike fractions have different denominators.
Step 2: Denominators are 4 and 5, which are different.
Answer: T