Step by step
The question
Question: find the volume when the density is 1.5 g/cm³ and the mass is 36 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 1.5.
The mass is 36.
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 36 is left on the right.
Now we have 1.5v = 36.
4 Remove the decimals
Decimals are hard to work with.
Let's get rid of them.
We multiply every part by 10.
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.
Times 10 moves the point 1 place to the right.
10 × 1.5v = 15v.
10 × 36 = 360.
Write the answers.
No more decimals!
5 Remove the 15
15v means 15 times v.
We want just v.
To remove times 15, we divide by 15.
We do it on both sides, so they stay equal.
15 divided by 15 is 1.
So just v is left.
360 divided by 15 is 24.
So v = 24!
6 Check
Let's check: put 24 in place of v.
We get 36, the same as the right side.
So v = 24 is right!
So the volume is 24 cm³.
Let's look back.
First: write the rule.
Then: put the numbers in.
Then: move v to the top.
Then: remove the decimals.
Then: remove the 15.
Last: check.