Worked examples
The question
Question: change 5 feet into inches.
5 ft = ? in
1 Find the link
1 foot is 12 inches.
1 ft = 12 in
2 Make the unit fraction
We want inches, so inches go on top.
We have feet, so feet go at the bottom.
Top and bottom are the same amount.
So the fraction is 1, and times 1 keeps the size.
12 in1 ft = 1
Careful!
Not upside down.
Then the feet would not cross out.
Careful: not 5 ft × 1 ft12 in ✗
3 Multiply
We multiply 5 feet by the fraction.
5 ft = 5 ft × 12 in1 ft
Feet on top and at the bottom cancel, like numbers.
Cross them out.
Inches are left.
What is left: 5 times 12.
= 5 × 12 in
5 times 12 is 60.
So 5 feet is 60 inches.
= 60 in
4 Check
Does it make sense?
Inches are smaller than feet.
So we need more of them.
60 is more than 5.
Yes.
in smaller than ft → more: 60 > 5
And back the other way: 60 divided by 12 = 5.
We get 5 feet again.
So the answer is right!
back: 60 ÷ 12 = 5
Let's look back.
First: find the link.
Then: make the unit fraction.
Then: multiply.
Last: check.
▶ Watch it solved
The question
Question: change 3.5 kilometers into meters.
3.5 km = ? m
1 Find the link
1 kilometer is 1000 meters.
1 km = 1000 m
2 Make the unit fraction
We want meters, so meters go on top.
We have kilometers, so kilometers go at the bottom.
Top and bottom are the same amount.
So the fraction is 1, and times 1 keeps the size.
1000 m1 km = 1
Careful!
Not upside down.
Then the kilometers would not cross out.
Careful: not 3.5 km × 1 km1000 m ✗
3 Multiply
We multiply 3.5 kilometers by the fraction.
3.5 km = 3.5 km × 1000 m1 km
Kilometers on top and at the bottom cancel, like numbers.
Cross them out.
Meters are left.
What is left: 3.5 times 1000.
= 3.5 × 1000 m
3.5 times 1000 is 3500.
So 3.5 kilometers is 3500 meters.
= 3500 m
4 Check
Does it make sense?
Meters are smaller than kilometers.
So we need more of them.
3500 is more than 3.5.
Yes.
m smaller than km → more: 3500 > 3.5
And back the other way: 3500 divided by 1000 = 3.5.
We get 3.5 kilometers again.
So the answer is right!
back: 3500 ÷ 1000 = 3.5
Let's look back.
First: find the link.
Then: make the unit fraction.
Then: multiply.
Last: check.
▶ Watch it solved
The question
Question: change 3 hours into seconds.
3 h = ? s
1 Find the links
There is no link straight from hours to seconds.
So we go in steps.
1 hour is 60 minutes.
1 h = 60 min
Then: 1 minute is 60 seconds.
1 min = 60 s
2 Make the unit fractions
We want minutes, so minutes go on top.
We have hours, so hours go at the bottom.
Top and bottom are the same amount.
So the fraction is 1, and times 1 keeps the size.
60 min1 h = 1
Next seconds, so seconds go on top.
We have minutes, so minutes go at the bottom.
60 s1 min = 1
Careful!
Not upside down.
Then the hours would not cross out.
Careful: not 3 h × 1 h60 min ✗
3 Multiply
We multiply 3 hours by the fractions.
3 h = 3 h × 60 min1 h × 60 s1 min
Hours and minutes on top and at the bottom cancel, like numbers.
Cross them out.
Seconds are left.
What is left: 3 times 60 times 60.
= 3 × 60 × 60 s
3 times 60 times 60 is 10,800.
So 3 hours is 10,800 seconds.
= 10,800 s
4 Check
Does it make sense?
Seconds are smaller than hours.
So we need more of them.
10,800 is more than 3.
Yes.
s smaller than h → more: 10,800 > 3
And back the other way: 10,800 divided by 60 divided by 60 = 3.
We get 3 hours again.
So the answer is right!
back: 10,800 ÷ 60 ÷ 60 = 3
Let's look back.
First: find the links.
Then: make the unit fractions.
Then: multiply.
Last: check.
▶ Watch it solved
