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

Jun 8, 2016

$\frac{5}{28}$

#### Explanation:

Firs, rewrite $1 \frac{1}{4}$ as an improper fraction. Do this by recognizing that

$1 \frac{1}{4} = 1 + \frac{1}{4}$

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

$1 + \frac{1}{4} = \frac{1}{1} + \frac{1}{4}$

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

$\frac{1}{1} + \frac{1}{4} = \frac{1 \times 4}{1 \times 4} + \frac{1}{4} = \frac{4}{4} + \frac{1}{4}$

We can do $\frac{4}{4} + \frac{1}{4}$ since the fractions have the same denominator: add the numerators, $1$ and $4$, and leave the denominators the same. Thus

$\frac{4}{4} + \frac{1}{4} = \frac{4 + 1}{4} = \frac{5}{4}$

So, instead of the original equation $1 \frac{1}{4} \div 7$, we have the new equation

$\frac{5}{4} \div 7$

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 $7 = \frac{7}{1}$. Thus, the reciprocal of $7$ is the same as saying the reciprocal of $\frac{7}{1}$, which is $\frac{1}{7}$.

So, saying $\frac{5}{4} \div 7$ is equal to $\frac{5}{4} \times \frac{1}{7}$.

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

$\frac{5}{4} \times \frac{1}{7} = \frac{5 \times 1}{4 \times 7} = \frac{5}{28}$

$\frac{5}{28}$ cannot be simplified since $5$ and $28$ share no common factors other than $1$.