Question

Shelagh and Luana realized that they could express their ages more specifically if they used fractions. Doing this will allow them to calculate the difference in their ages more precisely. If Shelagh describes her age as 17 1/2 years old and Luna is 9 1/12, what is the difference in their age

Answer 1

Given:

a.) Shelagh describes her age as 17 1/2 years old

b.) Luna is 9 1/12 years old

Let's determine the difference in their age

.

Step 1: Let's convert them into improper fractions.

`\text{ 17 }(1)/(2)\text{ = }\frac{\text{ (17 x 2) + 1}}{2}\text{ = }\frac{34\text{ + 1}}{2}\text{ = }(35)/(2)`
`\text{ 9 }(1)/(12)\text{ = }\frac{(9\text{ x 12) + 1}}{12}=\frac{108\text{ + 1}}{12}\text{ = }(109)/(12)`

Step 2: Let's make them into similar fractions. (Fractions with the same denominator.)

The LCM of 2 and 12 is 12. Let's transform the two fractions into one with a denominator of 12.

`\text{ }(35)/(2)\text{ = }\frac{35\text{ x 6}}{2\text{ x 6}}\text{ = }(210)/(12)`

Step 3: Proceed to subtract the two numbers.

`\text{ 17 }(1)/(2)\text{ - 9 }(1)/(12)\text{ = }(210)/(12)\text{ - }(109)/(12)`
`=\frac{\text{ 210 - 109 }}{12}`
`\text{ = }(101)/(12)`
`\text{ = 8 }\frac{\text{ 5}}{12}`

Therefore, the difference in their age is 8 5/12 years.