Step by step
The question
Question: find the volume when the density is 2.5 g/cm³ and the mass is 50 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 2.5.
The mass is 50.
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 50 is left on the right.
Now we have 2.5v = 50.
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 × 2.5v = 25v.
10 × 50 = 500.
Write the answers.
No more decimals!
5 Remove the 25
25v means 25 times v.
We want just v.
To remove times 25, we divide by 25.
We do it on both sides, so they stay equal.
25 divided by 25 is 1.
So just v is left.
500 divided by 25 is 20.
So v = 20!
6 Check
Let's check: put 20 in place of v.
We get 50, the same as the right side.
So v = 20 is right!
So the volume is 20 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 25.
Last: check.