Question

How do you multiply `1 1/4 div 7`?

Answer 1

`5/28`

Explanation:

Firs, rewrite `1 1/4` as an improper fraction. Do this by recognizing that

`1 1/4=1+1/4`

Now, to add these fractions, we need a common denominator. Note that:

`1+1/4=1/1+1/4`

The common denominator will be `4`, since it is the least common multiple of `1` and `4`.

`1/1+1/4=(1xx4)/(1xx4)+1/4=4/4+1/4`

We can do `4/4+1/4` since the fractions have the same denominator: add the numerators, `1` and `4`, and leave the denominators the same. Thus

`4/4+1/4=(4+1)/4=5/4`

So, instead of the original equation `1 1/4-:7`, we have the new equation

`5/4-:7`

The next step is to note that dividing by `7` is the same as multiplying by the reciprocal of `7`.

You may be confused, since `7` doesn't seem to be a fraction, so how can it have a reciprocal?

However, note that `7=7/1`. Thus, the reciprocal of `7` is the same as saying the reciprocal of `7/1`, which is `1/7`.

So, saying `5/4-:7` is equal to `5/4xx1/7`.

To multiply fractions, multiply the numerators straight across and the denominators straight across.

`5/4xx1/7=(5xx1)/(4xx7)=5/28`

`5/28` cannot be simplified since `5` and `28` share no common factors other than `1`.