Section 4 - Ratio, Proportion And Rates Of Change Flashcards
How can ratios and fractions be written differently
2/9 as many apples as oranges also means 9/2 as many oranges as apples
How are ratios expressed as fractions
8:12 also means 8/12
How do you simplify ratios with decimal
Multiply to make them whole
What do you do if a ratio has mixed units
Eg one side cm and one mm
Convert to same unit and simplify
What’s a part : whole ratio
When the LHS is included in the RHS
To work out a fraction of it do part divided by whole
What are parts
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
How do you work out changing ratios
Eg m:f = 5:3
Write them as equations
Turn ratios into equations
Solve the two equations simultaneously
What’s direct proportion
If one increases, the other one increases proportionally
What’s the golden rule of direct proportion
Divide for one, then times for all
What’s inverse proportion
If one increases, other will decrease proportionally
Golden rule is times for one, then divide for all
What’s simple proportion
Eg y is proportional to X
There’s a symbol that means is proportional to - like an infinity sign with right end cut off
How do you turn a proportional statement into an equation
Replace the proportional to sign with = k
Eg y symbol x^2
Turn into y = kx^2
V = k/r^3
How do you handle algebra questions on proportion
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
How do you find a percentage of an amount
Turn percentage into decimal/fraction then multiply
Eg 15% of £46 = 15/100 X 46 = 6.90
How do you find a new amount after a percentage increase/ decrease
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
How do you express X as a percentage of y
Divide X by y and multiply by 100
209 as a percentage of 400= 209/400 X 100
How do you find percentage change
Change divided by original X 100
How do you find the original value
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
What’s simple interest
Means a certain percentage of the original amount only is paid at regular intervals - same every time it’s paid
What’s compound interest
Amount added changes each time - it’s a percentage of new amount rather than original amount
What’s the formula for compound interest
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
What’s 1 tonne equivalent to
1000kg
What’s 1 litre equivalent
1000ml
1000cm^3
1ml= 1cm^3
What’s 1 yard equivalent
3 feet
What’s 1 foot equivalent
12 inches
What’s 1 gallon equivalent to
8 pints
How many pounds in a stone
14
How many ounces in a pound
16 ounces
How many pounds in a kg
2.2 pounds
How many cm in a foot
30cm
How many litres in a gallon
4.5 litres
How many km in a mile
1.6km
What’s 1m^2 equivalent to
100cm X 100cm = 10,000cm^2
Tell me the speed distance time triangle
Speed on top
Distance X time on bottom
Tell me the density mass volume triangle
Mass on top
Density X volume on bottom
What’s the pressure force area triangle
Force on top
Pressure X area on bottom
