Question

1. consider the fractions $\frac{1}{3}$ and $\frac{4}{9}$.$\frac{1}{3}$ $\frac{2}{6}$ $\frac{3}{9}$ $\frac{4}{12}$ $\frac{5}{15}$explain8b complete this table of equivalent fractions.$\frac{4}{9}$ $\frac{8}{18}$ $\frac{12}{27}$ $\frac{16}{36}$ $\frac{20}{45}$explain8c which fraction is larger?$\frac{4}{9}$ $\frac{1}{3}$

Explanation:

Step1: Convert $\frac{1}{3}$ to 9 denominator

To compare, rewrite $\frac{1}{3}$ with denominator 9:
$\frac{1}{3} = \frac{1 \times 3}{3 \times 3} = \frac{3}{9}$

Step2: Compare numerators of like fractions

Now compare $\frac{3}{9}$ and $\frac{4}{9}$. Since $3 < 4$, $\frac{3}{9} < \frac{4}{9}$.

Step3: Verify equivalent fractions for 8b

For $\frac{4}{9}$ equivalents:

• $\frac{4 \times 2}{9 \times 2} = \frac{8}{18}$
• $\frac{4 \times 3}{9 \times 3} = \frac{12}{27}$
• $\frac{4 \times 4}{9 \times 4} = \frac{16}{36}$
• $\frac{4 \times 5}{9 \times 5} = \frac{20}{45}$

All given fractions are valid equivalents.

Answer:

For 8b: The table is already correctly completed with equivalent fractions of $\frac{4}{9}$.
For 8c: The larger fraction is $\frac{4}{9}$.