SME
Grade 7 Math · Problem type
Rates with fractions
Use this for “1/2 cup of sugar for every 3/4 cup of flour: how much sugar for 1 cup of flour?”
Diagram
f = 3 cups on the top line sits over 2 cups on the bottom line: each 1 above is 2/3 below.
This is an example. Type your own values to start a new problem.
a
÷
b
=
2
3
k
f
Flour wanted
example · cups
s
Sugar needed
calculated · cups
Formulas
k
=
a
÷
b
(sugar
for
1
cup
of
flour
=
sugar
÷
flour)
2
3
=
1
2
÷
(
3
4
)
s
=
k
×
f
(sugar
needed
=
sugar
for
1
cup
of
flour
×
flour
wanted)
2
=
2
3
×
3
Assumptions
•
A unit rate with fractions works like one with whole numbers: divide to find the amount for 1.
•
Dividing by a fraction is multiplying by its reciprocal: 1/2 ÷ 3/4 = 1/2 × 4/3 = 2/3.
•
Then multiply the amount for 1 by how many you want.
Step-by-step
WE KNOW
a = 1/2 cup (sugar), b = 3/4 cup (flour), f = 3 cups (flour wanted)
FIND
sugar for 1 cup of flour (k), sugar needed (s)
Step 1 · Find sugar for 1 cup of flour (k)
Use k = a ÷ b (sugar for 1 cup of flour = sugar ÷ flour)
Sugar for 1 cup of flour: divide the sugar by the flour. Dividing by a fraction is multiplying by its reciprocal.
k
=
1
2
÷
(
3
4
)
k
=
2
3
cup
Step 2 · Find sugar needed (s)
Use s = k × f (sugar needed = sugar for 1 cup of flour × flour wanted)
Multiply the sugar for 1 cup of flour by the cups of flour wanted.
s
=
2
3
×
3
s
=
2
cups
Check
Put the numbers back in. Both sides should match.
2
3
=
1
2
÷
(
3
4
)
✓
2
=
2
3
×
3
✓
Topic check
See what you know: 5 questions on this topic
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