Question

Jack's height was `68 1/2` in June. He had grown `1 5/8` during the school year. How tall was he when school started?

Answer 1

Jack was 66 7/8 at the beginning of the school year

Explanation:

To find how tall he was when school started, we have to find his initial height. To find this, we can make up our own formula

(Note: this formula was created from the fact that if someone grows by a certain amount, they will be that much taller than the height they originally were)

Initial Height + Growth = Final Height

Since we know that at the end of the school year he was 68`1/2` tall and that he grew 1`5/8` in the school year, we can substitute those in our equation as final height and growth respectively

Initial Height + 1`5/8` = 68`1/2`
Initial Height = 68`1/2` - 1`5/8`

Now to subtract these two fractions, you can convert the mixed fractions to improper fractions by multiplying the whole number by the denominator of the fraction then adding that to the numerator

Initial Height = `(68*2+1)/2` - `(1*8+5)/8`
Initial Height = `137/2` - `13/8`

Now that we have the fractions in improper fractions, all we have to do is make them have the fractions have common denominators before adding them! We do this by finding what one denominator has to multiplied by to equal the other one. In this case, `2*4` = 8, so we must multiply `137/2` by `4/4` to make it have the same denominator as `13/8`

Initial Height = `137/2`(`4/4`) - `13/8`
Initial Height = `(137*4)/(2*4)` - `13/8`
Initial Height = `548/8` - `13/8`

Now we just subtract the numerators!

Initial Height = `(548-13)/8`
Initial Height = `535/8`

We can convert back into mixed fractions by finding what `535/8` is with a remainder as the numerator of the fraction. (`535/8` = 66 and 7 as the remainder)

`:.`, Initial Height = 66`7/8`