Lesson 9: Divide Whole Numbers by Fractions6.NOS.1

I can…

I can explain what dividing a whole number by a fraction means — how many pieces fit, or how much is in one whole — find the quotient with a model or by multiplying by the reciprocal, and check it by multiplying.

Key words

• Divide Whole Numbers by Fractions — Find how many fractional groups fit in a whole number by multiplying by the reciprocal.
• Whole Number — A counting number with no fraction or decimal, like 0, 1, 2, 3.
• Fraction — A number that shows part of a whole, like 3/4.
• Reciprocal — A fraction turned upside down.
• Keep, Change, Flip — A shortcut for dividing fractions: keep the first number, change ÷ to ×, flip the second. It works because dividing by a fraction gives the same answer as multiplying by its reciprocal.
• Quotient — The answer when you divide.

Steps

1. Agent Park has 4 pounds of powder and each bag holds 1/2 pound. I want 4 ÷ 1/2.
2. Each pound fills 2 half-pound bags, so 4 pounds fill 4 × 2 = 8 bags.
3. That is the same as multiplying by the reciprocal of 1/2: 4 × 2/1 = 8. Dividing by 1/2 doubles the count, because every whole holds 2 halves.
4. Check by multiplying: 8 bags × 1/2 pound = 4 pounds. So 4 ÷ 1/2 = 8. He can fill 8 bags.

Try it

What is 7 ÷ 1/2? (Think: how many half-cup scoops are in 7 cups of rice?)

Check your answer

14

7 ÷ 1/2 = 7 × 2/1 = 14. There are 14 halves in 7 wholes. Check: 14 × 1/2 = 7.

Sentence starter

I know ___ because ___.

Goal: I can explain why multiplying by the reciprocal works, using the words fraction, reciprocal, quotient, and Keep, Change, Flip.