SME
Grade 5 Math · Problem type
Add mixed numbers
Use this for “Mia used 3 3/4 cups of flour and Leo 2 5/6 cups. How much in all?”
Diagram
3 9/12 + 2 10/12
This is an example. Type your own values to start a new problem.
First numerator
First denominator
+
Second numerator
Second denominator
=
6
7
12
Sum
Common denominator
worked out (not typed)
First new numerator
worked out (not typed)
Second new numerator
worked out (not typed)
Parts added
worked out (not typed)
Formulas
4 and 6 both go into 12
The smallest number both denominators go into = common denominator
3 × (12 ÷ 4) = 9
First numerator × (common denominator ÷ first denominator) = first new numerator
5 × (12 ÷ 6) = 10
Second numerator × (common denominator ÷ second denominator) = second new numerator
9
12
+
10
12
=
19
12
Add the new numerators; the denominator stays
3
+
2
+
19
12
=
6
7
12
First whole number + second whole number + parts added = sum
Assumptions
•
Give the fraction parts a common denominator: the smallest number both denominators go into.
•
Add the whole numbers and add the parts. Parts that make a whole or more add one more whole.
•
Whole numbers to 10; each fraction part is less than 1, with denominators 2 to 12.
Step-by-step
WE KNOW
First whole number: 3
First numerator: 3
First denominator: 4
Second whole number: 2
Second numerator: 5
Second denominator: 6
FIND
common denominator, first new numerator, second new numerator, parts added, sum
Step 1 · Find common denominator
4 and 6 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 6: 6, 12 → 12 is also a multiple of 4
Common denominator = 12
Step 2 · Find first new numerator
3 × (12 ÷ 4) = ?
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 = 9
Step 3 · Find second new numerator
5 × (12 ÷ 6) = ?
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 = 10
Step 4 · Find parts added
9
12
+
10
12
=
?
12
Add the new numerators; the denominator stays
Same denominator now: add the numerators of the parts.
9 + 10 = 19
Parts added = 19
Step 5 · Find sum
3
+
2
+
19
12
=
?
First whole number + second whole number + parts added = sum
Add the whole numbers, then put the parts with them.
3 + 2 = 5
19
12
=
1
7
12
5
+
19
12
=
6
7
12
Sum
=
6
7
12
Check
Put the numbers back in. Both sides should match.
4 and 6 both go into 12 ✓
3 × (12 ÷ 4) = 9 ✓
5 × (12 ÷ 6) = 10 ✓
9
12
+
10
12
=
19
12
✓
5
+
19
12
=
6
7
12
✓
Topic check
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