Succeed with maths – Part 1
Succeed with maths – Part 1

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Succeed with maths – Part 1

2 Multiplying fractions

The last part of the previous activity does not give a surprising result, mathematically speaking. One-third of one-half is indeed one-sixth. If you want to convince yourself, take a piece of paper again. Fold it in half along the long side and shade one half of the paper. Then, fold it into thirds along the short side. The paper is now split into six equal pieces, or sixths. If you look at the shaded half, you can see that one out of three parts of this portion represents one out of six parts of the entire piece of paper, as shown in Figure 4. This is the same as saying that it is one-third of a half.

Figure _unit5.2.1 Figure 4 Folding a piece of paper into sixths

Mathematically, this is written as equation left hand side one divided by three multiplication one divided by two equals right hand side one divided by six.

If you look at this carefully, you should be able to see that to multiply these two fractions, the numerators were multiplied, and the denominators. This is the way that all fractions are multiplied. You must just remember to show any answer in its simplest form.

It is often easier to cancel or simplify before multiplying, as this can give us easier numbers to deal with. For example, looking at two divided by three multiplication one divided by two.

Multiplying the numerators and then the denominators together gives equation left hand side two divided by three multiplication one divided by two equals right hand side two multiplication one divided by three multiplication two, but you can cancel the 2s using division:

equation sequence two super one multiplication one divided by three multiplication two sub one equals one multiplication one divided by three multiplication one equals one divided by three

This calculation is equivalent to cancelling at the start of the calculation: equation sequence two super one divided by three multiplication one divided by two sub one equals one multiplication one divided by three multiplication one equals one divided by three

Try this for yourself in the next activity.

Activity _unit5.2.1 Activity 3 Multiplying fractions

Timing: Allow approximately 10 minutes

Carry out the following examples, showing your final answers in the simplest form.

  • a.two divided by three multiplication six divided by 11

Discussion

Remember to multiple the numerators and then the denominators together.

Answer

  • a.Cancel by dividing by 3.

    equation left hand side two divided by three sub one multiplication six squared divided by 11 equals right hand side four divided by 11
  • b.22 divided by 50 multiplication three divided by five

Answer

  • b.Cancel by dividing by 2.

    equation left hand side 22 super 11 divided by 50 sub 25 multiplication three divided by five equals right hand side 33 divided by 125
  • c.24 divided by 25 multiplication five divided by 12

Answer

  • c.Cancel by dividing by 5 and 12.

    equation left hand side 24 squared divided by 25 sub five multiplication five super one divided by 12 sub one equals right hand side two divided by five

You’ve now looked at multiplying proper fractions. However, you will remember from Week 3 that you will also come across as mixed numbers, which are a combination of whole numbers and proper fractions. The next section will look at calculations involving mixed numbers.

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