Cogito
Grade 4 Math · Chapter 5 · Lesson 7
Multiplying a Fraction by a Whole Number
Repeated copies of the same unit.
10 problems · about 16 minutes · 4.NF.B.4
What this lesson teaches
The child multiplies a fraction by a whole number and explains the result.
- Multiplying a fraction by a whole number makes copies of it.
- Only the top number is multiplied. The unit stays.
- Multiplying does not always make things bigger.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Mixed Numbers: 17/5 as a mixed number. What is the whole number part?
Answer 3
Why 3 wholes, with 2 fifths left: 3 2/5.
Review — Why 1/2 + 1/3 Is Not 2/5: 1/4 + 1/2, in quarters. What is the top number?
Answer 3
Why 1/4 + 2/4 = 3/4.
Warm Up
Straightforward practice. Get the method working first.
4 problems4 × 2/9. What is the top number of the answer?
Answer 8
Why 8/9.
Does multiplying always make a number bigger?
Answer No. 1/4 of 8 is only 2.
Why Multiplying by less than 1 makes the answer smaller.
5 × 1/6. What is the top number of the answer?
Answer 5
Why 5 copies of one sixth.
3 × 2/7. What is the top number of the answer?
Answer 6
Why 3 × 2 sevenths.
Build It Up
The same ideas with more to keep track of.
2 problems3 × 2/7. What is the bottom number of the answer?
Answer 7
Why Still sevenths.
What is 1/4 of 12?
Answer 3
Why 12 ÷ 4.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Recipe: A recipe needs 2/3 of a cup. Ana makes it 3 times. How many thirds in all?
Answer 6 thirds
Why 6/3, which is 2 whole cups.
The Walk: Leo walks 3/10 of a mile, 4 times. How many tenths in all?
Answer 12 tenths
Why 12/10 of a mile.