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:
$\displaystyle \frac{10}{9}\div\frac{1}{2}$
Flip the second, and multiply:
$\displaystyle \frac{10}{9}\times\frac{2}{1}$
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.
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, $\displaystyle 4 \div 2 = 4 \times \frac{1}{2}$
$\displaystyle \frac{1}{2}$ is the multiplicative inverse (reciprocal) of 2.
To divide two fractions like $\displaystyle \frac{2}{3} \div \frac{3}{4}$, we just multiply $\displaystyle \frac{2}{3} \times \frac{4}{3}=\frac{8}{9}$
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.