1. This is an essential collections of skills that you need to succeed at National 5 and progress to Higher Simplifying Fractions Fractions of fractions Multiplying and dividing Adding and subtracting Course level questions

2. Simplifying algebraic fractions 1 Simplifying an algebraic fraction means rewriting it as an equivalent fraction where all of the common factors have been cancelled out. Tip! Try to memorise some easy number fractions that show how each idea works With number fractions, you simplify by cancelling numbers that are factors of both the numerator and denominator: Fractions with algebraic factors simplify in the same way: You will usually have to do some factorising. Also, any terms inside brackets must be treated as single objects when simplifying. Beware the classic mistake: k is NOT a factor so DON’T do this: What can I expect in the unit test?

3. Simplifying algebraic fractions 2 Your factorisation skills will really be tested out here. Always fully factorise the numerator and denominator if there are any terms being added or subtracted: Simplify these fractions. Start by factorising as much as you can: Tip! You don’t have to have the brackets here because it is not being multiplied anymore 2 Tip! Once you’ve cancelled all you can, don’t expand brackets What can I expect in the unit test?

4. Unit Assessment of simplifying fractions At unit assessment level, you will either be given fully factorised fractions or have to do a simple common factor factorisation. Simplify the following algebraic fractions: 2

5. Dealing with fractions of fractions This is a very useful algebraic trick for simplifying complicated fractions where the numerator or denominator contains a fraction. The trick is to multiply the fraction by 1 (which will not change its value). The challenge is to find the best way of writing 1… Remember, If the numerator and denominator of a fraction are equal then the fraction equals 1: Example: simplify The fraction in the denominator is making this awkward so multiply by 1 in a form that lets you reduce it: Example: simplify Simplifying here means finding an equivalent fraction without fractions in the numerator and denominator.

7. Multiplying fractions This is much more straightforward process than adding fractions. Remember this pattern: The product of the numerators The product of the denominators Now try these on paper before pressing the spacebar for the answers. Express these products as fractions in their simplest form So how do I divide fractions?

8. Dividing fractions Convert divisions to multiplications by replacing the second fraction with its reciprocal. Remember this pattern: Now try these on paper before pressing the spacebar for the answers. Express these products as fractions in their simplest form What can I expect in the unit test?

9. Unit Assessment of multiplying and dividing fractions Simplify the following: 2 Calculate the Area and perimeter of this rectangle:

10. Adding and Subtracting Fractions 1 Fractions can only be added or subtracted if they have the same denominator. To answer this type of questions you will first find equivalent fractions then add or subtract the numerators. With number fractions, the technique called ‘cross-multiplying’ produces equivalent fractions with the same denominators: The denominators are 2 and 3 and the smallest number that both divide into is 6. So when each fraction is multiplied (top and bottom) by the opposite denominator we get equivalent fractions with the same denominator. Now we Can add or subtract as needed.

11. Adding and Subtracting Fractions 2 The same idea allows us to add or subtract algebraic fractions. Cross multiplying works here too: The denominators are x and 2y and the smallest expression that both divide into is 2xy. So when each fraction is multiplied (top and bottom) by the opposite denominator we get equivalent fractions with the same denominator. Now we Can add or subtract as needed. What can I expect in the unit test?

12. Unit Assessment of adding and subtracting fractions Express each of the following as a single fraction in its simplest form. Remember revising means doing questions first then checking the answers. Here you can add the fractions by cross-multiplying twice or notice that lcm(2,3,4) = 12

13. Typical Course level Questions