K-5 friendly lesson

One small step at a time.Read the idea, try the activity, and celebrate each win as you go.

Divide whole numbers by unit fractions

When you divide a whole number by a fraction, you're asking: 'How many pieces of this fraction can I fit into the whole?' The answer might surprise you—it gets bigger! 😮

Do this: Read the concept below, then try the quiz or activity.

Lesson 100 of 216

Concept

Dividing a whole number by a unit fraction is asking a simple question: "How many of these fractional pieces fit into the whole item(s)?"

Understanding the Question

Problem: 4 ÷ 1/3
*   This does NOT mean "split 4 into 3 parts."
*   It DOES mean: "How many 1/3-sized pieces can you get from 4 wholes?"

Visualizing the Answer

1.  Imagine you have 4 whole pizzas.
2.  You slice each pizza into thirds (1/3s).
3.  How many slices do you have in total?
    *   Pizza 1 gives you 3 slices.
    *   Pizza 2 gives you 3 slices.
    *   Pizza 3 gives you 3 slices.
    *   Pizza 4 gives you 3 slices.
    *   Total slices = 4 x 3 = 12.

So, 4 ÷ 1/3 = 12.

The "Keep, Change, Flip" Method This is the famous shortcut for dividing fractions:

1. Keep the first number (the whole number). 2. Change the division sign to a multiplication sign. 3. Flip the second number (the fraction). This is called finding the reciprocal.

Example: 6 ÷ 1/4

1. Keep the 6. (Write it as 6/1) 2. Change ÷ to x. 3. Flip 1/4 to become 4/1.

*   New problem: 6/1 x 4/1
*   Multiply straight across: 6 x 4 = 24, and 1 x 1 = 1.
*   Answer: 24/1 = 24.

Does this make sense? Yes! If you have 6 candy bars and cut each one into fourths, you will have 24 pieces.

Key Idea: Dividing by a fraction is the same as multiplying by its reciprocal. This is why dividing by a small fraction gives you a big answer! You are seeing how many small pieces fit into a big item.

Try it

Practice dividing by unit fractions!

Conceptual Questions: 1. How many 1/2-sized pieces are in 1 whole? 2. How many 1/4-sized pieces are in 1 whole? 3. How many 1/3-sized pieces are in 2 wholes?

Use "Keep, Change, Flip": 4. 5 ÷ 1/2 = ? 5. 3 ÷ 1/4 = ? 6. 7 ÷ 1/3 = ? 7. 10 ÷ 1/5 = ?

Word Problems: 8. A 5-mile race has water stops every 1/2 mile. How many water stops are there in total? 9. You have 3 large candy bars. You cut them into pieces that are each 1/4 of a bar. How many pieces do you have? 10. A carpenter has a board that is 8 feet long. He needs to cut it into sections that are 1/3 of a foot long. How many sections can he cut?

Challenge Problems: 11. 12 ÷ 1/6 = ? 12. If 15 ÷ 1/x = 45, what is x? 13. Which is greater: 10 ÷ 1/2 or 10 x 2? Why?

Complete & Continue →