Compare Mixed Numbers to 14%: Sorting Decimals and Fractions

Organise the following values into two groups of those greater than 14% and those less than 14%:

$0.1,\frac{6}{20},\frac{6}{40},\frac{14}{95},\frac{1}{3}$

To solve this problem, we'll convert all given values to decimal form and compare them with 0.14.

• Convert $\frac{6}{20}$ to a decimal: $\frac{6}{20} = 0.3$.
• Convert $\frac{6}{40}$ to a decimal: $\frac{6}{40} = 0.15$.
• Convert $\frac{14}{95}$ to a decimal: $\frac{14}{95} \approx 0.1474$.
• Convert $\frac{1}{3}$ to a decimal: $\frac{1}{3} \approx 0.3333$.
• $0.1$ is already a decimal.

Now compare each value to 0.14:

• $0.1 < 0.14$
• $0.3 > 0.14$
• $0.15 > 0.14$
• $0.1474 > 0.14$
• $0.3333 > 0.14$

Therefore, grouping the values:

• Values greater than 14%: $\frac{1}{3}$, $\frac{6}{40}$, $\frac{6}{20}$
• Values less than 14%: $\frac{14}{95}$, $0.1$

In conclusion, the values greater than 14% are $\frac{1}{3}$, $\frac{6}{40}$, $\frac{6}{20}$ and less than 14% are $\frac{14}{95}$, $0.1$.

The correct answer choice is:

$\frac{1}{3},\frac{6}{40},\frac{6}{20}>14\%$

$\frac{14}{95},0.1<14\%$