☰ Year plan · Mathematics

Unit rates and the best buy

Week 20 · Rates and unit rates; the best buy · 3 lessons
1

Rates and unit rates: the amount for one

Discover Mathematics P6: Term 2, Unit 10, Lessons 1–3
GoalExplain a rate and a unit rate, and find a unit rate by dividing.
New words
rate · a ratio that compares two different kinds of quantity, such as km and hoursunit rate · a rate with 1 in the second place, such as 6 km per 1 hourper · the word that means “for each one”
Explanation

A rate compares two different kinds of quantity, such as distance and time, or price and mass. “12 km in 2 hours” is a rate. A unit rate says how much for ONE of the second quantity: 6 km per hour, 18 LE per kg, 30 jumps per minute. To find it, divide the first quantity by the second: 12 ÷ 2 = 6 km for each hour. The unit rate has 1 in the second place: 6 : 1. Be careful with the order. “LE per kg” means LE divided by kg. If you are asked for kg per LE, the question is different.

★Remember
Unit rate = first quantity ÷ second quantity. “A per B” means ÷ B: LE per kg, km per hour.
Worked examples
Distance (km)126
Time (h)21
A cyclist rides 12 km in 2 hours. The rate is 12 km per 2 hours. The unit rate is 12 ÷ 2 = 6 km per hour, written 6 km/h.
3 kg of rice cost 54 LE. The unit rate is 54 ÷ 3 = 18 LE per kg. So 1 kg costs 18 LE, 2 kg cost 36 LE and so on. The other way round, 3 ÷ 54 gives kg per LE, a different (and much less useful) rate.
Seif does 90 jumps with a jump rope in 3 minutes. The unit rate is 90 ÷ 3 = 30 jumps per minute. He can use it to predict: in 5 minutes at the same speed he would do 30 × 5 = 150 jumps.
Class activity

Rates at home. Find three rates in your life: for example your steps per minute when you walk for one minute, the price per kg of a fruit, the pages you read per ten minutes. Write each as a unit rate with its unit.

Practice
1
A car travels 240 km in 4 hours. Find the unit rate.
2
Rana types 150 words in 5 minutes. How many words per minute?
3
8 notebooks cost 96 LE. What is the price of one notebook?
4
A tap fills 36 litres in 4 minutes. Find the unit rate in litres per minute.
5
45 LE for 5 kg of oranges. Which division gives LE per kg, and what is the answer?