Basic Numeracy Vocabulary and Notes

Numbers
Negative numbers – for example, -5 pronounced ‘minus five’
Multiples – 3, 6, 9, 12, 15 are multiples of 3
Factors – 1, 2, 3, 4, 6 are factors of 12
Double – multiply by 2 (verb: to double)
Half – divide by 2 (verb: to halve)
Go up – Increase – Ascending. E.g. 0, 1, 2, 3, 5, 6, 8
Go down – Decrease – Descending E.g. 8, 6, 5, 3, 2, 1, 0

Rounding
Example 1: Round 47 to the nearest 10. Is 47 nearer to 40 or to 50? It is nearer to 50, so 47 rounded to the nearest 10 is 50.
Example 2: Round 378 to the nearest 100. Is 378 nearer to 300 or 400? It is nearer to 400, so 378 rounded to the nearest 100 is 400.
Example 3: Round 1275 to the nearest 10. Is it nearer to 1270 or 1280? It is exactly half-way. In this situation, we go up, so the answer is 1280.
Example 4: Decimal rounding: Round 6.7 to the nearest whole number = 7
Round 5.38 to one decimal place = 5.4. Round 8.629 to two decimal places = 8.63.
Example 5: Round $2.76 to the nearest 10p. Is it nearer to $2.70 or $2.80? It is nearer to $2.80, so $2.76 rounded to the nearest 10p is $2.80.
Example 6: Round $12.36 to the nearest $1.00. Is it nearer to $12.00 or $13.00? It is nearer to $12.00, so $12.36 rounded to the nearest $1.00 is $12.00.

Estimating
Estimate the answer to 4.8 x 3.9. This is approximately the same as 5 x 4 = 20. So
the estimated answer to 4.8 x 3.9 is 20.
Estimate the answer to $6.95 x 5.8. This is approximately the same as $7 x 6 = $42.
So the estimated answer to $6.95 x 5.8 is $42.

Ratio and Proportion
Ratio – a quantity is divided into parts
For example, dilute one part orange juice with three parts water (Dilute – add water)
This is written as 1:3 (the order is very important – so 3:1 is not correct)
In this example, there are four parts altogether, so 1 litre of drink would contain
250ml of juice and 750ml of water

Proportion – increase or decrease a quantity in proportion
e.g. to double the amount, multiply everything by 2
to make five times as much, multiply everything by 5
to make half the amount, divide everything by 2

For example – change quantities in a recipe
If 100g butter is needed to make 4 small cakes, how much butter will be needed to make 6 small cakes?
100 ÷ 4 = 25g (for one cake) 25g x 6 = 150g (for six cakes)

Fractions
In any fraction, the ‘top number’ is called the numerator and the ‘bottom number’ is called the denominator.
A Unit Fraction is any fraction where the numerator is 1.
Fractions which are equal are called Equivalent, for example 2/4 and 1/2.

Find a fraction part
¾ of 240: divide by the bottom number, multiply answer by the top number.
Example:
240 ÷ 4 = 60, 3 x 60 = 180
So: ¾ of 240 = 180

Simplify (cancel down) fractions
3 / 9
Find a number that you can divide both top and bottom number by. In this case it would be 3. There is 1 three in 3 and 3 threes in 9,
therefore
3 ÷ 3 = 1
9 ÷ 3 3

Writing one number as a fraction of another
Write 20 as a fraction of 80 and cancel to the lowest terms
20 ÷ 20 = 1
80 ÷ 20 4

Fractions, Percentages and Decimals that are equal (the same)

Fraction - Decimal  - Percentage
1/1    1       100%
1/2   0.5    50%
1/4  0.25    25%
3/4  0.75    75%
1/10  0.1    10%
1/5   0.2     20%
1/3   0.33    33.33%
2/3  0.67    66.67%

Percentages

Finding percentage parts

10% method
Find 20% of 85
First find 10% by dividing 85 by 10, so 85 ÷ 10 = 8.5
10% = 8.5 so 20% = 2 x 10% = 2 x 8.5 = 17
So 20% of 85 = 17

Fraction method
To find 17% of 85
17 x 85 = 17x85 = 1445 ÷ 100 = 14.45
100 1 100
So 17% of 85 = 14.45

Writing one number as a percentage of another
Write 60 as a percentage of 240.
First write number as fraction: 60/240
Then cancel it down (make the numbers smaller) 60 ÷ 60 = 1
240 ÷ 60 4
To change this into %, multiply by 100 (add two zeroes to the 1 and make it 100), then
divide by 4. 100 ÷ 4 = 25 = 25%

Measurement

Length
100cm = 1m cm -> m ÷ 100
1m = 100cm m -> cm x 100
10mm = 1cm mm -> cm ÷ 10 cm -> mm x 10
1000mm = 1m mm -> m ÷ 1000 m -> mm x 1000
1000m = 1km m -> km ÷ 1000 km -> m x 1000

Liquid / Water / Capacity
1000 ml = 1l ml -> l ÷ 1000 l -> ml x 1000
100 cl = 1l cl -> l ÷ 100 l -> cl x 100
1ml = 0.1 cl ml -> cl ÷ 10 cl -> ml x 10 1cl = 10 ml

Weight
1000g = 1kg g -> kg ÷ 1000 kg -> g x 1000
1000kg = 1 ton kg -> t ÷ 1000 t -> kg x 1000

Time
Twelve Hour Clock Half past three in the afternoon is 3.30pm. In the morning it is 3.30am.
Twenty Four Hour Clock Half past three in the afternoon is 15.30. In the morning it is 03.30.

Temperature 25°C is said ‘Twenty five degrees Celsius’

Perimeter
Add (+) all the sides together
(but make sure they are all either in mm, cm or m before you add)
300mm = 30 cm
Perimeter: 30cm + 12cm + 30cm + 12cm = 84cm

Area
Multiply (x) width by the length
(Remember, again, to make sure your measurements are all in the same units)
A garden is 5m long and 250cm wide. What is the area?
250cm = 2.5 m
Area: 5m x 2.5m = 12.5m² (remember - area is always ²)

Volume
Length x width x height
(Remember, again, to make sure your measurements are all in the same units)
6m x 2m x 3m = 6m x 2m = 12m² x 3m = 36m³
Remember volume is always ³

Scale Drawings
Scale drawing – on a room plan, for example, 1cm = 2m so expressed as a ratio: 1:200.
Example: If the scale is 1:100 on a plan, what would one centimetre represent? (100 cm, which is 1 metre)

What would 10cm represent? (1000 cm, which is 10 metres)

Vocabulary
+ add, increase, go up, addition, more, plus
- reduce/reduction, minus, take away, subtract, less, decrease
x multiply, lots of, times, times as many/much
÷ divide, share, equally between, lots of, per person
= equals, same as
Perimeter – distance around, fence
Area – floor, lawn, covered
Volume – contains, water, sand, anything in a box / container
Capacity – millilitres, centilitres, litres
Weight – grams, kilograms
Length – millimetres, centimetres, metres, kilometres, miles
300mm
12cm
3m
2m
6m

Shape and space:
2D Shapes (flat shapes)
pentagon circle square
triangle rectangle hexagon
3D Shapes (solid shapes)
cube cone sphere
cylinder pyramid cuboid

Right angles
right angle = 90° right angle = 90°
So there are 2 right angles in a straight line

Data Handling
Bar Chart
Pie Chart
Line Graph
Pictogram

Tally Chart
In a Tally Chart, llll = 4 and llll = 5. So the line across is 5!
Colour of car Tally Frequency
Black llll llll ll 12
White llll lll 8
Green lll 3
Blue llll llll llll lll 18
Red llll 5

Averages
Mean: Add all the numbers together and divide by how many numbers you have.
Example: Find the mean for 2, 5, 8
2 + 5 + 8 = 15 15 ÷ 3 = 5 (you divide by 3 because you have 3 numbers)
Mean = 5
Range: Biggest number minus the smallest number.
Example: Find the mean for 2, 5, 8
8 - 2 = 6 so the range is 6