1. S1 Fractions
Parent Class

2. Fractions 2 5 Two fifths is written as: two parts Numerator out of
five parts altogether
Denominator
Ask pupils if they can remember the name given to the number at the top of a fraction and the number at the bottom of a fraction.
Reveal these key words on the board.

3. Fraction of an amount When we work out a fraction of an amount we
multiply by the numerator
and
divide by the denominator
Examples, 2 3
of 18 litres 5 6
of £24
Tell pupils that it doesn’t make any difference whether you multiply first or divide first. It depends on the problem.
Demonstrate using the numbers in the example, that multiplying 18 by 2 and then dividing by 3 (this gives us 36 ÷ 3 = 12) is the same as dividing 18 by 3 and then multiplying by 2 (this gives us 6 × 2 = 12).
Establish that in this example if we divide first, the numbers will be easier to work with.
= 18 ÷ 3 × 2
= 24 ÷ 6 × 5
= 6 × 2
= 4 × 5
= 12 litres
= £20

4. Question Time
(Question 1)

5. Simplifying fractions
A fraction is said to be expressed in its lowest terms if the numerator and the denominator have no common factors.
Which of these fractions are expressed in their lowest terms? 7 5 2 14 16 20 27 3 13 15 21 14 35 32 15 8 7 5
Ask pupils what we mean when we say a fraction has no common factors.
Establish that there is no number other than 1 that divides into both the numerator and the denominator.
For each fraction ask pupils whether or not they think this fraction has been shown in its lowest terms, before revealing the answer.
If pupils do not think that the fraction has been shown in its lowest terms, ask them for a number which will divide into both the numerator and the denominator.
Explain that when cancelling it is always best to divide both the numerator and the denominator by the highest number that divides into both, that is, the highest common factor. However, if you do not cancel by the highest common factor the first time round, you can always cancel again.
Go through the cancellation of each fraction asking what we are dividing by each time.
There is something different about the last fraction, what is it?
Point out that it is top-heavy. The numerator is bigger than the denominator.
This is called an improper fraction.
Ask how we could write this improper fraction as a mixed number. (2 and 2/15)
Fractions which are not shown in their lowest terms can be simplified by cancelling.

6. Question Time
(Question 2)

7. Mixed and Improper Fractions
When the numerator of a fraction is larger than the denominator it is called an improper fraction. 15 4
is an improper fraction or top heavy.
We can write improper fractions as mixed numbers. 15 4
can be visually shown as
Talk through the diagrammatic representation of 15/4. Every four quarters are grouped into one whole, and there are three quarters left over.
15 ÷ 4 =
3 remainder 3 15 4 3 4 =

8. Improper fractions to mixed numbers37 8
Convert to a mixed number. 37 8 = 8 + 5 5 8 1 + = = 4 5 8
This number is the remainder.
Explain that to convert an improper fraction to a mixed number we can divide the numerator by the denominator to find the value of the whole number part. Any remainder is written as a fraction.
Relate fractions to division. 37/8 means 37 ÷ 8.
Talk through the division of 37 by 8. Discuss the meaning of the remainder in this context. We are dividing by 8 and so the 5 represents 5/8. 37 8 = 4 5 8 4 5
37 ÷ 8 =
4 remainder 5
This is the number of times 8 divides into 37.

9. Mixed numbers to improper fractions2 7 3
Convert to an improper fraction. 2 7 3 = 2 7 1 + = 7 + 2 = 23 7
We can explain this conversion by asking for the number of 1/7 in 3 whole ones. Explain that there are 21 sevenths in three wholes. Two more sevenths makes 23 sevenths altogether.
Explain that to convert a mixed number to an improper fraction in one step we multiply the whole number part by the denominator of the fractional part and add the numerator of the fractional part (refer to the example). This gives us the numerator of the improper fraction. The denominator of the improper fraction is the same as the fractional part of the mixed number.
… and add this number …
To do this in one step, 3 3 2 2 23
… to get the numerator. = 7 7 7
Multiply these numbers together …

10. Question Time
(Question 3 & 4)

11. Multiplying Fractions3 8
What is × ? 2 5
To multiply two fractions together, multiply the numerators together and multiply the denominators together: 3 3 8 4 5 × = 12
Point out that we could also cancel before multiplying. 40 10 = 3 10

12. Multiplying Fractions5 6
What is × ? 12 25
Start by writing the calculation with any mixed numbers as improper fractions.
To make the calculation easier, cancel any numerators with any denominators. 7 2 12 25 35 6 × = 14 5 5 1 = 2 4 5

13. Question Time
(Question 6)

14. Adding & Subtracting Fractions
When fractions have the same denominator it is quite easy to add them together and to subtract them.
For example, 3 5 1 5
3 + 1 5 4 5 + = =
We can show this calculation in a diagram:
Talk about adding fractions with the same denominator.
What is three fifths plus one fifth?
What are we adding? (fifths)
Three fifths plus one fifth is four fifths.
Show the example on the slide and emphasise that when the denominator is the same we can add together the numerators. Show that by writing (3 + 1) over 5 using a single bar we can avoid adding the denominators together by mistake.
Show the calculation as a diagram. + =

15. Adding & Subtracting Fractions7 8 – 3
7 – 3 8 4 8 1 1 2 = = = 2
Fractions should always be cancelled down to their lowest terms.
We can show this calculation in a diagram:
Talk through the example on the board and remind pupils that fractions should always be cancelled down to their lowest terms.
The 4 and the 8 in 4/8 are both divisible by 4. Cancelling gives us 1/2. – =

16. Adding & Subtracting Fractions1 9 + 7 4 = 1 12 9 = 1 3 9 = 1 3 3
Top-heavy or improper fractions should be written as
mixed numbers.
Improper fractions (top-heavy fractions) should be written as mixed numbers.
In the fraction 12/9, 12 is bigger than 9. This is an improper (or top-heavy) fraction. 9/9 make one whole plus 3/9 left over.
Again, remind pupils that fractions must be cancelled if possible.
3 and 9 are both divisible by 3. Cancelling gives us 1/3.

17. Adding & Subtracting Fractions4 1 5 3 2 5 7 3 5 + =
Add your whole numbers together and then your fractions.
Improper fractions (top-heavy fractions) should be written as mixed numbers.
In the fraction 12/9, 12 is bigger than 9. This is an improper (or top-heavy) fraction. 9/9 make one whole plus 3/9 left over.
Again, remind pupils that fractions must be cancelled if possible.
3 and 9 are both divisible by 3. Cancelling gives us 1/3.

18. Question Time
(Question 5)

19. Fractions with different denominators
Fractions with different denominators are more difficult to add and subtract.
For example,
What is + 1 2 3 ?
We can show this sum using diagrams:
Point out, with reference to the diagrams that we cannot add 1/2 + 1/3 directly. The answer is certainly not 2/5, as some pupils may think!
Ask pupils to suggest ways of adding these fractions.
We know that 1/2 is equivalent to 3/6 and 1/3 is equivalent to 2/6.
Click to divide the shapes into sixths.
6 is the lowest common multiple of 2 and 3.
Once we have written both fractions with a common denominator, we can add them together. + = 3 6 2 6
3 + 2 6 5 6 + = =

20. What is + 1 3 4
1. Write each fraction over the lowest common denominator. ×3 4 3 + 1 ×4 12 9 12 4 = +
2) Add the fractions together.
Review the method for finding equivalent fractions.
Remind pupils that the answer should be written as a mixed number and cancelled down if possible. 12 13 = 1 12 =

21. What is + 1 3 5 2 4
1) Write each fraction over the lowest common denominator. 5 3 + 1 2 4 ×3 ×5 15 9 + 5 2 4 =
2) Add the fractions together.
Review the method for finding equivalent fractions.
Remind pupils that the answer should be written as a mixed number and cancelled down if possible. 15 9 + 5 6 = 6 15 14 =

22. What is - 1 7 2 3 5 2
1) Write each fraction over the lowest common denominator. 3 2 - 7 1 5 ×7 ×3 21 14 - 3 5 2 =
2) Subtract the fractions together.
Review the method for finding equivalent fractions.
Remind pupils that the answer should be written as a mixed number and cancelled down if possible. 3 21 14 - 3 = 3 21 11 =

23. A problem with subtractions
What about - 3 4 1 5 9 2
Review the method for finding equivalent fractions.
Remind pupils that the answer should be written as a mixed number and cancelled down if possible.

24. Question Time
(Question 7)