Today’s Mathematics
We will use models to multiply fractions and mixed numbers.
Do Now
Review what you already know.
- Simplify 618.
- Write 12 with denominator 6.
- Write 2 14 as an improper fraction.
- Find 7 × 8.
A bottle is half full.
You drink two-thirds of the water in it. How much of the whole bottle do you drink?
Draw a strip. Mark the half-full amount, split that amount into three equal parts, then shade the two parts you drink.
Why is the amount you drink less than half of the whole bottle?
Shade, count, and look for a pattern.
Work with a partner. Each rectangle is one whole. Shade the first fraction across the columns. Mark the second fraction across the rows using a different pattern. Count the cells marked both ways.
12 × 23
Record total cells, overlapping cells, and the simplest product.
34 × 23
Record total cells, overlapping cells, and the simplest product.
23 × 35
Record total cells, overlapping cells, and the simplest product.
What do you notice about the numerators and denominators? Use your models to explain a rule for multiplying fractions.
What we can conclude
“Of” can mean multiply. Multiply the numerators and multiply the denominators. Simplify the product. For mixed numbers, first write improper fractions.
One and one-half is three halves. Two-thirds of three halves is one whole.
Divide out common factors before multiplying if helpful. A square means multiply a fraction by itself: (25)² = 425.
Must Do
Show work. Write each product in simplest form.
- 35 × 14
- 49 × 38
- 2 23 × 34
- 1 12 × 2 25
5. A rectangular mat is 2½ feet long and 1⅓ feet wide. Find its area.
6. A student says multiplying always makes a number larger. Use a fraction example to explain why this is not always true.
Put your practice to work.
Why did the turkey volunteer to be the drummer in the popular bird band?
Complete the puzzle on pages 4–5 of your lesson PDF. Multiply, simplify, and match each result to a letter in the answer bank. Read the decoder across both rows.
Open Puzzle PracticeKeep working
Your teacher may select problems for follow-up practice or extended reasoning.
Additional Practice · PDFAoPS Problem Set · PDF