Question

use a benchmark to compare fractions — instruction — level 6
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a) choose a benchmark to compare the fractions.
b) i can use the benchmark? to compare 4/10 and 3/4. (options: 1, 1/2)

Explanation:

Step1: Analyze the fractions

We have two fractions, $\frac{4}{10}$ and $\frac{3}{4}$. We need to choose a benchmark to compare them. A common benchmark for comparing fractions is $\frac{1}{2}$ (0.5) because it's easy to see if a fraction is greater than, less than, or equal to $\frac{1}{2}$.

Step2: Compare each fraction to $\frac{1}{2}$

• For $\frac{4}{10}$: Simplify or convert to decimal. $\frac{4}{10} = 0.4$, and $\frac{1}{2}=0.5$. So $\frac{4}{10}<\frac{1}{2}$.
• For $\frac{3}{4}$: Convert to decimal. $\frac{3}{4} = 0.75$, and $0.75>0.5$ (which is $\frac{1}{2}$). So $\frac{3}{4}>\frac{1}{2}$.

Using $\frac{1}{2}$ as a benchmark helps us see that $\frac{4}{10}<\frac{3}{4}$ because one is less than $\frac{1}{2}$ and the other is greater than $\frac{1}{2}$.

Answer:

$\frac{1}{2}$