SME
Grade 4 Math · Fractions
Add and subtract fractions with like denominators
Use this for “Add 3/4 + 2/4. Write the sum as a mixed number.”
Diagram
5/4: 5 jumps of 1/4 from 0.
That is 1 whole and 1/4 more.
This is an example. Type your own values to start a new problem.
First numerator
Denominator
+
Second numerator
Denominator
=
Numerator of the sum
Denominator
Wholes in the sum
worked out (not typed)
Numerator of the fraction part
worked out (not typed)
Formulas
3
4
+
2
4
=
5
4
Add the numerators; the denominator stays
5
4
=
1
1
4
Numerator of the sum = wholes × denominator + numerator of the fraction part
full
wholes
in
5
4
:
1
Full wholes in the sum = wholes in the sum
Assumptions
•
Like denominators mean the same-size parts: add the numerators, keep the denominator.
•
A sum bigger than 1 can be written as wholes and parts: 7/4 = 1 whole and 3/4.
•
Fractions can be more than 1 (9/8 + 3/8). Denominators 2, 3, 4, 5, 6, 8, 10 and 12.
Step-by-step
WE KNOW
Denominator: 4
First numerator: 3
Second numerator: 2
FIND
numerator of the sum, wholes in the sum, numerator of the fraction part
Step 1 · Find numerator of the sum
3
4
+
2
4
=
?
4
Add the numerators; the denominator stays
Add the numerators. The denominator stays: the parts are the same size.
Numerator of the sum = 3 + 2
Numerator of the sum = 5
Step 2 · Find wholes in the sum
full
wholes
in
5
4
:
?
Full wholes in the sum = wholes in the sum
Every full set of parts makes 1 whole. Find how many full sets fit in the sum.
1 × 4 = 4: 1 whole
Wholes in the sum = 1
Step 3 · Find numerator of the fraction part
5
4
=
1
?
4
Numerator of the sum = 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 = 5 − 1 × 4
1 × 4 = 4
5 − 4 = 1
Numerator
of
the
fraction
part
=
1
(
5
4
=
1
whole
and
1
4
)
Check
Put the numbers back in. Both sides should match.
3 + 2 = 5 ✓
1 × 4 + 1 = 5 ✓
full
wholes
in
5
4
:
1
✓
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Subtract fractions with like denominators
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More problem types
Subtract fractions with like denominators
Use this for “5/8 − 2/8 =” and other like denominators.
Fractions and mixed numbers
Use this for “Write 2 3/4 as a fraction,” or 11/4 as a mixed number.
Add mixed numbers
Use this for “Find the value of 3 2/5 + 1 4/5.”
Subtract mixed numbers
Use this for “A kite string is 7 1/5 meters. 3 4/5 meters are wound up. How much is let out?”
Interpret line plots in eighths of an inch
Use this to add up lengths in eighths of an inch from a line plot, and find the longest minus the shortest.
Interpret line plots in quarter inches
Use this for a line plot of straws measured to the quarter inch: the total length, and the longest minus the shortest.