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Fractions

1.0 Numbers · 1.3 Fractions

Syllabus tag: Kenya CBC | Grade 7 Mathematics | Strand 1.0 Numbers | Sub-Strand 1.3 Fractions (9 lessons)

Lesson objectives

By the end of this topic, you will be able to:

  • Compare, add and subtract fractions
  • Multiply fractions by a whole number, a fraction, and a mixed number
  • Identify the reciprocal of a fraction
  • Divide fractions by a whole number, a fraction, and a mixed number, and divide a whole number by a fraction
  • Identify and create number sequences involving fractions

Fractions

A fraction shows part of a whole. The bottom number says how many equal parts the whole was cut into. The top says how many are taken.

a) Comparing fractions

To compare two fractions, give them the same denominator, then compare the tops.

For 2/3 and 3/5, the common denominator is 15. They become 10/15 and 9/15, so 2/3 is larger.

b) Adding and subtracting

Adding fractions Adding fractions 2/3 + 1/4 = ? different denominators common bottom = 12 the LCM of 3 and 4 2/3 + 1/4 = 8/12 + 3/12 rewrite both 2/3 + 1/4 = 11/12 add the tops only

Find a common denominator first, usually the LCM of the two denominators.

Rewrite each fraction with that denominator, then add or subtract the tops only. The denominator does not change.

Adding the bottoms as well is the classic error. 1/2 + 1/2 is 1, not 2/4.

c) Multiplying

Multiplying fractions Multiplying fractions 2/3 × 4/5 = (2 × 4) / (3 × 5) straight across 2/3 × 4/5 = 8/15 no common denominator needed 2/3 × 6 = 12/3 a whole number is 6/1 2/3 × 6 = 4 simplify

Multiplying is easier than adding. Multiply the tops together and the bottoms together. No common denominator is needed.

To multiply by a whole number, write it over 1.

For a mixed number, change it to an improper fraction first. So 2¼ becomes 9/4.

Cancel before multiplying where you can. It keeps the numbers small.

d) The reciprocal

The reciprocal of a fraction is that fraction turned upside down.

The reciprocal of 3/5 is 5/3. The reciprocal of 4, which is 4/1, is 1/4.

A fraction multiplied by its own reciprocal always gives 1.

e) Dividing

Dividing fractions Dividing fractions reciprocal of 3/5 = 5/3 turn it over 2/3 ÷ 3/5 = 2/3 × 5/3 multiply by the reciprocal 2/3 ÷ 3/5 = 10/9 multiply across 10/9 = 1 1/9 as a mixed number

To divide by a fraction, multiply by its reciprocal.

Only the second fraction is turned over. Turning the first one instead gives a wrong answer.

Dividing by a fraction less than 1 gives a larger answer. That feels wrong but is correct: how many quarters fit in 2? Eight.

f) Number sequences with fractions

A sequence can count in fractions. In ½, 1, 1½, 2 the rule is "add ½".

Find the rule by looking at the gap between terms, exactly as with whole numbers.

Some sequences shrink. In 1, ½, ¼, ⅛ each term is half the one before.

g) Where this is used

A cook halving a recipe. A tailor using three quarters of a metre. A trader splitting a sack into equal packets. A carpenter measuring in fractions of an inch.

Words to know

  • Common denominator — a shared denominator that two or more fractions are converted to, needed for addition and subtraction.
  • Reciprocal — the result of flipping a fraction upside down; a fraction multiplied by its reciprocal equals 1.
  • Mixed number — a number written as a whole number plus a fraction, such as 1 1/2.
  • Improper fraction — a fraction where the numerator is greater than or equal to the denominator, such as 3/2.

:::checkpoint Check yourself

  1. Which is larger, 3/4 or 5/8?
  2. Work out 1/2 + 2/5.
  3. Work out 3/4 × 2/9.
  4. Work out 3/5 ÷ 2/3. :::

Bridge to practice

Try the exercises below — on comparing, adding, subtracting, multiplying and dividing fractions.

Check yourselfPractise Fractions — 10 questions →Next in MathematicsDecimals →