SME
Grade 4 Math · Fractions
Multiply a fraction by a whole number
Use this for “Each runner drinks 2/3 of a liter. How much do 5 runners drink?”
Diagram
10/3: 10 jumps of 1/3 from 0.
That is 3 wholes and 1/3 more.
This is an example. Type your own values to start a new problem.
Whole number
×
Numerator
Denominator
=
Numerator of the product
Denominator
Wholes in the product
worked out (not typed)
Numerator of the fraction part
worked out (not typed)
Formulas
5
×
2
3
=
10
3
Whole number × numerator = numerator of the product; the denominator stays
10
3
=
3
1
3
Numerator of the product = wholes × denominator + numerator of the fraction part
full
wholes
in
10
3
:
3
Full wholes in the product = wholes in the product
Assumptions
•
A whole number times a fraction is that many copies of the fraction: 5 × 2/3 is 2/3 five times.
•
Multiply the whole number by the numerator. The denominator stays: the parts are the same size.
•
A product past 1 can be written as wholes and parts: 10/3 = 3 wholes and 1/3.
•
Any fraction, even past 1 (3 × 4/3). Whole numbers to 10; denominators 2, 3, 4, 5, 6, 8, 10, 12.
Step-by-step
WE KNOW
Whole number: 5
Numerator: 2
Denominator: 3
FIND
numerator of the product, wholes in the product, numerator of the fraction part
Step 1 · Find numerator of the product
5
×
2
3
=
?
3
Whole number × numerator = numerator of the product; the denominator stays
Add the fraction that many times, or multiply the whole number by the numerator.
Numerator of the product = 5 × 2
2
3
+
2
3
+
2
3
+
2
3
+
2
3
=
10
3
Numerator of the product = 10
Step 2 · Find wholes in the product
full
wholes
in
10
3
:
?
Full wholes in the product = wholes in the product
Every full set of parts makes 1 whole. Divide by the denominator.
10 ÷ 3 = 3, remainder 1: 3 wholes
Wholes in the product = 3
Step 3 · Find numerator of the fraction part
10
3
=
3
?
3
Numerator of the product = wholes × denominator + numerator of the fraction part
Take away the parts that make wholes. The rest is the fraction part.
Numerator of the fraction part = 10 − 3 × 3
3 × 3 = 9
10 − 9 = 1
Numerator
of
the
fraction
part
=
1
(
10
3
=
3
wholes
and
1
3
)
Check
Put the numbers back in. Both sides should match.
5 × 2 = 10 ✓
3 × 3 + 1 = 10 ✓
full
wholes
in
10
3
:
3
✓
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Fractions and decimals: tenths and hundredths
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