Multiplying and Dividing Mixed Numbers
Grade 8 math lesson on multiplying and dividing mixed numbers by converting them to improper fractions. Students learn to change mixed numbers to improper fractions, multiply or divide, then convert back to a mixed number and simplify.
Key Concepts
New Concept To multiply or divide mixed numbers, we first write each mixed number as an improper fraction. Here is how we convert: $$3\frac{2}{5} = \frac{5 \times 3 + 2}{5} = \frac{17}{5}$$ What’s next Soon, we’ll walk through worked examples of both multiplication and division, and then apply this skill to solve a construction based word problem.
Common Questions
How do you multiply mixed numbers?
Convert each mixed number to an improper fraction first. Multiply the numerators together and the denominators together. Simplify and convert back to a mixed number if needed. For example, 2 and 1/2 x 1 and 1/3 = 5/2 x 4/3 = 20/6 = 3 and 1/3.
How do you convert a mixed number to an improper fraction?
Multiply the whole number by the denominator, then add the numerator. This gives the new numerator; the denominator stays the same. For example, 3 and 2/5 = (3 x 5 + 2)/5 = 17/5.
How do you divide mixed numbers?
Convert both mixed numbers to improper fractions, then multiply the first by the reciprocal of the second (flip the second fraction). Simplify and convert the result back to a mixed number.
Why do we convert mixed numbers to improper fractions before multiplying?
The fraction multiplication algorithm only works with pure fractions. Converting first ensures you can apply the numerator-times-numerator, denominator-times-denominator method correctly.