☰ Year plan · Mathematics

Unit rates and the best buy

Week 20 · Rates and unit rates; the best buy · 3 lessons
2

Finding a unit rate by dividing and with a ratio table

Discover Mathematics P6: Term 2, Unit 10, Lessons 1–3
GoalFind a unit rate by dividing and with a ratio table, and compare different methods.
New words
ratio table · a table that keeps the same ratio in every columndivide · to find how much for each onemethod · a way of solving a problem
Explanation

There are two good ways to find a unit rate. The first is to divide: the price divided by the number of kilograms. The second is a ratio table: start with the rate you know and divide both rows by the same numbers until the second row shows 1. The table is useful when the numbers do not divide in one step, because you can go halfway first. Both methods give the same answer, so you can use one to check the other. The unit rate may be a decimal: 70 LE for 4 kg is 17.5 LE per kg.

★Remember
Divide, or use a ratio table: divide both rows by the same number until the second row is 1.
Worked examples
Mass (kg)631
Price (LE)904515
6 kg of dates cost 90 LE. Ratio table: divide both by 2 to get 3 kg for 45 LE, then divide by 3 to get 1 kg for 15 LE. Division gives the same: 90 ÷ 6 = 15 LE per kg.
Pens12621
Price (LE)301552.5
12 pens cost 30 LE. 30 ÷ 12 = 2.5, so one pen costs 2.5 LE. Check with the table: 12 pens for 30 LE, 6 pens for 15 LE, 2 pens for 5 LE, 1 pen for 2.5 LE.
Three methods, one answer. 4 kg of cheese cost 70 LE. Mina divides: 70 ÷ 4 = 17.5. Seif halves twice: 4 kg for 70 LE, 2 kg for 35 LE, 1 kg for 17.5 LE. Hana first finds 35 LE for 2 kg, then halves. All three get 17.5 LE per kg.
Class activity

Table or division? Take a price tag from home (for example 6 eggs for 21 LE, or 4 bottles for 60 LE). Find the price of one in two ways, by division and with a ratio table, and check that you get the same answer.

Practice
1
7 litres of petrol cost 42 LE. Find the unit rate.
2
A machine makes 45 bottles in 3 minutes. Complete the ratio table and find the unit rate.
Minutes31
Bottles45?
3
6 mangoes cost 27 LE. What does one mango cost?
4
A car uses 10 litres of fuel to travel 150 km. How many km per litre?
5
Salma buys 5 kg of potatoes for 80 LE and says the unit rate is 5 ÷ 80. What is wrong? Find the price per kg.