SME
Grade 7 Math · Problem type
Solve a proportion
Use this for “If 3/20 = n/300, what is n?” and “450 g of oats makes 12 bars; how much for 20 bars?”
Diagram
d = 300 on the top line sits over 45 on the bottom line: each 1 above is 0.15 below.
This is an example. Type your own values to start a new problem.
a
b
=
c
d
k
Unit rate
worked out (not typed)
Formulas
k
=
a
÷
b
(unit
rate
=
first
numerator
÷
first
denominator)
0.15 = 3 ÷ 20
c
=
k
×
d
(second
numerator
=
unit
rate
×
second
denominator)
45 = 0.15 × 300
Assumptions
•
Both fractions are the same ratio written with different numbers.
•
Find the unit rate of one pair, then multiply.
•
Check: the cross products are equal.
Step-by-step
WE KNOW
a = 3 (first numerator), b = 20 (first denominator), d = 300 (second denominator)
FIND
unit rate (k), second numerator (c)
Step 1 · Find unit rate (k)
Use k = a ÷ b (unit rate = first numerator ÷ first denominator)
The unit rate: the first numerator for 1 of the first denominator.
k
=
3
20
k
=
0.15
Step 2 · Find second numerator (c)
Use c = k × d (second numerator = unit rate × second denominator)
The same rate for the second pair: multiply the unit rate by the second denominator.
c
=
0.15
×
300
c
=
45
Check
Put the numbers back in. Both sides should match.
0.15 = 3 ÷ 20 ✓
3 × 300 = 20 × 45 ✓
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Proportional relationships and the constant of proportionality
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Rates with fractions
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Proportional relationships and the constant of proportionality
Main lesson
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