SME
Grade 5 Math · Fractions
Add and subtract fractions with unlike denominators
Use this for “Find the value of 1/2 + 1/3.”
Diagram
3/6 + 2/6 = 5/6
This is an example. Type your own values to start a new problem.
First numerator
First denominator
+
Second numerator
Second denominator
=
Numerator of the sum
Common denominator
First new numerator
worked out (not typed)
Second new numerator
worked out (not typed)
Formulas
2 and 3 both go into 6
The smallest number both denominators go into = common denominator
1 × (6 ÷ 2) = 3
First numerator × (common denominator ÷ first denominator) = first new numerator
1 × (6 ÷ 3) = 2
Second numerator × (common denominator ÷ second denominator) = second new numerator
3
6
+
2
6
=
5
6
Add the new numerators; the denominator stays
Assumptions
•
Fractions can only be added when the parts are the same size: give them a common denominator.
•
Use the smallest number both denominators go into. Rewrite each fraction over it, then add the numerators.
•
Each fraction is at most 1. Denominators 2, 3, 4, 5, 6, 8, 10 and 12.
Step-by-step
WE KNOW
First numerator: 1
First denominator: 2
Second numerator: 1
Second denominator: 3
FIND
common denominator, first new numerator, second new numerator, numerator of the sum
Step 1 · Find common denominator
2 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 3: 3, 6 → 6 is also a multiple of 2
Common denominator = 6
Step 2 · Find first new numerator
1 × (6 ÷ 2) = ?
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 = 3
Step 3 · Find second new numerator
1 × (6 ÷ 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 = 2
Step 4 · Find numerator of the sum
3
6
+
2
6
=
?
6
Add the new numerators; the denominator stays
Same denominator now: add the numerators and keep the denominator.
Numerator of the sum = 3 + 2
Numerator of the sum = 5
Check
Put the numbers back in. Both sides should match.
2 and 3 both go into 6 ✓
1 × (6 ÷ 2) = 3 ✓
1 × (6 ÷ 3) = 2 ✓
3 + 2 = 5 ✓
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Estimate products of decimals
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Subtract fractions with unlike denominators
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