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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Divide mixed numbers
Convert mixed quantities to improper fractions, divide them exactly and interpret the resulting quotient.
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Convert both mixed numbers to improper fractions before taking any reciprocal. Multiply the first fraction by the reciprocal of the second, simplify and check with the original divisor.
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What this activity builds
Combine mixed-number conversion with correct divisor inversion while preserving the original quantities.
Worked example
Find 2 1/4 ÷ 1 1/2.
(9/4) ÷ (3/2) = (9/4) × (2/3) = 3/2 = 1 1/2.
The quantities are nine-fourths and three-halves. A reciprocal applies to the entire divisor 3/2, so it becomes 2/3. The quotient times 1 1/2 equals the original 2 1/4.
Teaching notes
Make the practice count
- Put a checkpoint between conversion and division so errors can be located.
- Estimate how many divisor-sized groups should fit before using the algorithm.
- Write a mixed final answer only after obtaining and simplifying an exact fraction.
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