5th Grade Multiplying Fractions and Mixed Numbers Lesson (Free PDF)
To multiply fractions, multiply the numerators, multiply the denominators, and simplify. To multiply a fraction by a whole number, write the whole number over 1. For mixed numbers, first change them to improper fractions. An area model shows why: the overlap of the shaded parts is the product.
Grade 5 · Common Core State Standards: 5.NF.B.4a, 5.NF.B.6
- A fraction of a number means fraction times that number.
- Fraction times fraction: multiply numerators, multiply denominators, then simplify.
- Write a whole number as a fraction over 1 before multiplying.
- Change mixed numbers to improper fractions, multiply, then write the answer as a mixed number.
- An area model shows the product as the overlap of shaded parts.
How do you multiply a fraction by a whole number?
Finding a fraction of a number means multiplying. To find \(\frac{2}{3}\) of 12, split 12 into 3 equal parts. Each part is 4. Take 2 of the parts: \(\frac{2}{3} \times 12 = 8\).
How do you multiply two fractions?
Use an area model. Draw a square for 1 whole. Cut the width into the parts of the first fraction and the height into the parts of the second fraction. Shade both. The overlap shows the product. Here \(\frac{3}{4} \times \frac{2}{3}\) has an overlap of 6 squares out of 12, so the product is \(\frac{6}{12} = \frac{1}{2}\).
How do you multiply mixed numbers?
One way is to split each mixed number into wholes and a fraction. For \(1\frac{1}{2} \times 2\frac{1}{3}\), the rectangle has four parts with areas \(2\), \(1\), \(\frac{1}{3}\), and \(\frac{1}{6}\). The total is \(3\frac{1}{2}\).
What are the steps for multiplying mixed numbers?
- Estimate the product with whole numbers.
- Write each mixed number as an improper fraction.
- Multiply the numerators and multiply the denominators.
- Simplify and write the answer as a mixed number.
- Compare with the estimate.
Worked example: Find \(2\frac{1}{3} \times 1\frac{1}{2}\). The estimate is \(2 \times 2 = 4\), so the answer should be a little less than 4. Then \(\frac{7}{3} \times \frac{3}{2} = \frac{21}{6} = 3\frac{1}{2}\).
When you multiply by a fraction less than 1, the product is smaller than the other factor. When you multiply by a number greater than 1, the product is larger.
Questions about multiplying fractions and mixed numbers
Why is a fraction times a fraction smaller than both factors?
You take a part of a part. For example, 1/2 of 1/3 is only 1/6. Each fraction less than 1 shrinks the amount, so the product is smaller than either factor.
Do I need a common denominator to multiply fractions?
No. Common denominators are needed to add or subtract. To multiply, just multiply the numerators and multiply the denominators.
How do I multiply a whole number by a fraction?
Write the whole number as a fraction over 1, then multiply across. For example, 5 times 3/4 is 5/1 times 3/4, which is 15/4, or 3 3/4.
How do I multiply mixed numbers?
Change each mixed number to an improper fraction, multiply the numerators and denominators, and simplify. Then write the result as a mixed number.
What does “of” mean in a fraction word problem?
The word “of” usually means multiply. Three fourths of 20 means 3/4 times 20, which is 15.
All Grade 5 chapters: Grade 5 math.
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