3. Direct Proportion:
• Two quantities are in direct proportion when they
increase or decrease in the same ratio.
• For example, if 12 cans of milk have a mass of 4 kg,
then 24 cans of milk will have a mass of 8 kg
• i.e., if the quantity of cans doubles then so does
the mass
• If cost of 2 pens is 10 rupess then cost of 5 pens will
be ……?
4. Real life examples of Direct
Proportion:
H.W: Write another 3
examples of direct
proportion??
5.
6. Example: Charles’s law states that for a given mass of gas at constant pressure, the volume is
directly proportional to its thermodynamic temperature. A gas occupies a volume of 2.4 liters
at 600 K. Determine
a) the temperature when the volume is 3.2 liters
b) the volume at 540 K
7. Inverse Proportion
• Inverse proportion means that, as the value of one variable increases, the value of
another decreases, and that their product is always the same.
• For example, the time for a journey is inversely proportional to the speed of travel.
• So, if at 30 m.p.h. a journey is completed in 20 minutes, then at 60 m.p.h. the
journey would be completed in 10 minutes.
• Double the speed, half the journey time.
• Note that 30 × 20 = 60× 10
• Two variables, x and y, are in inverse proportion to one another if y is proportional
to 1/ x ,
y α
1
𝑥
• or y = k x or k = x y where k is a constant, called the coefficient of proportionality.
8. In another example,
The time needed to dig a hole is inversely proportional to the
number of people digging.
So, if 4 men take 3 hours to dig a hole, then 2 men (working at the
same rate) would take 6 hours.
Half the men, twice the time. (Note that 4 × 3 = 2 × 6.)
