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

`(7)/(10)` is larger than
`(5)/(12)`

Solution:

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

Here given fractions are:

`(7)/(10) \text{ and } (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 (7)/(10) = (7 * 6)/(10 * 6) = (42)/(60)\\\\\rightarrow (5)/(12) = (5 * 5)/(12 * 5) = (25)/(60)`

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

Therefore,

`(42)/(60) > (25)/(60)`

Thus,
`(7)/(10)` is larger than
`(5)/(12)`