# Thread: I need the right steps to dividing fractions with different denominators

1. ## I need the right steps to dividing fractions with different denominators

I need help solving (10/9) divided by 1/2

2. Originally Posted by nykhris22
I need help solving (10/9) divided by 1/2
There is a neat trick that you can use when dividing fractions: flip the second fraction, and then multiply them together!

So here, instead of trying to fathom:

$\frac{10}{9}\div\frac{1}{2}$

Flip the second, and multiply:

$\frac{10}{9}\times\frac{2}{1}$

Can you manage from here?

Essentially, you can think of this as "doing the opposite twice" - you invert the fraction, and then invert the operation, so the result is the same.

3. 10/9 : 1/2 = 10/9 x 2 = 20/9

4. Originally Posted by nykhris22
I need help solving (10/9) divided by 1/2
Hi nykhris22,

We don't care so much about denominators when we're dividing or multiplying fractions.

Remember that dividing is the same as multiplying a number by its multiplicative inverse or reciprocal.

For instance, $4 \div 2 = 4 \times \frac{1}{2}$

$\frac{1}{2}$ is the multiplicative inverse (reciprocal) of 2.

To divide two fractions like $\frac{2}{3} \div \frac{3}{4}$, we just multiply $\frac{2}{3} \times \frac{4}{3}=\frac{8}{9}$

5. Originally Posted by nykhris22
I need help solving (10/9) divided by 1/2
$\frac{\left(\frac{10}{9}\right)}{\left(\frac{1}{2} \right)}=\frac{\frac{1}{2}\left(\frac{20}{9}\right )}{\left(\frac{1}{2}\right)}$

$=\frac{0.5\left(\frac{20}{9}\right)}{0.5}=\frac{20 }{9}$

6. Originally Posted by nykhris22
I need help solving (10/9) divided by 1/2
The "stay, change, flip" method works well, but it helps if you realise that "divided by" means "how many" or "how much".

So it's asking "How many halves in 10/9".

Well, 10/9 = 1 + 1/9. Since there are two halves in 1, so you know the answer will be slightly more than 2.