Question

Estimate the difference between the given fractions using benchmarks:

$\frac{8}{9}-\frac{6}{11}\approx$

• A. $\frac{1}{4}$
• B. $\frac{3}{4}$
• C. $\frac{1}{3}$
• D. $\frac{1}{2}$

Answer 1

The correct option is D $\frac{1}{2}$

$\text{The benchmark fractions are:}$$0,\frac{1}{2},1$

$\text{Comparing}\frac{8}{9}\text{to its nearest benchmark,}\text{we get:}$


$\text{As 8 is close to 9, the fraction can be}\text{rounded off to 1}$

$\text{Now, comparing}\frac{6}{11}\text{to its nearest}\text{benchmark, we get:}$


$\text{As 11 is close to 12, the fraction can be}\text{rounded off to}\frac{1}{2}$

$\text{So, we can write:}$

$\frac{8}{9}-\frac{6}{11}\approx 1-\frac{1}{2}=\frac{1}{2}$

$\therefore \text{The difference between the given}$ $\text{fractions using the benchmark fractions}$
$\text{is}\frac{1}{2}.$