Everyday maths 2 (Wales)
Everyday maths 2 (Wales)

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Everyday maths 2 (Wales)

7.2 Writing a quantity of an amount as a fraction

Sometimes you will need to show one amount as a fraction of another. This might sound complicated, but it’s actually very logical. Look at the examples below.

Example 1: Fraction of an amount

In Figure 8, what fraction of Smarties are red?

Described image
Figure 8 Smarties in different colours

italic number of red smarties divided by italic total number of smarties = four divided by 30

To express the fraction of Smarties that are red, you simply need to count the red Smarties (4) and the total number of Smarties (30). Since there are 4 red Smarties out of 30 altogether, the fraction is four divided by 30. It is worth noting here that this could also be written as 4/30.

You may well be asked to give your answer as a fraction in its simplest form, so always check to see if you can simplify your answer. In this case four divided by 30 will simplify to two divided by 15.

Example 2: Fraction of an amount

250 g of flour is taken from a 1 kg bag. What fraction is this?

Hint: there are 1000 g in a kg.

To express quantities as fractions, the top and bottom numbers need to be in the same units, so here you need to make sure that you express both the top and bottom values in grams:

  • The flour removed is already expressed in grams: 250 g

  • The total amount is in kilograms so you need to convert to grams: 1 kg = 1000 g

Now write the amount taken over the total amount to express as a fraction:

  • 250 divided by 1000 (250 g of flour out of the 1000 g bag has been taken or used)

Then cancel down (or simplify) if possible:

  • 250 divided by 1000 = one divided by four

So one divided by four of the flour has been used.

Activity 15: Expressing one number as a fraction of another

  1. What fraction of a kilogram is:

    • a.100 g

    • b.750 g

    • c.640 g

    • d.20 g

Answer

  1. 100 g = 1000 g, so:

    • a.100 g 100 divided by 1000 = one divided by 10 of a kilogram

       

    • b.750 g 750 divided by 1000 = three divided by four of a kilogram

       

    • c.640 g 640 divided by 1000 = 16 divided by 25 of a kilogram

       

    • d.20 g = 20 divided by 1000 = one divided by 50 of a kilogram

  1. What fraction of an hour is:

    • a.15 minutes

    • b.20 minutes

    • c.35 minutes

    • d.48 minutes

Answer

  1. 1 hour = 60 minutes so:

    • a.15 minutes = 15 divided by 60 = one divided by four of an hour.

       

    • b.20 minutes = 20 divided by 60 = one divided by three of an hour.

       

    • c.35 minutes = 35 divided by 60 = seven divided by 12 of an hour.

       

    • d.48 minutes = 48 divided by 60 = four divided by five of an hour.

  1. A farmer takes 120 eggs to the local farmer’s market. She has 24 eggs left at the end of the day. What fraction of the eggs are left?

Answer

  1. 24 divided by 120 are left. This cancels down to one divided by five, so one divided by five of the eggs are left.

  1. A class of students sit a test. 18 pass and 12 fail. What fraction passed the test?

Answer

  1. Work out the total number of students by adding the number who passed to those who failed 18 + 12 = 30. Now work out the fraction that passed:

    • 18 divided by 30 (18 out of 30 students passed)

    Now cancel down:

    • 18 divided by 30 = three divided by five.

      So three divided by five passed the test.

  1. Mary bought her car for £12 500. When she goes to trade it in she is offered £8750. What fraction of the original price is this?

Answer

  1. 8750 divided by 12500 = seven divided by 10

  1. 30 people entered a raffle. 6 of these people won a prize. What fraction of people did not win a prize? Give your answer as a fraction in its simplest form.

Answer

  1. As this question wants the number of people who did not win a prize we must first do:

          30 − 6 = 24 people did not win a prize.

    As a fraction this becomes 24 divided by 30 which simplifies to four divided by five.

Sometimes fractions will not cancel down easily. When this happens, you estimate the fraction by rounding the numbers to values that will cancel. Sometimes this means breaking the ‘rules’ of rounding.

Example: Estimating fractions

1347 divided by 2057 will not cancel.

By rounding 1347 up to 1400 and 2057 to 2100 we can cancel down the fraction to get:

  • 1400 divided by 2100 = two divided by three

Note: Round to numbers that are easy to cancel, but if you round off too much, you will lose the accuracy of your answer.

Now that you can express a quantity as a fraction, estimate and simplify fractions, the next step is to be able to work out fractions of amounts. For example, if you see a jacket that was priced at £80 originally but is in the sale with two divided by five off, it’s useful to be able to work out how much you will be paying.

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