Lesson 11: Fraction Division Problem Solving6.NOS.1

I can…

I can solve real-world problems by deciding whether the question asks how many groups fit or how much is in one group, writing a fraction division equation, and checking the solution by multiplying.

Key words

• Fraction Division Problem Solving — Use fraction division to find an unknown number of groups or the size of each group.
• Model — A picture or math way to show a problem so you can solve it.
• Equation — A math sentence with an equal sign showing both sides are the same.
• Solution — A number that makes the equation or inequality true.
• Reasonableness — Checking if your answer makes sense.
• Inverse operations — Two math actions that undo each other, like × and ÷.

Steps

1. Agent Torres has 2/3 gallon of dust and each test uses 1/6 gallon. I ask: how many tests fit?
2. The total 2/3 is the dividend. The size of each test 1/6 is the divisor. My equation is 2/3 ÷ 1/6.
3. In sixths, 2/3 = 4/6, and 4 sixths ÷ 1 sixth = 4. Multiplying by the reciprocal gives the same answer: 2/3 × 6/1 = 12/3 = 4.
4. So she can run 4 tests. I check by multiplying back: 4 × 1/6 = 4/6 = 2/3. It matches the total, so the answer is reasonable.

Try it

A garden hose is 5/6 of a yard long. Each piece cut from it is 5/12 of a yard. How many pieces can be cut?

Check your answer

2

5/6 ÷ 5/12 = 5/6 × 12/5 = 60/30 = 2. Two pieces can be cut. Check by multiplying: 2 × 5/12 = 10/12 = 5/6.

Sentence starter

I know ___ because ___.

Goal: I can explain my reasoning using the words model, equation, solution, and reasonableness.