Question

Use a benchmark fraction to compare the fractions 7/10 and 5/12.explain how yolu found your answer.

Answer 1

Using bench mark fraction, we found

$\frac{7}{10}$ is larger than $\frac{5}{12}$

Solution:

Benchmark fractions are created when we make two different fractions have the same numerator or denominator

Here given fractions are:

$\frac{7}{10} \text{ and } \frac{5}{12}$

In this case, we can make the denominator same

Find L.C.M for denominators 10 and 12

List all prime factors for each number.

The prime factor of 10 = 2 x 5

The prime factor of 12 = 2 x 3 x 2

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

2, 2, 3, 5

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 3 x 5 = 60

Thus make the denominator as 60

$\rightarrow \frac{7}{10} = \frac{7 \times 6}{10 \times 6} = \frac{42}{60}\\\\\rightarrow \frac{5}{12} = \frac{5 \times 5}{12 \times 5} = \frac{25}{60}$

When, the denominators are same, the fraction with the larger numerator has a larger value

Therefore,

$\frac{42}{60} > \frac{25}{60}$

Thus, $\frac{7}{10}$ is larger than $\frac{5}{12}$