Worked examples
The question
Question: find the density when the mass is 240 g and the volume is 30 cm³.
Mass 240 g, volume 30 cm³. Find the density.
1 Write the rule
The rule: density is the mass divided by the volume.
density = massvolume
Density tells us how much mass there is in 1 cm³.
So its unit is g per cm³.
density = the mass of 1 cm³
unit: g ÷ cm³ → g/cm³
2 Put the numbers in
The mass is 240.
The volume is 30.
d = 24030
3 Work it out
Careful!
The mass goes on the top.
The unit, g/cm³, shows it: g on the top.
Careful: not 30240 ✗
240 divided by 30 is 8.
density = 8 g/cm³
Both end in a zero: we cross it out first.
24 divided by 3 is 8.
240 ÷ 30 = 24 ÷ 3 = 8
So the density is 8 g/cm³.
4 Check
Let's check.
8 in each cm³, for 30 cm³: 8 times 30 is 240.
That is the mass.
So the answer is right!
8 g in each cm³: 8 × 30 = 240 g
Let's look back.
First: write the rule.
Then: put the numbers in.
Then: work it out.
Last: check.
Answer 240 ÷ 30 = 24 ÷ 3 = 8
▶ Watch it solved
The question
Question: find the mass when the density is 8 g/cm³ and the volume is 15 cm³.
Density 8 g/cm³, volume 15 cm³. Find the mass.
1 Write the rule
The rule: density is the mass divided by the volume.
density = massvolume
Density tells us how much mass there is in 1 cm³.
So its unit is g per cm³.
density = the mass of 1 cm³
unit: g ÷ cm³ → g/cm³
2 Put the numbers in
The density is 8.
The volume is 15.
The mass is what we want: we call it m.
8 = m15
Careful!
The mass goes on the top.
The unit, g/cm³, shows it: g on the top.
Careful: not 158 ✗
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 × 8 = 15 × m15
15 divided by 15 is 1.
Write what is left.
15 × 8 = m
Do the multiplications.
No more fractions!
120 = m
Let's swap the two sides, so m is on the left.
m = 120
So m = 120!
4 Check
Let's check: put 120 in place of m.
First the left side.
Left: 8
Now the right side.
Right: 12015 = 8
Both sides are 8.
So m = 120 is right!
Both sides equal 8
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.
▶ Watch it solved
The question
Question: find the volume when the density is 2.5 g/cm³ and the mass is 50 g.
Density 2.5 g/cm³, mass 50 g. Find the volume.
1 Write the rule
The rule: density is the mass divided by the volume.
density = massvolume
Density tells us how much mass there is in 1 cm³.
So its unit is g per cm³.
density = the mass of 1 cm³
unit: g ÷ cm³ → g/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.
2.5 = 50v
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.
2.5 × v = 50v × v
v divided by v is 1.
So just 50 is left on the right.
Now we have 2.5v = 50.
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.
10 × 2.5v = 10 × 50
Times 10 moves the point 1 place to the right.
10 × 2.5v = 25v.
10 × 2.5v = 25v
10 × 50 = 500.
10 × 50 = 500
Write the answers.
No more decimals!
25v = 500
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.
25v25 = 50025
25 divided by 25 is 1.
So just v is left.
500 divided by 25 is 20.
50025 = 20
So v = 20!
v = 20
6 Check
Let's check: put 20 in place of v.
Check: 2.5(20) = 50
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.
▶ Watch it solved
