PROPORTION
PROPORTION
• When two ratios are given as equal.
• Examples of proportion:
! #
=
" $
% '% %*+ '%
= because =
& () &*+ ()
• When ratios are in proportion, their cross products are also equal.
DIRECT PROPORTION
• The ratio between quantities stays the same. When one increases, the other also
increases by the same factor.
• E.g. If there are 4 rowers per boat in a regatta then the following table applies:
Nr of 0 1 2 3 4
boats
Nr of 0 4 8 12 16
rowers
• There is a constant ratio between the nr of boats and nr of rowers.
CALCULATIONS WITH RATIOS IN DIRECT
PROPORTION
CROSS MULTIPLICATION
1. Find the missing value in the following ratios
! # # '
a. : b. =
" !$ %& (
USES OF DIRECT PROPORTION: EXAMPLE 1
Sthembile must paint his room. The total surface are is 28m2. He goes to the paint store and
selects the colour he wants to use. He is told that 1 litre of paint covers 9m2. How many tins of
paint must he buy?
ANSWER:
1. Write down the known/given fact as a ratio:
9m2 : 1 litre
2. Create a ratio containing the unknown quantity in the same order as the given ratio.
28m2 : x litres
3. Equate the two ratios:
9m2 28m2
=
1 litre x litres
4. Solve for the unknown value
*leave 5 lines open*
EXAMPLE 2
Mrs Jones has 400g of flour and more than enough of the other ingredients to make
pancakes. How many pancakes will she be able to bake if she wants to use up all her
flour?
110g : 6 pancakes
400g : x pancakes
!!" $""
:
# %
*Solve for x using cross multiplication
*leave 7 lines open
ACTIVITY
1. Find the value of x in each of the following, if the ratios are in direct proportion
1.1 64 : x = 4 : 5
1.2. 1,4 : 7 = x : 20
1.3. 3 : 25 = x : 30
( 4
1.4. :
# 5
2. A tiler, tiling with linoleum tiles, uses 2 tubes of glue per 5m2. How many tubes of
glue will he need to buy to tile a floor with an area of 27m2 ?
3. Lindiwe must dilute fabric softener using water in the ratio 1:3.
3.1. If she has 450 ml fabric softener, how much water must she use for the diluted
solution?
3.2. How much total mixture can she make from the 450ml fabric softener?
4. A cardboard model of a Honda motorbike is part of an outdoor display. Its height
is 122cm. The actual Honda motorbike is 152cm long and 60cm high. Find the
length of the cardboard model if its dimensions are in proportion to the real
motorbike.
