Question

What is `2 1/7 div 2 1/2`?

Answer 1

Convert to fractions, multiply to get a common denominator, divide, giving you `6/7` .

Explanation:

Start by writing the problem as fractions.

`(2 1/7) / (2 1/2) = (2/1+1/7)/(2/1 + 1/2)`

Working with one set of numbers at a time, multiply to get a common denominator. The easiest and fastest route is usually to multiply one of your fractions by `1/1` using factors from the other fraction, so that you don't change the equation from the original value. Since our denominator in `2/1` is 1, we can multiply that denominator by the other fraction's denominator, to get our common denominator.

First the numerator of the original problem.

`((2/1*7/7)+1/7)/(2/1 + 1/2)=(14/7+1/7)/(2/1 + 1/2)`

Then we'll do the denominator of the original, multiplying `2/1` by `2/2`, which we got from the other fraction's denominator.

`(14/7+1/7)/((2/1*2/2) + 1/2)=(14/7+1/7)/(4/2 + 1/2)`

Now that all the addition fractions are over a common denominator and are all equal slices of the same pie, we can add numerators together.

`((14+1)/7)/((4+1)/2)=(15/7)/(5/2)`

Dividing by a fraction is the same as multiplying by the inverse of that fraction. Flip the numerator and denominator of the original denominator and multiply that against the original numerator.

`(15/7)*(2/5)`

Multiply numerators by numerators and denominators by denominators.

`(15/7)*(2/5) = 30/35`

From there you could see both top and bottom are divisible by 5, so you can pull out 5 from the top and bottom, which is just one, and simplifying your problem to `6/7` .

`30/35=5/5*6/7=1*6/7=6/7`

Alternatively, you can cancel: 15 divided by 5 from the second fraction which leaves 3 in the numerator of the first, and then multiply numerators and denominators.

`15/7*2/5=3/7*2/1=6/7`

Answer 2

`6/7`

Explanation:

First change the mixed numbers into improper fractions.

`2 1/7 div2 1/2`

`=15/7 xx 5/2`

Multiply by the reciprocal:

`15/7 xx2/5`

`cancel15^3/7 xx2/cancel5`

`=6/7`

Note that by multiplying by `2/5`, you are first finding how many 'halves' there are in `2 1/7` and then by dividing by `5`, you are finding how many 'groups of '`5` halves' there are .... which is what `div 2 1/2` actually means,