Step by step
The question
Question: find the mass when the density is 8 g/cm³ and the volume is 15 cm³.
1 Write the rule
The rule: density is the mass divided by the volume.
Density tells us how much mass there is in 1 cm³.
So its unit is g per cm³.
2 Put the numbers in
The density is 8.
The volume is 15.
The mass is what we want: we call it m.
Careful!
The mass goes on the top.
The unit, g/cm³, shows it: g on the top.
3 Remove the fraction
The bottom number is 15.
Times 15 will remove it.
We multiply every part 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.
Write what is left.
Do the multiplications.
No more fractions!
Let's swap the two sides, so m is on the left.
So m = 120!
4 Check
Let's check: put 120 in place of m.
First the left side.
Now the right side.
Both sides are 8.
So m = 120 is right!
So the mass is 120 g.
Let's look back.
First: write the rule.
Then: put the numbers in.
Then: remove the fraction.
Last: check.