SME
Grade 5 Math · Problem type
Multiply fractions and whole numbers
Use this for “Sam walked 3/4 of a 6 mile path. How far did he walk?”
Diagram
8 in 4 equal parts of 2: 3 parts make 6.
This is an example. Type your own values to start a new problem.
Numerator
Denominator
×
Whole number
=
Product
One part
worked out (not typed)
The rest
worked out (not typed)
Formulas
8 ÷ 4 = 2
Whole number ÷ denominator = one part
3 × 2 = 6
Numerator × one part = product
8 − 6 = 2
Whole number − product = the rest
Assumptions
•
3/4 of 8: cut 8 into 4 equal parts, then take 3 of the parts.
•
One part is the whole number ÷ the denominator. Then multiply by the numerator.
•
Whole numbers to 60. A part can be a fraction: 7 ÷ 4 = 1 3/4, so 3/4 of 7 = 21/4 = 5 1/4.
Step-by-step
WE KNOW
Numerator: 3
Denominator: 4
Whole number: 8
FIND
one part, product, the rest
Step 1 · Find one part
8 ÷ 4 = ?
Whole number ÷ denominator = one part
Cut the whole number into that many equal parts.
8
÷
4
=
8
4
=
2
One part = 2
Step 2 · Find product
3 × 2 = ?
Numerator × one part = product
Take that many of the parts.
Product = 6
Step 3 · Find the rest
8 − 6 = ?
Whole number − product = the rest
The parts not taken.
The rest = 2
Check
Put the numbers back in. Both sides should match.
2 × 4 = 8 ✓
3 × 2 = 6 ✓
8 − 6 = 2 ✓
← Previous lesson
Multiply fractions and mixed numbers
Next lesson →
Area of a rectangle with fractional sides
Topic check
See what you know: 5 questions on this topic
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