Ratios and proportions
- Course
- Problem-Solving and Data Analysis
- Question type
- Ratios, rates, and units
- Practice
- Strategy lesson
- Language
- Vietnamese · English
Terminology
| Ratio | A comparison of two quantities by number or size. The ratio of a to b can be written as a:b or a/b. Ex: Bình has 15 apples and 30 oranges. The ratio of apples to oranges is 15:30, or 1:2. |
| Rate | A special type of ratio that compares two quantities with different units. Ex: Nam's motorbike travels at a speed of 40km/h. |
| Proportion | An equation stating that two or more ratios are equal; it is often used to find unknown quantities Ex: To make one cake, Thảo needs 2 cups of flour and 1 cup of water. So to make 5 cakes, Thảo needs 10 cups of flour and 5 cups of water. |
| Percentage | A ratio out of 100 that represents a part-to-whole relationship. Percent (%) means 1/100. |
| Percent value | The values needed to find a percentage. There are 2 of them: the part and the whole. |
| Complementary percentages | Two percentages that add up to 100%. Ex: 30%+ 70%= 100%. |
| Decimal | A way of writing a number using the digits 0 to 9 and a decimal point to show the fractional part. Ex: the number 3.14 is a decimal whose whole-number part is 3 and whose fractional part is 0.14. |
| Fraction | A way of writing a number as one quantity divided by another. It has two parts: the numerator and the denominator. The numerator is the number above the fraction bar and the denominator is the number below it. The two parts are separated by a slash or a fraction bar. Ex: the fraction 1/2 has numerator 1 and denominator 2. |
| Discount | A reduction in the price of a product or service. Ex: If a product is listed at $100 and is discounted by 20%, its actual selling price is only $80. |
| Tip | Extra money paid to service staff in restaurants, eateries, hotels, or other services. Ex: If the tip is 10% and the total bill is 100.000 đồng, then the tip is 10% x 100.000 đồng = 10.000 đồng. |
| Commission rate | The percentage of a transaction or sale that is paid to the person or company that completed it. Ex: A salesperson earns a 5% commission rate on the total value of the products sold. If the total value sold is 100 million đồng, the commission is 5% x 100 million đồng = 5 million đồng. |
Formulas
A ratio is a comparison of two quantities. The ratio of a to b can be written as a : b or 
or a to b.
Example: Pepper has 3 hats and 2 scarves ⇒ The ratio of hats to scarves is 3 to 2 or 
Two types: part-to-part ratios and part-to-whole ratios.
Example: A basket holds 5 blue balls and 3 red balls
- Part-to-part ratio: The ratio of blue balls to red balls is
- Part-to-whole ratio: The ratio of blue balls to all the balls is
A proportion is an equation stating that two ratios are equal. Proportions help us find equivalent ratios and solve for unknown quantities.
Example: A recipe calls for 3 cups of flour for every cup of water. We want to use 6 cups of flour. To find how much water we need, we set up a proportion:
A rate is a special kind of ratio in which the two quantities have different units.
Example: A person travels 10 km in 2 hours. The person's average speed is 
On the SAT, rates are often used to solve unit-conversion problems.
Example: A deer can run at a top speed of 30 miles per hour. Convert this speed to feet per minute. (1 mile = 5280 feet)
Step 1: Identify the given unit and the unit you need:
- Given unit: miles per hour
- Unit you need: feet per minute
Step 2: Find the relationships between the given unit and the unit you need:
- 1 mile = 5280 feet
- 1 hour = 60 minutes
Step 3: Write the conversion so that the given unit cancels out and the unit you need ends up in the right place:
Note: If a unit is raised to a power, the measurement must also be raised to that power
Example: 1 m = 100 cm ⇒ 1 m2 = 1002 m2
A percentage is a part-to-whole ratio with a denominator of 100.
Example: A basket has 5 blue balls and 3 red balls
⇒ The percentage of blue balls is 62.5%
Formula:
- a is b% of c ⇒
Example: 36 is what percent of 60 ⇒ 
⇒ x = 60
- Percent change:
Percent change = 
Example: The price of a vacuum cleaner decreases from $200 to $170. By what percent did the price of the vacuum cleaner decrease?
Percent change = 
17.65%