SME
Grade 5 Math · Problem type
Subtract fractions with unlike denominators
Use this for “Find the value of 5/6 − 3/8.”
Diagram
9/12 − 4/12 = 5/12
This is an example. Type your own values to start a new problem.
First numerator
First denominator
−
Second numerator
Second denominator
=
Numerator of the difference
Common denominator
First new numerator
worked out (not typed)
Second new numerator
worked out (not typed)
Formulas
4 and 3 both go into 12
The smallest number both denominators go into = common denominator
3 × (12 ÷ 4) = 9
First numerator × (common denominator ÷ first denominator) = first new numerator
1 × (12 ÷ 3) = 4
Second numerator × (common denominator ÷ second denominator) = second new numerator
9
12
−
4
12
=
5
12
Subtract the new numerators; the denominator stays
Assumptions
•
Give both fractions a common denominator: the smallest number both denominators go into.
•
Then subtract the smaller new numerator from the bigger one and keep the denominator.
•
The first fraction is the bigger one. Denominators 2, 3, 4, 5, 6, 8, 10 and 12.
Step-by-step
WE KNOW
First numerator: 3
First denominator: 4
Second numerator: 1
Second denominator: 3
FIND
common denominator, first new numerator, second new numerator, numerator of the difference
Step 1 · Find common denominator
4 and 3 both go into ?
The smallest number both denominators go into = common denominator
Count by the bigger denominator until you reach a multiple of the smaller one.
Multiples of 4: 4, 8, 12 → 12 is also a multiple of 3
Common denominator = 12
Step 2 · Find first new numerator
3 × (12 ÷ 4) = ?
First numerator × (common denominator ÷ first denominator) = first new numerator
Multiply the first numerator by the same number its denominator was multiplied by.
First new numerator = 9
Step 3 · Find second new numerator
1 × (12 ÷ 3) = ?
Second numerator × (common denominator ÷ second denominator) = second new numerator
Multiply the second numerator by the same number its denominator was multiplied by.
Second new numerator = 4
Step 4 · Find numerator of the difference
9
12
−
4
12
=
?
12
Subtract the new numerators; the denominator stays
Same denominator now: subtract the numerators and keep the denominator.
Numerator of the difference = 9 − 4
Numerator of the difference = 5
Check
Put the numbers back in. Both sides should match.
4 and 3 both go into 12 ✓
3 × (12 ÷ 4) = 9 ✓
1 × (12 ÷ 3) = 4 ✓
9 − 4 = 5 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Refresh
Related lessons
Add and subtract fractions with unlike denominators
Main lesson
Add mixed numbers
Use this for “Mia used 3 3/4 cups of flour and Leo 2 5/6 cups. How much in all?”
Subtract mixed numbers
Use this for “Find the value of 4 1/3 − 1 5/8.”
Line plots with fractions
Use this for “The line plot shows beakers holding 1/8, 1/4, 3/8 or 1/2 liter.”
Estimate sums of fractions
Use this for “Is the sum more or less than 1?” before adding.