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Fractions

Numbers · Fractions

CBC Grade 5 Mathematics — Fractions

Lesson Objectives

By the end of this topic, a learner should be able to:

  • Simplify a fraction to its lowest terms
  • Compare two fractions to say which is larger
  • Order a set of fractions with denominators up to 12
  • Add and subtract fractions with the same denominator
  • Add and subtract fractions where one needs renaming
  • Appreciate the use of fractions in everyday situations

Fractions

A fraction is part of a whole. The bottom number tells you how many equal pieces the whole was cut into. The top number tells you how many pieces you have.

a) The two numbers

The top number is the numerator. It counts the pieces.

The bottom number is the denominator. It says how many pieces make the whole.

In 3/4 the whole was cut into 4 pieces, and we have 3 of them.

b) Simplifying

The same amount can be written in different ways. Cut a cake into 24 pieces and take 18. That is the same as cutting it into 4 and taking 3.

Simplifying a fraction Simplifying a fraction 18/24 = ? write it more simply their HCF = 6 the biggest number in both top → 18 ÷ 6 = 3 divide the top bottom → 24 ÷ 6 = 4 divide the bottom 18/24 = 3/4 same amount, fewer pieces

To simplify, find the biggest number that divides into both the top and the bottom. That is the HCF.

Divide both by it.

Use the HCF, not just any common number. Dividing 18/24 by 2 gives 9/12, which is smaller but not yet simplest.

Check at the end. If another number still divides both, keep going.

c) Comparing fractions

You cannot compare 3/8 and 5/12 as they stand. The pieces are different sizes.

Comparing two fractions Comparing two fractions 3/8 and 5/12 = ? which is larger common bottom = 24 8 and 12 both go into 24 3/8 = 9/24 times top and bottom by 3 5/12 = 10/24 times top and bottom by 2 10 beats 9 = 5/12 is larger now easy to see

Give them the same bottom number first. Then the pieces match and you can just compare the tops.

Find a number both bottoms go into. For 8 and 12, that is 24.

d) Ordering fractions

To put several fractions in order, give them all the same bottom number.

Take 2/3, 5/6, 1/2 and 3/4. All the bottoms go into 12.

They become 8/12, 10/12, 6/12 and 9/12.

Now order the tops: 6, 8, 9, 10. So the order is 1/2, 2/3, 3/4, 5/6.

Write the answer using the original fractions, not the renamed ones.

e) Adding and subtracting with the same bottom

When the bottoms match, just add or subtract the tops. The bottom stays the same.

So 3/9 + 4/9 = 7/9. And 8/9 − 3/9 = 5/9.

Never add the bottoms. 3/9 + 4/9 is 7/9, not 7/18.

f) Adding and subtracting with renaming

Adding with renaming Adding with renaming 1/4 + 3/8 = ? different bottoms rename 1/4 = 2/8 times top and bottom by 2 2/8 + 3/8 = 5/8 same bottom now check = can it simplify? 5 and 8 share nothing

If the bottoms are different, change one so that they match. That is called renaming.

Multiply the top and the bottom by the same number. The value does not change, only the way it is written.

To take 1/3 from 5/6, rename 1/3 as 2/6. Then 5/6 − 2/6 = 3/6, which simplifies to 1/2.

Always check whether your answer can be simplified.

g) Where this is used

Sharing food between friends. Measuring in a recipe. Reading half or a quarter of an hour. Splitting money fairly.

:::checkpoint Check yourself

  1. Simplify 12/18.
  2. Which is larger, 2/5 or 3/8?
  3. Work out 2/7 + 3/7.
  4. Work out 1/2 + 1/6. :::

Definitions

  • Numerator — the top number; how many pieces are counted.
  • Denominator — the bottom number; how many equal pieces the whole is split into.
  • Simplify — writing with the smallest numerator/denominator describing the same amount.
  • Renaming — rewriting with a different denominator without changing the value.

Must Remember

  1. Simplify using the HCF, not just any common factor.
  2. Different denominators must be converted to a common one before comparing or adding.
  3. Same-denominator addition/subtraction only changes the numerators.
  4. Always check if the final answer can be simplified further.

Conclusion

A fraction's value doesn't change just because it's written differently — simplifying, comparing, ordering, and renaming are all about recognising or creating fractions that describe the same amount.

Check yourselfPractise Fractions — 10 questions →Next in MathematicsTime →