Neft Teacher · Learn It

Unit 6 · Standard 6.NOS.1

Divide Whole Numbers by Fractions

Lesson 6-9 · Learn It — how the math works

Why we're learning this

Agent Park has 4 pounds of evidence powder. Each testing bag holds exactly 1/2 pound. He needs to prepare as many testing bags as possible before the lab deadline. How many bags can he fill?

✱ Math Workbench

Learn It

How do I divide a whole number by a fraction?

Dividing a whole number by a fraction asks how many of those pieces fit, or how much is in one whole. 4 ÷ 1/2 counts halves: every whole holds 2 halves, so the answer is 4 × 2 = 8. That is why the shortcut called Keep, Change, Flip works — dividing by a fraction gives the same answer as multiplying by its reciprocal. Check by multiplying: 8 × 1/2 = 4.

Picture itSee what the math looks like before you read about it

A STEM summer camp has a 3-hour afternoon session. Campers choose from afternoon activities that are each 45 minutes long.
Where you see this in real lifeA STEM summer camp has a 3-hour afternoon session. Campers choose from afternoon activities that are each 45 minutes long.

Watch me solve itI do — read one step at a time

The problem looks like this
A bar model. 4 whole bars, each labelled 1, sit above a bar of exactly the same length cut into 8 equal pieces, each one half of a whole. It shows that 8 pieces of size 1/2 fit inside 4 wholes, so 4 divided by 1/2 is 8.4 ÷ 1/2 = 84 wholes1111cut into pieces of 1/2 pound1/21/21/21/21/21/21/21/2Count them: 8 pieces of 1/2 fit inside 4 wholes.
  1. Agent Park has 4 pounds of powder and each bag holds 1/2 pound. I want 4 ÷ 1/2.4 ÷ 1/2
  2. Each pound fills 2 half-pound bags, so 4 pounds fill 4 × 2 = 8 bags.4 × 2 = 8
  3. That is the same as multiplying by the of 1/2: 4 × 2/1 = 8. Dividing by 1/2 doubles the count, because every holds 2 halves.4 × 2/1 = 8
  4. Check by multiplying: 8 bags × 1/2 pound = 4 pounds. So 4 ÷ 1/2 = 8. He can fill 8 bags.4 ÷ 1/2 = 8

Watch out — mistakes students make here

  • 1/27 is 1/3 ÷ 9 — the dividend and divisor are switched. Ask how many 1/3s fit in 9.
  • 3 is 9 ÷ 3 — that divides by 3 instead of by 1/3. Each whole holds 3 thirds, so 9 wholes hold 9 × 3 = 27.
  • 12 is 9 + 3 — that adds instead of multiplying. Each whole holds 3 thirds, so multiply the 9 wholes by 3.

Try it with meWe do — you answer first, then check

Same steps, new numbers.

  1. Let's try 3 ÷ 1/4 together. How many 1/4s fit in 3?3 ÷ 1/4
    Check this step
    Each holds 4 fourths.
  2. So 3 hold 3 × 4 = 12 fourths — the same as 3 × 4/1, multiplying by the .3 × 4 = 12
  3. Check by multiplying: 12 × 1/4 = 12/4 = 3. So 3 ÷ 1/4 = 12.12 × 1/4 = 12/4 = 3

On your ownYou do — solve this one by yourself

Before you start, remember:

  • Now use the number line to show how many 1/4-jumps fit into 3 — a new problem, not the 4 ÷ 1/2 we just watched.
  • Then try one that asks how much is in ONE : 6 cups of rice fill 3/4 of a pot. 6 ÷ 3/4 = 6 × 4/3 = 8 cups fill the whole pot, and 3/4 × 8 = 6 checks it.

Solve: What is 6 ÷ 2/3?

My answer

Stuck? Open one hint at a time.

Hint 1

The divisor is 2/3 — not a unit fraction — so the flip matters even more here.

Hint 2

Keep 6, change ÷ to ×, and flip the whole fraction 2/3 (both numbers trade places).

Hint 3

2/3 flips to 3/2, giving 6 × 3/2. Multiply, then simplify the result before choosing.

Check my answer
✅ Answer: 9
6 ÷ 2/3 = 6 × 3/2 = 18/2 = 9. Keep 6, change ÷ to ×, flip 2/3 to 3/2.

Turn & TalkSay it out loud with a partner

Agent Park has 4 pounds of evidence powder and fills bags that hold 1/2 pound each. How many bags can he fill, and how do you know?

Try starting with:

  • 1/2 pound fits into 4 pounds a total of ___ times.1/2 libra cabe en 4 libras un total de ___ veces.
  • I know because each pound holds ___ bags, so ___.Lo sé porque cada libra contiene ___ bolsas, así que ___.
Use these wordswhole numberfractionquotient