Question

exercise a (answers on page 42)
order these fractions from smallest to largest.

1. \\(\frac{3}{4}\\), \\(\frac{3}{7}\\), \\(\frac{2}{3}\\)
2. \\(\frac{1}{7}\\), \\(\frac{3}{14}\\), \\(\frac{3}{28}\\)

exercise b (answers on page 42)
order these fractions from largest to smallest.

1. \\(\frac{8}{11}\\), \\(\frac{3}{4}\\), \\(\frac{13}{22}\\)
2. \\(\frac{7}{8}\\), \\(\frac{35}{64}\\), \\(\frac{5}{16}\\)

Explanation:

Exercise A (Order from Smallest to Largest)

1. $\boldsymbol{\frac{3}{4}, \frac{3}{7}, \frac{2}{3}}$

Step1: Find a common denominator

The least common multiple (LCM) of 4, 7, and 3 is 84. Convert each fraction:

• $\frac{3}{4} = \frac{3 \times 21}{4 \times 21} = \frac{63}{84}$
• $\frac{3}{7} = \frac{3 \times 12}{7 \times 12} = \frac{36}{84}$
• $\frac{2}{3} = \frac{2 \times 28}{3 \times 28} = \frac{56}{84}$

Step2: Compare numerators

Since $36 < 56 < 63$, we have $\frac{36}{84} < \frac{56}{84} < \frac{63}{84}$.

Step1: Find a common denominator

The LCM of 7, 14, and 28 is 28. Convert each fraction:

• $\frac{1}{7} = \frac{1 \times 4}{7 \times 4} = \frac{4}{28}$
• $\frac{3}{14} = \frac{3 \times 2}{14 \times 2} = \frac{6}{28}$
• $\frac{3}{28} = \frac{3}{28}$

Step2: Compare numerators

Since $3 < 4 < 6$, we have $\frac{3}{28} < \frac{4}{28} < \frac{6}{28}$.

Step1: Find a common denominator

The LCM of 11, 4, and 22 is 44. Convert each fraction:

• $\frac{8}{11} = \frac{8 \times 4}{11 \times 4} = \frac{32}{44}$
• $\frac{3}{4} = \frac{3 \times 11}{4 \times 11} = \frac{33}{44}$
• $\frac{13}{22} = \frac{13 \times 2}{22 \times 2} = \frac{26}{44}$

Step2: Compare numerators

Since $33 > 32 > 26$, we have $\frac{33}{44} > \frac{32}{44} > \frac{26}{44}$.

Answer:

$\frac{3}{7}, \frac{2}{3}, \frac{3}{4}$

2. $\boldsymbol{\frac{1}{7}, \frac{3}{14}, \frac{3}{28}}$