SME
Grade 5 Math · Fractions
Multiply fractions and mixed numbers
Use this for “What is 2/3 of 3/4?”
Diagram
2/3 of the columns and 3/4 of the rows overlap in 6 of the 12 small pieces: 6/12.
The product is 6/12.
This is an example. Type your own values to start a new problem.
First numerator
First denominator
×
Second numerator
Second denominator
=
Product numerator
Product denominator
Formulas
2 × 3 = 6
First numerator × second numerator = product numerator
3 × 4 = 12
First denominator × second denominator = product denominator
Assumptions
•
A fraction of a fraction: multiply the numerators and multiply the denominators.
•
The square shows why: columns for one fraction, rows for the other, and the overlap.
•
A fraction can be more than 1 (10/3): the picture adds whole squares. Denominators 2 to 12.
Step-by-step
WE KNOW
First numerator: 2
First denominator: 3
Second numerator: 3
Second denominator: 4
FIND
product numerator, product denominator
Step 1 · Find product numerator
2 × 3 = ?
First numerator × second numerator = product numerator
Multiply the numerators: the shaded columns times the shaded rows.
Product numerator = 6
Step 2 · Find product denominator
3 × 4 = ?
First denominator × second denominator = product denominator
Multiply the denominators: all the columns times all the rows.
Product
denominator
=
12
(
6
12
=
1
2
)
Check
Put the numbers back in. Both sides should match.
2 × 3 = 6 ✓
2
3
×
3
4
=
6
12
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.