Question

Find the difference 34/31 - 9/45

Answer 1

`\sf (34)/(31) - (9)/(45) = (139)/(155)`

Explanation:

`\sf (34)/(31) - (9)/(45) = \, ?`

The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

LCD(34/31, 9/45) = 1395

Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.

`\sf \left((34)/(31) * (45)/(45)\right) - \left((9)/(45) * (31)/(31)\right) = \, ?`

Complete the multiplication and the equation becomes

`\sf (1530)/(1395) - (279)/(1395) = \, ?`

The two fractions now have like denominators so you can subtract the numerators.

Then:

`\sf (1530 - 279)/(1395) = (1251)/(1395)`

This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 1251 and 1395 using

GCF(1251,1395) = 9

`\sf (1251 / 9)/(1395 / 9) = (139)/(155)`

Therefore:

`\sf (34)/(31) - (9)/(45) = (139)/(155)`