Fractions
Add mixed numbers
Combine whole-number and fractional parts, renaming fractional totals that make an additional whole.
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Convert mixed numbers and improper fractions
Rename quantities greater than one as a mixed number or a single improper fraction without changing their value.
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To form an improper fraction, multiply the whole part by the denominator and add the numerator. To form a mixed number, divide the numerator by the denominator and use the remainder as the fractional numerator. Simplify where possible.
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What this activity builds
Connect whole groups of fractional units with quotient-and-remainder reasoning in both conversion directions.
Worked example
Convert 3 2/7 to an improper fraction and 17/5 to a mixed number.
3 2/7 = 23/7; 17/5 = 3 2/5.
Three wholes contain 21 sevenths, so two more sevenths give 23/7. Seventeen fifths contain three complete groups of five fifths with two fifths left over.
Teaching notes
Make the practice count
- Show the whole groups in a model before introducing the conversion shortcut.
- Keep the original denominator through the quotient-and-remainder step.
- Convert the result back to its starting form as a check.
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