RATES A RATE is almost the same as a ratio except the units of the two quantities must be different. Units are different!! Example of a Rate: Arthur runs.

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Presentation transcript:

RATES A RATE is almost the same as a ratio except the units of the two quantities must be different. Units are different!! Example of a Rate: Arthur runs 10 km every 2 hours. (In words)

Writing Rates Remember that you MUST include the units beside each term in your rate. Fraction Forms Ratio Form 10 km 2 h 10 km : 2 h 10 km / 2 h

Writing Rates We often use the words “for every” or “per” when writing a rate in words. 10 km : 2 h “10 km per 2 h” or “10 km for every 2 h”

Writing Rates As a general rule: 1 When one of your units is money, this term should go FIRST in the rate. 2 When one of your units is time, this term should go LAST in the rate.

Examples Write the following rates in fraction form a) Money! (should be 1st term) a) $2 for every 20 apples. $2 / 20 apples Time! (should be 2nd term) b) 3 hours for every 200 km. 200 km / 3 h

Money! (should be 1st term) Examples Write the following rates in fraction form c) 5 births per 100 people. 5 births / 100 people Money! (should be 1st term) d) 25 L of gasoline for every $26. $26 / 25 L

UNIT RATES A UNIT RATE is a rate whose 2nd term must be 1. 2nd term is a 1 Example of a Unit Rate: Liam walks 2 km every 1 hour. or 2 km/h Liam walks 2 km per hour.

UNIT RATES Example of Unit Rates we see often: 100 km/h Speed limits How far you can travel in 1 hour. $1.06 / L Unit prices The price of 1 litre of gasoline.

The amount of mass in 1 mL of a substance UNIT RATES Example of Unit Rates we see often: 1 g/mL Density The amount of mass in 1 mL of a substance

Changing a Rate into a Unit Rate If you are given a rate, how do you turn it into a unit rate which is the same value? Answer: Divide the 1st term by the 2nd term.

Changing a Rate into a Unit Rate Examples: Convert these rates into Unit rates ÷ $5 / 20 apples $0.25 / apple The cost of 1 apple ÷ $9 / 8 L $1.125 / L The cost of 1 L of gasoline

Changing a Rate into a Unit Rate Examples: Convert these rates into Unit rates ÷ 220 km / 2 h 110 km/h The distance travelled in 1 hour Also, the speed of this vehicle!

Changing a Rate into a Unit Rate Examples: Convert these rates into Unit rates ÷ $5.60 / 4 items $1.40 / item The cost of 1 item