SME
Grade 4 Math · Problem type
Add mixed numbers
Use this for “Find the value of 3 2/5 + 1 4/5.”
Diagram
2 1/6 + 1 5/6 = 4.
Jump on 1 whole, then on 5/6.
This is an example. Type your own values to start a new problem.
First numerator
Denominator
+
Second numerator
Denominator
=
First, as a fraction: numerator
worked out (not typed)
Second, as a fraction: numerator
worked out (not typed)
Numerator of the sum
worked out (not typed)
Formulas
2
wholes
and
1
6
=
13
6
First wholes × denominator + first numerator = first, as a fraction: numerator
1
whole
and
5
6
=
11
6
Second wholes × denominator + second numerator = second, as a fraction: numerator
13
6
+
11
6
=
24
6
Add the numerators; the denominator stays
full
wholes
in
24
6
:
4
Full wholes in the answer = wholes in the answer
24
6
=
4
Numerator − wholes × denominator = fraction part
Assumptions
•
Write each mixed number as a fraction: 3 4/5 is 3 × 5 + 4 = 19 fifths.
•
Add the numerators. The denominator stays.
•
Write the answer as wholes and a fraction again.
Step-by-step
WE KNOW
Denominator: 6
First wholes: 2
First numerator: 1
Second wholes: 1
Second numerator: 5
FIND
first, as a fraction: numerator, second, as a fraction: numerator, numerator of the sum, wholes in the answer, fraction part of the answer
Step 1 · Find first, as a fraction: numerator
2
wholes
and
1
6
=
?
6
First wholes × denominator + first numerator = first, as a fraction: numerator
Each whole is that many parts. Multiply, then add the extra parts.
First, as a fraction: numerator = 2 × 6 + 1
2 × 6 = 12
12
+
1
=
13,
so
13
6
First, as a fraction: numerator = 13
Step 2 · Find second, as a fraction: numerator
1
whole
and
5
6
=
?
6
Second wholes × denominator + second numerator = second, as a fraction: numerator
Each whole is that many parts. Multiply, then add the extra parts.
Second, as a fraction: numerator = 1 × 6 + 5
1 × 6 = 6
6
+
5
=
11,
so
11
6
Second, as a fraction: numerator = 11
Step 3 · Find numerator of the sum
13
6
+
11
6
=
?
6
Add the numerators; the denominator stays
Add the numerators. The parts are the same size.
Numerator of the sum = 13 + 11
Numerator of the sum = 24
Step 4 · Find wholes in the answer
full
wholes
in
24
6
:
?
Full wholes in the answer = wholes in the answer
Every full set of parts makes 1 whole. Find how many full sets fit.
4 × 6 = 24: 4 wholes
Wholes in the answer = 4
Step 5 · Find fraction part of the answer
24
6
=
4
?
6
Numerator − wholes × denominator = fraction part
Take away the parts that make wholes. The rest is the fraction part.
Fraction part of the answer = 24 − 4 × 6
4 × 6 = 24
24 − 24 = 0
Fraction
part
of
the
answer
=
0
(
24
6
=
4)
Check
Put the numbers back in. Both sides should match.
2 × 6 + 1 = 13 ✓
1 × 6 + 5 = 11 ✓
13 + 11 = 24 ✓
full
wholes
in
24
6
:
4
✓
4 × 6 + 0 = 24 ✓
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