Question

Express the following ratio in lowest terms.
105 knives to 120 spoons

Answer 1

the ratio in lowest terms is: 7 knives to 8 spoons = 7/8

Explanation:

First express the ratio 105 knives to 120 spoons as the quotient:

`(105)/(120)`

next write each of the numbers in prime-factor form:

105 = 3 x 5 x 7

120 = 2 x 2 x 2 x 3 x 5

Now notice that when we express the quotient sing the factor form of the numbers, the factor 3, and 5 can be cancelled out because they appear in numerator an in denominator at the same time. therefore our quotient becomes:

`(105)/(120) =(3*5*7)/(2*2*2*3*5) =(7)/(2*2*2) =(7)/(8)`

Therefore the ratio in lowest terms is: 7 knives to 8 spoons