Everyday maths 1
Everyday maths 1

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Everyday maths 1

3 Fractions

Described image
Figure 10 Looking at fractions

What is a fraction?

A fraction is defined as a part of a whole. So for example one divided by three, or ‘one third’, is one part of three parts, all of equal size.

Fractions are an important feature of everyday life. They could ensure that you get the best deal when shopping – or that you receive the largest slice of pizza! As you go through this section, you’ll see how fractions could be used when you are shopping or within the workplace.

Fractions are related to decimals and percentages, which you’ll look at in the sections that follow this one.

This section will help you to:

  • order and compare fractions
  • identify equivalencies between fractions
  • calculate parts of whole quantities and measurements (e.g. calculate discounts in sales).

Please look at the following example before you carry out the activity:

A half can be written as one divided by two, i.e. one of two equal parts.

A quarter can be written as one divided by four, i.e. one of four equal parts.

An eighth can be written as one divided by eight, i.e. one of eight equal parts.

Hint: The top of the fraction is called the numerator. The bottom of the fraction is called the denominator. Notice that one divided by two is bigger than one divided by four, even though the denominator 2 is smaller than the denominator 4. How would you explain one third? How would you write it as a fraction? Which is bigger: one third or two quarters?

Example: Where there’s a will, there’s a fraction

Lord Walton draws up a will to decide who will inherit the family estate. He proposes to leave one divided by two of the estate to his son, one divided by three to his daughter and one divided by six to his brother.

  1. Who gets the biggest share?
  2. Who gets the smallest share?

Method

When numerators of fractions are all 1, the larger the denominator of the fraction, the smaller the fraction.

Looking at the example above, the fractions can be put in order of size starting from the smallest:

one divided by six, one divided by three, one divided by two

So:

  1. The biggest share (one divided by two) goes to his son.
  2. The smallest share (one divided by six) goes to his brother.

If you’re asked to arrange a group of fractions into size order, it’s sometimes helpful to change the denominators to the same number. This can be done by looking for the lowest common multiple – that is, the number that all of the denominators are multiples of.

Example: Looking at equivalent fractions

Arrange the following fractions in order of size, starting with the smallest:

  • three divided by six, one divided by three, two divided by 12

Method

The lowest common multiple is 12:

  • 6 × 2 = 12
  • 3 × 4 = 12
  • 12 × 1 = 12

Whatever you do to the bottom of the fraction you must also do to the top of the fraction, so that it holds the equivalent value. The third fraction, two divided by 12, already has 12 as its denominator, so we don’t need to make any further calculations for this fraction. But what about three divided by six and one divided by three?

  • 2 × three divided by six means calculating (2 × 3 = 6) and (2 × 6 = 12), so the equivalent fraction is six divided by 12
  • 4 × one divided by three means calculating (4 × 1 = 4) and (4 × 3 = 12), so the equivalent fraction is four divided by 12

Now you can now see the size order of the fractions clearly:

  • two divided by 12, four divided by 12, six divided by 12

So the answer is:

  • two divided by 12, one divided by three, three divided by six

Use the examples above to help you with the following activity. Remember to check your answers once you have completed the questions.

Activity 8: Fractions in order of size

  1. Put these fractions in order of size, with the smallest first:
  • one divided by five, one divided by three, one divided by four, one divided by 10, one divided by two

Answer

Remember that when the numerator of a fraction is 1, the larger the denominator, the smaller the fraction.

From smallest to largest, the order is:

  • one divided by 10, one divided by five, one divided by four, one divided by three, one divided by two
  1. What should you replace the question marks with to make these fractions equivalent?
  • one divided by three = question mark divided by six
  • one divided by four = question mark divided by eight
  • one divided by five = question mark divided by 10
  • one divided by two = question mark divided by 10

Answer

  • one divided by three = two divided by six
  • one divided by four = two divided by eight
  • one divided by five = two divided by 10
  • one divided by two = five divided by 10

Example: Drawing the fractions

If you need to compare one fraction with another, it can be useful to draw the fractional parts.

Look at the mixed numbers below. (A mixed number combines a whole number and a fraction.) Say you wanted to put these amounts in order of size, with the smallest first:

2 one divided by two, 3 one divided by four, 1 one divided by three

Method

To answer this you could look at the whole numbers first and then the fractional parts. If you were to draw these, they could look like this:

Described image
Figure 11 Drawing the fractions

So the correct order would be:

1 one divided by three, 2 one divided by two, 3 one divided by four

Use the example above to help you with the following activity. Remember to check your answers once you have completed the questions.

Activity 9: Putting fractions in order

  1. Put these fractions in order of size, smallest first:
  • 5 one divided by four, 6 one divided by five, 2 one divided by two
  1. Put these fractions in order of size, smallest first:
  • 2 two divided by five, 1 nine divided by 10, 2 one divided by two

Answer

  1. The correct order would be:
  • 2 one divided by two, 5 one divided by four, 6 one divided by five
  • In this case, even though one divided by two is bigger than one divided by four and one divided by four is bigger than one divided by five, you need to look at the whole numbers first and then the fractions. The diagram illustrates this more clearly:
Described image
Figure 12 Drawing the fractions
  1. The correct order would be:
  • 1 nine divided by 10, 2 two divided by five, 2 one divided by two
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