Fractions
Find the least common multiple
Find the smallest positive multiple shared by two numbers and use it to plan common-denominator work.
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Add fractions with common denominators
Rename fractions as equivalent amounts with a common denominator before finding and simplifying their sum.
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Find a common denominator for the two fractions. Multiply each numerator and denominator by the same factor, add the new numerators and simplify the result.
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What this activity builds
Choose a shared fractional unit, preserve both operand values and add the resulting numerators.
Worked example
Find 1/3 + 3/4.
4/12 + 9/12 = 13/12 = 1 1/12.
Twelve is a common multiple of 3 and 4. Renaming thirds as twelfths multiplies both parts by 4; renaming fourths as twelfths multiplies both parts by 3. The equivalent fractions can then be added.
Teaching notes
Make the practice count
- Write the scale factor beside each fraction to make value preservation visible.
- A least common denominator keeps the numbers smaller, but another valid common denominator can still give the correct value.
- Use the worked solution to locate whether an error occurred during renaming, addition or simplification.
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