Fractions
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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Multiply mixed numbers
Convert mixed numbers into single fractions before multiplying and expressing the product clearly.
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Convert each mixed number to an improper fraction. Cancel common factors when useful, multiply and simplify. Convert an improper result to a mixed number when that form helps interpret the quantity.
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What this activity builds
Preserve each mixed number as one quantity rather than multiplying its whole and fractional parts separately.
Worked example
Find 1 1/2 × 2 2/3.
(3/2) × (8/3) = 4.
One and one-half equals 3/2, while two and two-thirds equals 8/3. Their product is 24/6, or 4. Converting first ensures that every part of each mixed number is included.
Teaching notes
Make the practice count
- Check both mixed-to-improper conversions before multiplication begins.
- Estimate using nearby whole numbers to catch a badly scaled result.
- Use an area or distributive explanation if the conversion feels disconnected from the original amounts.
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