Fractions During this topic you will learn to: Understand the equivalence of fractions. Simplify a fraction. Change proper fractions to improper fractions. Change improper to proper fractions Add and Subtract fractions Multiply and Divide fractions

Which are the same as A Quarter Two Fifths A Third A Half 1 2 3 3 14 4 5 9 12 35 8 2 4 8 19 25 25 6 12 16 76 75 70 2 5 30 1 9 33 8 15 75 4 18 99 49 4 2 4 3 5 98 6 4 10 7 9 Two Fifths A Quarter A Third A Half

Equivalent Fractions Before we can look at adding fractions we need to get some practice in finding equivalent fractions. So long as you multiply the top and the bottom of a fraction by the same number you will not change its size (because all you are doing is multiplying by 1!) 2 4 8 2 8 e.g., x = so = 5 4 20 5 20 This is just 1 whole

Equivalent Fractions Match up the fraction on the left with its equivalent on the right. 2 19 5 57 3 12 7 28 1 24 3 60 4 24 9 64 3 84 8 189

Improper Fractions An improper fraction is one where the numerator (top number) is bigger than the denominator (bottom number). This means that there must be more than one whole one. 3 e.g. = 1 = 2 15 = 4

Improper Fractions And Mixed Numbers = 1 = 1 = 3 An improper fraction can also be written as a mixed number. This means a whole number and a fraction. 3 1 e.g. = 1 = = 1 2 2 15 3 = = 3 4 4

Now Do Time Up Exercises 3, 4 & 5 You Have 10 min.

Simplifying Fractions If you can find equivalent fractions then simplifying fractions should not be a problem. Give me some equivalent fractions for: 12 18

Simplifying Fractions Which one do you think is the simplest and why? 12 18

Simplifying Fractions Simplifying a fraction just means finding an equivalent fraction with the smallest numbers possible 12 18

Now Do Time Up Exercises 1 & 2 You Have 7 min.

Improper Fractions And Mixed Numbers To convert an improper fraction into a mixed number: How many times does the denominator go into the numerator ? This is the whole number part. The remainder is the numerator of the fraction part.

4 Improper Fractions And Mixed Numbers Example: 38 2 = 9 9 How many times does 9 go into 38? What is the remainder?

Improper Fractions And Mixed Numbers To convert a mixed number into an improper fraction : Multiply the whole number by the denominator then add the numerator This is the numerator of the improper fraction The denominator stays the same.

3 Improper Fractions And Mixed Numbers Example: 5 21 5 26 = + = 7 7 7 How many sevenths is 3 whole ones? 3 x 7 = 21

Now Do Time Up Exercise 8 You Have 7 min.

Adding Fractions 1 What do you think the answer to this is: + = = We can’t just add numerators and denominators or we end up saying 2 halves make a half 1 1 2 1 + = = 2 2 4 2 We know that 2 halves make a whole one: 1 1 2 + = = 1 2 2 2 All we add are the numerators, the denominator stays the same.

Now Do Time Up Exercise 9 You Have 5 min.

Adding Fractions Before we can add fractions we have to make sure the denominators are the same This is where our equivalent fractions come in: 2 5 + 3 6 We have to turn the thirds into sixths 2 5 4 5 9 + = + = 3 6 6 6 6

Now Do Time Up Exercise 10 You Have 10 min.

Multiplying Fractions This is the easiest operation to do with fractions. Just multiply the numerators to get the numerator of the answer, And multiply the denominators to get the denominator of the answer. 2 3 6 e.g. x = 5 7 35

Dividing Fractions You can treat division just like multiplication – there is just one step to do first. Turn the fraction you are dividing by upside down. Then change the division to a multiplication. 2 3 2 7 14 e.g.  = x = 5 7 5 3 15