Step by step
The question
Question: find the volume when the density is 7 g/cm³ and the mass is 84 g.
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 7.
The mass is 84.
The volume is what we want: we call it v.
3 Move v to the top
v is at the bottom.
Times v moves it up.
We do it on both sides, so they stay equal.
v divided by v is 1.
So just 84 is left on the right.
Now we have 7v = 84.
4 Remove the 7
7v means 7 times v.
We want just v.
To remove times 7, we divide by 7.
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.
7 divided by 7 is 1.
So just v is left.
84 divided by 7 is 12.
So v = 12!
5 Check
Let's check: put 12 in place of v.
We get 84, the same as the right side.
So v = 12 is right!
So the volume is 12 cm³.
Let's look back.
First: write the rule.
Then: put the numbers in.
Then: move v to the top.
Then: remove the 7.
Last: check.