SME
Grade 6 Math · Problem type
How much in each group?
Use this when 2/3 gallon fills 3/4 of a tank: how much fills the whole tank?
Diagram
2/3 fills 3 of the 4 parts, so one part holds 2/3 ÷ 3 = 2/9.
The whole holds 4 × 2/9 = 8/9.
This is an example. Type your own values to start a new problem.
a
b
÷
c
d
=
e
f
Formulas
2
3
÷
3
=
2
9
Amount ÷ parts it fills = one part
4
×
2
9
=
8
9
Parts in the whole × one part = whole amount
Assumptions
•
The amount fills some parts of the whole. Find what one part holds, then the whole.
•
This is the same as dividing the amount by the fraction of the whole it fills.
•
Denominators from 1 to 20; the whole is at most 144 times the amount.
Step-by-step
WE KNOW
Amount numerator: 2
Amount denominator: 3
Part filled: numerator: 3
Part filled: denominator: 4
FIND
whole amount denominator, whole amount numerator
Step 1 · Find whole amount denominator
2
3
÷
3
=
2
?
Amount ÷ parts it fills = one part
The amount fills 3 parts of the whole. One part holds the amount ÷ 3: multiply the denominator by 3.
Whole amount denominator = 3 × 3
Whole amount denominator = 9
Step 2 · Find whole amount numerator
4
×
2
9
=
?
9
Parts in the whole × one part = whole amount
The whole is 4 of those parts: multiply the numerator by 4.
Whole amount numerator = 2 × 4
Whole
amount
numerator
=
8
(the
whole
holds
8
9
:
the
same
as
2
3
÷
3
4
=
8
9
)
Check
Put the numbers back in. Both sides should match.
3 × 3 = 9 ✓
4 × 2 = 8 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.