SME
Grade 4 Math · Problem type
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?”
Diagram
7 1/5 − 3 4/5 = 3 2/5.
Jump back 3 wholes, then back 4/5.
This is an example. Type your own values to start a new problem.
First numerator
Denominator
−
Second numerator
Denominator
=
Fraction part of the answer
Denominator
First, as a fraction: numerator
worked out (not typed)
Second, as a fraction: numerator
worked out (not typed)
Numerator of the difference
worked out (not typed)
Formulas
7
wholes
and
1
5
=
36
5
First wholes × denominator + first numerator = first, as a fraction: numerator
3
wholes
and
4
5
=
19
5
Second wholes × denominator + second numerator = second, as a fraction: numerator
36
5
−
19
5
=
17
5
Subtract the numerators; the denominator stays
full
wholes
in
17
5
:
3
Full wholes in the answer = wholes in the answer
17
5
=
3
2
5
Numerator − wholes × denominator = fraction part
Assumptions
•
Write each mixed number as a fraction: 3 4/5 is 3 × 5 + 4 = 19 fifths.
•
Subtract the numerators. The denominator stays. A whole number like 2 is 2 wholes and 0/4.
•
Write the answer as wholes and a fraction again.
Step-by-step
WE KNOW
Denominator: 5
First wholes: 7
First numerator: 1
Second wholes: 3
Second numerator: 4
FIND
first, as a fraction: numerator, second, as a fraction: numerator, numerator of the difference, wholes in the answer, fraction part of the answer
Step 1 · Find first, as a fraction: numerator
7
wholes
and
1
5
=
?
5
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 = 7 × 5 + 1
7 × 5 = 35
35
+
1
=
36,
so
36
5
First, as a fraction: numerator = 36
Step 2 · Find second, as a fraction: numerator
3
wholes
and
4
5
=
?
5
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 = 3 × 5 + 4
3 × 5 = 15
15
+
4
=
19,
so
19
5
Second, as a fraction: numerator = 19
Step 3 · Find numerator of the difference
36
5
−
19
5
=
?
5
Subtract the numerators; the denominator stays
Subtract the numerators. The parts are the same size.
Numerator of the difference = 36 − 19
2
16
3
6
−
1
9
1
7
Numerator of the difference = 17
Step 4 · Find wholes in the answer
full
wholes
in
17
5
:
?
Full wholes in the answer = wholes in the answer
Every full set of parts makes 1 whole. Find how many full sets fit.
3 × 5 = 15: 3 wholes
Wholes in the answer = 3
Step 5 · Find fraction part of the answer
17
5
=
3
?
5
Numerator − wholes × denominator = fraction part
Take away the parts that make wholes. The rest is the fraction part.
Fraction part of the answer = 17 − 3 × 5
3 × 5 = 15
17 − 15 = 2
Fraction
part
of
the
answer
=
2
(
17
5
=
3
2
5
)
Check
Put the numbers back in. Both sides should match.
7 × 5 + 1 = 36 ✓
3 × 5 + 4 = 19 ✓
36 − 19 = 17 ✓
full
wholes
in
17
5
:
3
✓
3 × 5 + 2 = 17 ✓
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