SME
Grade 6 Math · Problem type
How many groups?
Use this for “How many 3/4-cup servings are in 2 1/4 cups?” (type 2 1/4 as 9/4).
Diagram
3 groups of 3/4 fit in 2 1/4.
This is an example. Type your own values to start a new problem.
a
b
÷
c
d
=
g
Common denominator
worked out (not typed)
Formulas
least common multiple of 4 and 4: 4
Least common multiple of the denominators = common denominator
9
4
÷
3
4
=
3
Amount in the common denominator ÷ group size in it = number of groups
Assumptions
•
Write both amounts with the same denominator. Then divide the numerators.
•
A part of a group left over is a fraction of a group.
•
Denominators from 1 to 20, up to 144 groups; write mixed numbers as fractions (2 1/4 = 9/4).
Step-by-step
WE KNOW
Amount numerator: 9
Amount denominator: 4
Group size numerator: 3
Group size denominator: 4
FIND
common denominator, number of groups
Step 1 · Find common denominator
least common multiple of 4 and 4: ?
Least common multiple of the denominators = common denominator
The least common multiple of the two denominators.
Both denominators are already 4
Common denominator = 4
Step 2 · Find number of groups
9
4
÷
3
4
=
?
Amount in the common denominator ÷ group size in it = number of groups
Write both with the common denominator. Then divide the numerators.
9 ÷ 3 = 3
Number of groups = 3
Check
Put the numbers back in. Both sides should match.
least common multiple of 4 and 4: 4 ✓
9
4
÷
3
4
=
3
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.