Things You Need to Know
Sample Problems
Interactive Activities
Class Notes
- Numerators are the top number in a fraction.
- Denominators are the bottom number in a fraction.
- Ratios are a comparison of two different things. They can be represented with a ":" or as a fraction. The order they are written matters. (ex: The ratio of males to females is 18:12, or 18/12. The ratio of females to males is 12:18 or 12/18.)
- Proportions are a statement of equality between two ratios. They can be used to find an equivalent amount of something if the ratio were to be scaled larger or smaller.
- When you set up a proportion, make sure the units of each numerator match, and the units of each denominator match.
- We can solve for a missing part of a proportion:
- If "x" is the numerator, multiply the other numerator by the "x" fraction's denominator. Then divide that amount by the other fraction's denominator.
- If the "x" is the denominator, flip BOTH fractions on each side of the equation upside down. Then do the previous step.
- Rates are ratios comparing two numbers with different units. (ex: kilometers over hours, kilograms over number of people, etc.).
- Unit price is a rate that gives the cost of something per 1 unit (ex: dollars per 1 liter, euros per 1 carton of milk, etc.).
- A percentage can be converted to a decimal by dividing by 100. A decimal can be converted to a percentage by multiplying by 100.
- A fraction can be converted to a percentage by dividing the numerator by the denominator, then multiplying by 100.
- To calculate the amount a percentage is of a number:
- Convert the percent to a decimal.
- Multiply the decimal by the number.
- Example: 15% of 500: 0.15 x 500 = 75.
- To calculate how many percent a number is of another number, just divide them and then multiply by 100.
- Example: What percent is 50 of 200? 50 / 200 = 0.25.
- 0.25 x 100 = 25%.
- Mark up is the amount you add on to a price.
- Mark down is the amount you take off of a price.
- Example: A TV was $200 but has been marked down to $150.
- Find the difference: 200 - 150 = 50.
- The TV was marked down by $50, but what is the mark down percent?
- Divide the $50 by the original price: 50/200 = 0.25
- Change to a percent: 25%.
- The TV was marked down 25%.
- Currency exchange rates are a rate of one currency to another. These problems can be solved using proportions.
- When an exchange rate is given, the currency with the smaller number is the more valuable currency.
- Example: 1 Canadian dollar = 0.75 US dollars
- If you gave someone 1 Canadian dollar, they wouldn't even give you 1 US dollar back. So the Canadian dollar is worth less.
- When language is unclear, like "exchange between Norwegian krone and Canadian dollars is 0.16", assume the first is the "1" in the proportion (e.g.: 1 krone = 0.17 Canadian).
- If a currency is listed with an exchange, again assume that the exchange number is for Canadian dollars.
- Example: Mexican peso, 0.085
- This would be 1 peso = 0.085 Canadian.
- Banks often have different exchange rates based on whether you are buying a foreign currency from them or selling a foreign currency to them.
- The rates given are always in terms of 1 foreign currency for the exchange rate amount of Canadian dollars.
- The "buying rate" is when the bank is buying the foreign currency (buying your foreign currency, giving you Canadian). The "selling rate" is when the bank is selling foreign currency to you (taking your Canadian, selling you foreign).
- Example: Euros have a buying rate of 1.45 and a selling rate of 1.50. This means for when the bank is buying your Euros, they consider a Euro worth 1.45 Canadian. When the bank is selling Euros to you, they consider a Euro worth 1.50 Canadian.
Sample Problems
Interactive Activities
Class Notes