الرياضيات (بالإنجليزية) الصف السادس الابتدائي، الأسبوع 20: Best buy: comparing prices with unit rates

Unit rates and the best buy

الأسبوع 20 · المعدل ومعدل الوحدة وأفضل صفقة شراء · 3 دروس

Best buy: comparing prices with unit rates

Discover Mathematics P6: Term 2, Unit 10, Lessons 1–3

GoalUse unit rates to find the best buy and to solve problems about speed and price.

New words

best buy · the choice with the lowest price for one unitprice per unit · the unit rate in LE for one kg, one litre or one itemcompare · to decide which is greater or smaller

Explanation

To decide which of two packs is the better buy, find the price of ONE unit of each, using the same unit (for example LE per litre for both), and compare. The pack with the lower price per unit is the better buy. A bigger pack is not always cheaper per unit, so always check. A unit rate also solves problems: if a bus goes 45 km each hour, in 4 hours it goes 45 × 4 = 180 km; if rice costs 18 LE per kg, 2.5 kg cost 18 × 2.5 = 45 LE.

★Remember

Best buy: find the price of one unit for each pack (same unit) and choose the lowest. Use a unit rate: total = unit rate × amount.

Worked examples

Pack	Price	Bottles	LE per bottle
A	24	6	4
B	45	10	4.5

Water. Pack A has 6 bottles for 24 LE: 24 ÷ 6 = 4 LE a bottle. Pack B has 10 bottles for 45 LE: 45 ÷ 10 = 4.5 LE a bottle. Pack A is the better buy.

Juice. 2 litres cost 38 LE: 19 LE per litre. 3 litres cost 54 LE: 18 LE per litre. The 3-litre bottle is the better buy. But a bigger size is not always cheaper: 1 kg of tea costs 30 LE, and 2 kg cost 62 LE, which is 31 LE per kg, so the small pack is better.

Using a unit rate. A bus travels at 60 km/h. In 3.5 hours it goes 60 × 3.5 = 210 km. Rice costs 18 LE per kg, so 2.5 kg cost 18 × 2.5 = 45 LE.

Class activity

Market detective. Visit a shop or look at a leaflet with a grown-up. Find two sizes of the same product (for example oil, rice or yoghurt). Work out the price per kilogram or litre for both and decide the better buy. Is the bigger size always cheaper?

Practice

Tomatoes: 3 kg cost 27 LE or 5 kg cost 40 LE. Which is the better buy?

Pencils: 12 for 30 LE or 20 for 48 LE. Which is the better buy?

A bus goes at 45 km/h for 4 hours. How far does it go?

Milk: 4 litres cost 60 LE or 6 litres cost 84 LE. Which is cheaper per litre?

Omar says: “The bigger pack is always cheaper.” Show with the numbers 1 L for 20 LE and 2 L for 42 LE that he is wrong.