# Proportions and Equations

```Proportions and Equations
Remember that RATES in these equations must be expressed as decimals.
Examples: 8% = .08 7.5% = .075
20% = .20 or .2
5.25% = .0525
OPTION A
12.5% = .125
π π’ππ‘ππ‘ππ π₯ π ππππ  π‘ππ₯ πππ‘π = π ππππ  π‘ππ₯
π π’ππ‘ππ‘ππ + π ππππ  π‘ππ₯ = π‘ππ‘ππ
OPTION B
π π’ππ‘ππ‘ππ π₯ (1 + π ππππ  π‘ππ₯ πππ‘π) = π‘ππ‘ππ
π π’ππ‘ππ‘ππ π₯ ππππ‘π’ππ‘π¦/π‘ππ πππ‘π = ππππ‘π’ππ‘π¦/π‘ππ
π π’ππ‘ππ‘ππ + ππππ‘π’ππ‘π¦/π‘ππ = π‘ππ‘ππ
π‘ππ‘ππ π ππππ  π₯ ππππππ π πππ πππ‘π = ππππππ π πππ
πππ π πππ¦ + ππππππ π πππ = π‘ππ‘ππ
π π’ππ‘ππ‘ππ π₯ πππ πππ‘π = πππ ππππ’ππ‘
π π’ππ‘ππ‘ππ + πππ ππππ’ππ‘ = π‘ππ‘ππ
ππππππππ πππππ π₯ πππππ’π πππ‘π = πππππ’π ππππ’ππ‘
OPTION A
ππππππππ πππππ + πππππ’π ππππ’ππ‘ = π‘ππ‘ππ
OPTION B
OPTION A
ππππππππ πππππ π₯ (1 + πππππ’π πππ‘π) = π‘ππ‘ππ
ππππππππ πππππ π₯ πππππππ€π/πππ πππ’ππ‘ πππ‘π = πππππππ€π/πππ πππ’ππ‘ ππππ’ππ‘
ππππππππ πππππ β πππππππ€ππππ πππ’ππ‘ ππππ’ππ‘ = πππππππ€π/πππ πππ’ππ‘ πππππ
OPTION B
ππππππππ πππππ π₯ (1 β πππππππ€π/πππ πππ’ππ‘ πππ‘π) = ππππππ€π/πππ πππ’ππ‘ πππππ
Remember that RATES in these equations must be expressed as decimals.
Examples: 8% = .08 7.5% = .075
20% = .20 or .2
5.25% = .0525
πΌ = πππ‘
12.5% = .125
I = interest
p = principal (original amount)
r = rate (years)
t = time (in YEARS)
πππππππππ + πππ‘ππππ π‘ = π‘ππ‘ππ
If the time is given in the problem in months instead of years, you can simply place the number
of months over 12 in your equation.
π
Examples: 4 months would be ππ of a year
π
9 would be ππ of a year
πππ€ π΄πππ’ππ‘βππππππππ π΄πππ’ππ‘
ππππππππ π΄πππ’ππ‘
ππππππππ π΄πππ’ππ‘βπππ€ π΄πππ’ππ‘
ππππππππ π΄πππ’ππ‘
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πΈπ π‘ππππ‘ππ ππππ’π βπ΄ππ‘π’ππ ππππ’π
π΄ππ‘π’ππ ππππ’π
π₯ 100
π₯ 100
| π₯ 100
```
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