SME
Grade 5 Math · Problem type
Subtract mixed numbers
Use this for “Find the value of 4 1/3 − 1 5/8.”
Diagram
4 8/24 − 1 15/24
This is an example. Type your own values to start a new problem.
First numerator
First denominator
−
Second numerator
Second denominator
=
2
17
24
Difference
Common denominator
worked out (not typed)
First new numerator
worked out (not typed)
Second new numerator
worked out (not typed)
Parts left
worked out (not typed)
Formulas
3 and 8 both go into 24
The smallest number both denominators go into = common denominator
1 × (24 ÷ 3) = 8
First numerator × (common denominator ÷ first denominator) = first new numerator
5 × (24 ÷ 8) = 15
Second numerator × (common denominator ÷ second denominator) = second new numerator
8
24
−
15
24
→
17
24
(rename
1
whole
as
24
24
first
if
needed)
Subtract the new numerators, renaming 1 whole when the first is smaller
4
−
1
(1
less
if
8
24
is
less
than
15
24
)
and
17
24
=
2
17
24
First whole number − second whole number (1 less if renamed) + parts left = difference
Assumptions
•
Give the fraction parts a common denominator: the smallest number both denominators go into.
•
Take away the parts, then the whole numbers. If the part to take away is bigger, rename 1 whole as parts first.
•
Whole numbers to 10; each fraction part is less than 1, with denominators 2 to 12. The first number is the bigger one.
Step-by-step
WE KNOW
First whole number: 4
First numerator: 1
First denominator: 3
Second whole number: 1
Second numerator: 5
Second denominator: 8
FIND
common denominator, first new numerator, second new numerator, parts left, difference
Step 1 · Find common denominator
3 and 8 both go into ?
The smallest number both denominators go into = common denominator
Count by the bigger denominator until you reach a multiple of the smaller one.
Multiples of 8: 8, 16, 24 → 24 is also a multiple of 3
Common denominator = 24
Step 2 · Find first new numerator
1 × (24 ÷ 3) = ?
First numerator × (common denominator ÷ first denominator) = first new numerator
Multiply the first numerator by the same number its denominator was multiplied by.
First new numerator = 8
Step 3 · Find second new numerator
5 × (24 ÷ 8) = ?
Second numerator × (common denominator ÷ second denominator) = second new numerator
Multiply the second numerator by the same number its denominator was multiplied by.
Second new numerator = 15
Step 4 · Find parts left
32
24
−
15
24
=
?
24
Subtract the new numerators, renaming 1 whole when the first is smaller
8
24
is
less
than
15
24
:
rename
1
whole
as
24
24
,
then
subtract.
Parts left = 8 + 24 − 15
Parts left = 32 − 15
Parts left = 17
Step 5 · Find difference
4
−
1
−
1
+
17
24
=
?
First whole number − second whole number (1 less if renamed) + parts left = difference
Take away the whole numbers (one fewer if a whole was renamed), then put the parts with them.
4 − 1 − 1 = 2
2
+
17
24
=
2
17
24
Difference
=
2
17
24
Check
Put the numbers back in. Both sides should match.
3 and 8 both go into 24 ✓
1 × (24 ÷ 3) = 8 ✓
5 × (24 ÷ 8) = 15 ✓
8 + 24 − 15 = 17 ✓
2
+
17
24
=
2
17
24
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Refresh
Related lessons
Add and subtract fractions with unlike denominators
Main lesson
Subtract fractions with unlike denominators
Use this for “Find the value of 5/6 − 3/8.”
Add mixed numbers
Use this for “Mia used 3 3/4 cups of flour and Leo 2 5/6 cups. How much in all?”
Line plots with fractions
Use this for “The line plot shows beakers holding 1/8, 1/4, 3/8 or 1/2 liter.”
Estimate sums of fractions
Use this for “Is the sum more or less than 1?” before adding.