Cogito
Grade 6 Math · Chapter 3 · Lesson 1
Dividing a Fraction by a Fraction
How many of these fit into that.
10 problems · about 18 minutes · 6.NS.A.1
What this lesson teaches
The child divides a fraction by a fraction and explains the quotient in context.
- Dividing by a fraction asks how many fit.
- Multiplying by the reciprocal is the shortcut.
- The reciprocal counts how many pieces are in one whole.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Converting Units with Rates: 5 km in metres?
Answer 5000
Why 5000 m.
Review — Finding the Whole from a Percent: 25% of a number is 11. What is the number?
Answer 44
Why 44.
Warm Up
Straightforward practice. Get the method working first.
4 problems3/4 ÷ 1/12 = ?
Answer 9
Why 9.
Why does dividing by a fraction mean multiplying by its reciprocal?
Answer Counting how many fit means multiplying by how many are in one whole.
Why The reciprocal counts the pieces in one whole.
1/2 ÷ 1/6 = ?
Answer 3
Why 1/2 is 3/6.
3/5 ÷ 1/10 = ?
Answer 6
Why 3/5 is 6/10.
Build It Up
The same ideas with more to keep track of.
2 problems2/3 ÷ 1/3 = ?
Answer 2
Why Two thirds hold two thirds.
What is the reciprocal of 1/5?
Answer 5
Why Turn it over.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Ribbon: 3/4 metre cut into pieces of 1/8 metre. How many pieces?
Answer 6 pieces
Why 6 pieces.
The Juice: 2/3 litre poured into 1/12 litre cups. How many cups?
Answer 8 cups
Why 8 cups.