Math: Percentages & Ratios
Ontario Mathematics Proficiency Test — study tool.
Scroll down past the quiz for the complete study guide on this topic.
Scroll down past the quiz for the complete study guide on this topic.
1
A club has 30 members. 80% attend a virtual event that costs $10 per member. What is the total cost?
2
Amale converts 1,000 euros to CAD. Kumar converts 1,100 SGD to CAD. (1 CAD = 0.6169 EUR, 1 CAD = 0.9288 SGD.) Which statement is true?
3
A bicycle costs $300 in January and $426 in June. What is the percent increase?
4
A video game has 15 levels. Brom completed 6. What percentage has he completed?
5
Two associates sell an item for $175. Christopher's share is 80%. How much does he get?
6
Students who walk to school: Grade 4 = 18, Grade 5 = 10, Total = 65. What percentage of walkers are in Grade 6?
7
A business sold 800 necklaces last year and 1,080 this year. What is the percent increase?
8
The ratio of red to green peppers is 2:3. There are 30 peppers total. How many are green?
9
Felix has 3 mangoes and 4 papayas. Which ratio is equivalent to 3:4?
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Study Guide: Percentages & Ratios
WHAT IS A PERCENTAGE?
A percentage is a number out of 100. "Percent" literally means "per hundred."
40% means 40 out of 100, which is 40/100 = 0.40
To convert a percentage to a decimal: divide by 100 (move decimal 2 left)
80% = 0.80 35% = 0.35 8% = 0.08
FINDING A PERCENTAGE OF A NUMBER
Multiply the number by the decimal form of the percentage.
Example: 80% of 30 members
30 × 0.80 = 24 members
Example: 80% of $175
$175 × 0.80 = $140
Example: What percentage is 6 out of 15?
6 ÷ 15 = 0.4 = 40%
FINDING A PERCENTAGE FROM DATA
When given a table with parts and a total:
Step 1: Find the missing part (subtract known parts from total)
Step 2: Divide the part by the total
Step 3: Multiply by 100
Example: Total walkers = 65. Grade 4 = 18, Grade 5 = 10. Grade 6 = ?
Grade 6 = 65 - 18 - 10 = 37
Percentage = 37 ÷ 65 = 0.569 = 57%
PERCENT INCREASE
This is one of the most common question types.
FORMULA: Percent Increase = (New - Old) / Old × 100
Example: Bicycle costs $300 in January, $426 in June.
Increase = $426 - $300 = $126
Percent increase = $126 / $300 = 0.42 = 42%
Example: 800 necklaces last year, 1,080 this year.
Increase = 1,080 - 800 = 280
Percent increase = 280 / 800 = 0.35 = 35%
COMMON MISTAKE: Dividing by the NEW number instead of the OLD number.
Always divide by the ORIGINAL (old) amount.
RATIOS
A ratio compares two quantities. 3:4 means "for every 3 of one thing,
there are 4 of another."
EQUIVALENT RATIOS
Multiply or divide both sides by the same number.
3:4 = 6:8 = 9:12 = 12:16
To check if two ratios are equivalent, simplify both to lowest terms.
9:12 → divide both by 3 → 3:4 ✓ 8:6 → divide both by 2 → 4:3 ✗ (that's 4:3 not 3:4)
RATIOS AND TOTALS
When given a ratio and a total, find the value of each part.
Example: Red to green peppers = 2:3, total = 30.
Total parts = 2 + 3 = 5
Value of each part = 30 ÷ 5 = 6
Red = 2 × 6 = 12
Green = 3 × 6 = 18
CURRENCY CONVERSION
Currency conversion is just unit rate math.
If 1 CAD = 0.6169 EUR, then to convert EUR to CAD:
CAD = EUR ÷ 0.6169
Example: Convert 1,000 EUR to CAD
1,000 ÷ 0.6169 = $1,621 CAD
Example: Convert 1,100 SGD to CAD (1 CAD = 0.9288 SGD)
1,100 ÷ 0.9288 = $1,184 CAD
The key: if they give you "1 CAD = X foreign currency," then
divide the foreign amount by X to get CAD.
KEY FORMULAS
Percentage of a number: number × (percent/100) Finding a percentage: part ÷ whole × 100 Percent increase: (new - old) / old × 100 Equivalent ratios: multiply/divide both parts by the same number Ratio to total: total ÷ sum of ratio parts = value per part Currency to CAD: foreign amount ÷ exchange rate
