Skill: Use benchmark fractions

Benchmark fractions help you quickly understand how large a fraction is. Useful benchmarks include $0$, $\tfrac14$, $\tfrac12$, $\tfrac34$, and $1$.

Example: Estimate $\frac{5}{16}+\frac{9}{10}$

Step 1: Place each fraction near a benchmark.

For $\frac{5}{16}$, write the benchmarks with denominator $16$:

$$\frac14=\frac{4}{16} \qquad\text{and}\qquad \frac12=\frac{8}{16}$$

Since $\frac{5}{16}$ is just above $\frac{4}{16}$, it is close to $\frac14$.

For $\frac{9}{10}$, compare it with $1$:

$$\frac{9}{10}$$

is just $\frac{1}{10}$ less than $1$, so it is close to $1$.

Step 2: Replace each fraction with its nearby benchmark.

$$\frac{5}{16}+\frac{9}{10} \approx \frac14+1$$

Step 3: Add the benchmarks.

$$\frac14+1=1\frac14$$

So,

$$\boxed{\frac{5}{16}+\frac{9}{10}\approx 1\frac14}$$

The estimate is reasonable because $\frac{5}{16}$ is a little bigger than $\frac14$, and $\frac{9}{10}$ is a little less than $1$. Their exact sum is close to $1\frac14$.