Question

The length of a board is 2 2/8 feet long. If 5/6 of a foot is trimmed off, find the new length.

Answer 1

new length:
`(17)/(12)`

Explanation:

Basically the question wants you to find what is
`2(2)/(8) -(5)/(6)`

Realize that both fractions have different denominators so we CANNOT subtract yet

Instead, we need to set both fractions with a Common Denominator.

What is a Common Denominator?

A common denominator is when you have both fractions with the same denominator

In order to set both fractions with the same denominator, we need to find the Least Common Multiple

What do I mean by Least Common Multiple?

The Least Common Multiple of any number would be the smallest positive integer that is divisible by both numbers

For example: The Least Common Multiple of 16 and 12 would be 48 because that is the Smallest Multiple they have in common.

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

so going back to the question: The length of a board is 2 2/8 feet long. If 5/6 of a foot is trimmed off, find the new length.

Step 1. Set both fractions with the same Common denominator by finding they're Least Common Multiple.

6: 6, 12, 18, 24, 30, 36, 48,...

8: 8, 16, 24, 32, 40, 48,...

The Least Common Multiple of 6 and 8 is 24!

Now we're ready to convert both fractions having the same denominator.

`2(2)/(8) =2(x)/(24)`

`(5)/(6) =(x)/(24)`

x represents numerator but since both fractions have a new denominator, therefore, they've a new numerator.

Simply multiply the denominator of the original fraction by a number that would result into the Common Denominator.

8 times what equals 24? The answer is 3.

6 times what equals 24? The answer is 4.

So then whatever number you got, simply multiply that number by the numerator and that should be your new numerator.

2 × 3 = 6 (new numerator)

5 × 4 = 20 (new numerator)

New fractions:
`2(6)/(24)` ,
`(20)/(24)`

Now, we're ready to subtract!

BUT WAIT!

6 take away 20 equals -14 and no that is NOT how you subtract fractions!

Instead, borrow from the 2 which is the whole number of the first fraction and then add 6 and that number that you get after converting the 2 into a fraction.

2 =
`(48)/(24)`

`(48)/(24)+(6)/(24)=(54)/(24)`

And NOW, we're READY to subtract!

`(54)/(24) -(20)/(24) =(34)/(24)`

Finally, we need to simplify!

`(17)/(12)`