Step by step
The question
Question: solve 5/x = 15/24.
Two fractions are equal.
Let's find x.
There are four choices.
First we solve it, the normal way.
Then we pick.
1 Cross multiply
When two fractions are equal, we cross multiply: each top times the other bottom.
Top left times bottom right: 5 times 24.
Top right times bottom left: 15 times x.
These two are equal.
5 times 24 is 120.
15 times x is 15x.
Let's swap the two sides, so x is on the left.
Both sides are the same amount, so we can swap them.
Is x alone now?
Not yet: 15x means 15 times x.
How do we remove it?
2 Remove the 15
To remove times 15, we divide by 15.
We do it on both sides.
Why both sides?
The = sign means both sides are the same amount.
If we change only one side, they are not the same any more.
15 divided by 15 is 1.
They cancel each other.
So just x is left.
120 divided by 15 is 8.
So x = 8!
3 Check
Let's check: put 8 in place of x.
First the left side.
Now the right side.
Both sides are 5/8.
So x = 8 is right!
4 Pick the choice
Our answer is x = 8.
That is choice B.
5 Why not the others
A is 3.
Wrong: 15 ÷ 5 = 3: that is how many times bigger, not x.
C is 14.
Wrong: 24 − 15 + 5: took away instead of dividing.
D is 72.
Wrong: 15 × 24 ÷ 5: mixed up the cross products.
Let's look back.
First: cross multiply.
Then: remove the 15.
Then: check.
Then: pick the choice.
Last: why not the others.