Ratio and fractions

﻿Hello. My name is Mr. Clasper, and today we are going to be comparing the cost of two items by using the unitary method.

Eight pens cost 7 pounds 60, how much does one pen cost? Let's use a double number line. We want to know the cost of one pen. If I take my eight pens and divide this amount by eight, this would leave me with one pen Because the number of pens and the cost is directly proportional, I can also divide the cost by eight. This means that one pen is 95 Pence. Because we found the cost of one pen, we call this a unitary amount. How much does 13 pens cost? Well, if I take my one pen, and multiply this by 13, I would have 13 pens. And again, because of the relationship between the number of pens and the cost, I can also multiply my unitary cost by 13. This means that 13 pens, must cost 12 pound 35. We can also see another, the relationship here. If we multiplied our unitary number of pens, by 0.95, it gave us our cost. And if we divided our unitary cost by 0.95, we got the number of pens. This relationship also happens with 13 pens. So if we had 13 pens and multiplied by the unitary cost, it gave us the total cost. And likewise, if we had a total cost. And divided by the unitary price, this would give us the number of pens. Here are some questions for you to try. Pause the video, to complete your task and click resume once you're finished. And here are your solutions. So for one part A, to find one hour, you needed to divide 36 by four, and once you've done this, you should be able to find parts B, C and D relatively easily. And for question two, the first part asked for 60 litres. So this is 1.5 times greater than 40 litres. So you could multiply 42.4 by 1.5. Another way to do this will be to find one litres cost and then multiply it by 60 and 75 respectively for A and B.

A pack of five pencils cost two pound 35, a pack of eight of the same pencils costs three pounds, 68, which is better value? Let's have a look at our pack of five. Here's the double number line. What we can do, is to compare the price of one pencil in each pack. Or find the unitary price in each pack. So in this double number line, if I take my amount and divide it by five, this will give me the cost of one pencil. So in my pack of five, one pencil costs 47P. Looking at our pack of eight, our double number line tells us that eight pencils cost three pounds 68. Again, if I find my unitary price or the price of one pencil, I can divide the cost by eight. This means in the pack of eight, one pencil was 46 P. Comparing these two, which is better value? The answer is the pack of eight, as this is slightly cheaper. Here's some questions for you to try. Pause the video, to complete your task and click resume once you're finished. And here are your solutions. So for question three, if you find the cost per millilitre, you will find that the bottle of lemonade was the best value. For question four, just remember that 1.2 kilogrammes is equivalent to 1,200 grammes. And if you find the price per gramme, you should find that the 1.2 kilogramme pack is the best value. And for question five, if you work out how much each person earns per hour, and then multiply this by 35, you could arrive at your conclusion. And that is the end of our lesson. So we've been comparing the cost of two items using the unitary method. Well, I haven't got the exit quiz to show off your skills. I'll hopefully see you soon.

Compare the cost of two items using the unitary method

In this lesson, we will compare the cost of two items using the unitary method. We will learn how to reduce ratios to 1:n using a double number line.

Lesson overview:Compare the cost of two items using the unitary method

Core Content

Ratio 2 (Ratio and Fractions/Direct Proportion/Best Buy):