Section 4 - Ratio, Proportion And Rates Of Change

Question 1

How can ratios and fractions be written differently

Answer 1

2/9 as many apples as oranges also means 9/2 as many oranges as apples

Question 2

How are ratios expressed as fractions

Answer 2

8:12 also means 8/12

Question 3

How do you simplify ratios with decimal

Answer 3

Multiply to make them whole

Question 4

What do you do if a ratio has mixed units

Eg one side cm and one mm

Answer 4

Convert to same unit and simplify

Question 5

What’s a part : whole ratio

Answer 5

When the LHS is included in the RHS

To work out a fraction of it do part divided by whole

Question 6

What are parts

Answer 6

The Titian amount in a ratio is split into parts

Eg 2:4:7 will be total of 13 parts

Divide total amount by the number of parts to get 1 part

Multiply to find the amounts of some parts

Question 7

How do you work out changing ratios

Answer 7

Eg m:f = 5:3

Write them as equations

Turn ratios into equations

Solve the two equations simultaneously

Question 8

What’s direct proportion

Answer 8

If one increases, the other one increases proportionally

Question 9

What’s the golden rule of direct proportion

Answer 9

Divide for one, then times for all

Question 10

What’s inverse proportion

Answer 10

If one increases, other will decrease proportionally

Golden rule is times for one, then divide for all

Question 11

What’s simple proportion

Answer 11

Eg y is proportional to X

There’s a symbol that means is proportional to - like an infinity sign with right end cut off

Question 12

How do you turn a proportional statement into an equation

Answer 12

Replace the proportional to sign with = k

Eg y symbol x^2

Turn into y = kx^2

V = k/r^3

Question 13

How do you handle algebra questions on proportion

Answer 13

Replace the symbol with =k

Find a pair of values and substitute to find k

Put back value of k into equation

Find other values

Question 14

How do you find a percentage of an amount

Answer 14

Turn percentage into decimal/fraction then multiply

Eg 15% of £46 = 15/100 X 46 = 6.90

Question 15

How do you find a new amount after a percentage increase/ decrease

Answer 15

Find the multiplier that represents percentage change -

Then multiply multiplier by value
Eg 25% increase of £2 = 2 X 1.25

25% decrease of £2 = 0.75

Question 16

How do you express X as a percentage of y

Answer 16

Divide X by y and multiply by 100

209 as a percentage of 400= 209/400 X 100

Question 17

How do you find percentage change

Answer 17

Change divided by original X 100

Question 18

How do you find the original value

Answer 18

Write the amount in the question as a percentage of the original value eg 10% increase of £15 is 110%

Divide to find 1%

Multiply by 100

Question 19

What’s simple interest

Answer 19

Means a certain percentage of the original amount only is paid at regular intervals - same every time it’s paid

Question 20

What’s compound interest

Answer 20

Amount added changes each time - it’s a percentage of new amount rather than original amount

Question 21

What’s the formula for compound interest

Answer 21

N (amount after n days/hours/years) = n(little corner 0) X (multiplier)^n

N(little 0) = initial amount

(Multiplier)^n = percentage change multiplier eg 1.05 is a 5% increase

^n= number of days/ hours/ years

Question 22

What’s 1 tonne equivalent to

Answer 22

1000kg

Question 23

What’s 1 litre equivalent

Answer 23

1000ml

1000cm^3

1ml= 1cm^3

Question 24

What’s 1 yard equivalent

Answer 24

3 feet

Question 25

What’s 1 foot equivalent

Answer 25

12 inches

Question 26

What’s 1 gallon equivalent to

Answer 26

8 pints

Question 27

How many pounds in a stone

Answer 27

14

Question 28

How many ounces in a pound

Answer 28

16 ounces

Question 29

How many pounds in a kg

Answer 29

2.2 pounds

Question 30

How many cm in a foot

Answer 30

30cm

Question 31

How many litres in a gallon

Answer 31

4.5 litres

Question 32

How many km in a mile

Answer 32

1.6km

Question 33

What’s 1m^2 equivalent to

Answer 33

100cm X 100cm = 10,000cm^2

Question 34

Tell me the speed distance time triangle

Answer 34

Speed on top

Distance X time on bottom

Question 35

Tell me the density mass volume triangle

Answer 35

Mass on top

Density X volume on bottom

Question 36

What’s the pressure force area triangle

Answer 36

Force on top

Pressure X area on bottom