Fractions
1.0 Numbers · 1.2 Fractions
Syllabus tag: Kenya CBC | Grade 8 Mathematics | Strand 1.0 Numbers | Sub-Strand 1.2 Fractions (6 lessons)
Lesson objectives
By the end of this sub-strand, you should be able to:
- Work out the reciprocal of fractions in different situations
- Carry out combined operations on fractions
- Promote the use of fractions in real-life situations
Fractions
A fraction is a part of a whole. You already add, subtract and multiply them. This topic adds two things: turning a fraction over, and handling several operations at once.
a) The reciprocal
The reciprocal of a fraction is that fraction turned upside down.
A number multiplied by its own reciprocal always gives 1. That is what makes the reciprocal useful.
A whole number has a reciprocal too. Write 5 as 5/1, turn it over, and you get 1/5.
Zero has no reciprocal, because nothing multiplied by zero gives 1.
b) Why reciprocals matter
Dividing by a fraction is the same as multiplying by its reciprocal.
Turn the second fraction over and change the sign to multiply. Then multiply across the tops and across the bottoms.
Only the second fraction is turned over. Turning both, or turning the first, gives the wrong answer.
c) Combined operations
When a calculation has several operations, work in the usual order. Brackets first, then multiply and divide, then add and subtract.
Do not work left to right. In 1/2 + 1/3 × 3/4, the multiplication is done before the addition.
d) The order in practice
Work through brackets first, whatever is inside them.
Then any multiplication or division, taken left to right.
Then any addition or subtraction, taken left to right.
Adding and subtracting still need a common denominator. Multiplying and dividing do not.
e) Simplifying as you go
Cancel common factors before multiplying where you can. It keeps the numbers small and the final simplification easy.
Always give the answer in its simplest form. Turn a top-heavy fraction into a mixed number if the question asks.
f) Where this is used
A tailor dividing a length of cloth into equal parts. A cook halving a recipe that already uses three quarters of a cup. A trader working out how many quarter-kilo packets come from a sack.
Words to know
- Reciprocal -- the result of swapping a fraction's numerator and denominator; multiplying a number by its reciprocal always gives 1.
- Common denominator -- a shared denominator used to add or subtract fractions with different original denominators.
:::checkpoint Check yourself
- What is the reciprocal of 2/7?
- Work out 3/5 ÷ 2/3.
- Work out 1/4 + 1/2 × 2/3.
- Why does a number times its reciprocal always give 1? :::
Bridge to practice
Try the exercises below -- on reciprocals, dividing fractions, and combined operations.