Cogito
Grade 7 Math · Chapter 2 · Lesson 4
Unit Rates with Fractions
Rates when neither quantity is whole.
10 problems · about 19 minutes · 7.RP.A.1
What this lesson teaches
The child computes a unit rate where both quantities are fractions.
- A unit rate is still the first quantity divided by the second.
- Dividing by a fraction means multiplying by its reciprocal.
- Check the size: dividing by a number below one makes the answer larger.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — The Graph of a Proportional Relationship: Proportional graph through (4, 24). What is k?
Answer 6
Why k = 6.
Review — Telling Proportional from Not: y = 3x + 7. What is y when x = 6?
Answer 25
Why 25.
Review — The Constant of Proportionality: 5 pairs with 35. What is k?
Answer 7
Why 7.
Warm Up
Straightforward practice. Get the method working first.
3 problems⅖ mile in ⅕ hour. Miles per hour?
Answer 2
Why 2 mph.
¼ mile in ⅛ hour. Miles per hour?
Answer 2
Why Dividing by ⅛ multiplies by 8.
½ litre in ¼ minute. Litres per minute?
Answer 2
Why × 4 then halve.
Build It Up
The same ideas with more to keep track of.
2 problems3 miles in ½ hour. Miles per hour?
Answer 6
Why Dividing by ½ doubles.
¾ kg for ¼ of a box. Kilograms for a whole box?
Answer 3
Why × 4.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Walk: ½ mile in ¼ hour. How many miles per hour?
Answer 2
Why 2 mph.
The Recipe: ⅔ cup for ⅓ of a batch. How many cups for a whole batch?
Answer 2
Why 2 cups.