Add Fractions with Different Denominators
Use equal-sized parts before adding fractions of the same whole.
Supplied materials
- Paper and a pencil, or say your answers aloud.
Learn the idea
Fractions can be added by counting parts of the same size. With different denominators, first rename them as equivalent fractions with a shared denominator. Adding the denominators would change the size of the parts and would not count the combined amount correctly.
For 1/2 + 1/4, split the half into quarters: 1/2 = 2/4. Then 2/4 + 1/4 = 3/4. Both fractions must refer to the same-sized whole; half of one small strip and a quarter of a larger strip cannot use this model unchanged.
- Draw a strip split into four equal sections.
- Show one half as two of the quarters, then add one more quarter.
- Write 1/2 + 1/4 = 2/4 + 1/4 = 3/4.
- For the check, use sixths to rename one half before adding one sixth.
See the method in action
For matching strips, 1/2 + 1/4 = 2/4 + 1/4 = 3/4. Three selected quarter-parts make three quarters of one whole.
Check your reasoning
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See the answer and explanation
2/3
One half equals 3/6. Adding 1/6 gives 4/6, which equals 2/3. The denominator stays six while counting sixths; reducing both counts by two gives 2/3.
Take it further
Find 1/2 − 1/6 using the same six-part model. 3/6 − 1/6 = 2/6 = 1/3. Check that the subtraction result is less than one half.
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