AFM Enlistment (Maths) key terms

The value a digit has because of its position in a number. In 4,073 the 4 means four thousands and the 7 means seven tens.

Writing a number with digits only, with each digit in its correct place-value column, rather than in words or expanded form.

A number written as the sum of the values of its digits, for example 3,506 = 3,000 + 500 + 6.

Replacing a number by a nearby value with fewer significant digits, chosen by looking at the next digit. 4,682 rounded to the nearest hundred is 4,700.

Finding an approximate answer, usually by rounding numbers first, to check whether an exact calculation is reasonable.

The agreed sequence for evaluating expressions: brackets first, then powers, then multiplication and division left to right, then addition and subtraction left to right.

Grouping symbols that show which part of an expression is calculated first. Anything inside brackets is evaluated before operations outside them.

A whole number with no fractional or decimal part. Integers may be positive, negative or zero, for example -7, 0 and 12.

A number less than zero, written with a minus sign. On a number line it lies to the left of zero, and it is used for debts or temperatures below zero.

A straight line marked with evenly spaced numbers, used to compare values and to show addition, subtraction and negative numbers visually.

A whole number that divides another number exactly with no remainder. The factors of 12 are 1, 2, 3, 4, 6 and 12.

The result of multiplying a number by a whole number. Multiples of 5 are 5, 10, 15, 20 and so on.

A whole number greater than 1 whose only factors are 1 and itself, such as 2, 3, 5, 7 and 11.

Writing a number as a product of prime numbers only, for example 60 = 2 x 2 x 3 x 5.

The largest number that divides two or more given numbers exactly. The highest common factor of 18 and 24 is 6.

The smallest number that is a multiple of two or more given numbers. The lowest common multiple of 4 and 6 is 12.

The top number of a fraction, which states how many equal parts are being counted. In 3/5 the numerator is 3.

The bottom number of a fraction, which states how many equal parts the whole is divided into. In 3/5 the denominator is 5.

Fractions that name the same value even though the numbers differ, such as 1/2, 2/4 and 5/10. Multiplying or dividing top and bottom by the same number produces them.

Dividing the numerator and denominator by their highest common factor so the fraction is written with the smallest possible whole numbers, for example 12/18 = 2/3.

A single denominator shared by two or more fractions, so they can be added, subtracted or compared. It is usually the lowest common multiple of the original denominators.

A fraction whose numerator is greater than or equal to its denominator, so its value is 1 or more, for example 7/4.

A number made of a whole number and a proper fraction together, such as 2 3/4, meaning 2 plus three quarters.

The fraction turned upside down, so numerator and denominator swap places. The reciprocal of 3/4 is 4/3, and multiplying a number by its reciprocal gives 1.

To divide by a fraction, multiply by its reciprocal instead. For example 2/3 divided by 4/5 equals 2/3 multiplied by 5/4.

A position after the decimal point showing a value of tenths, hundredths, thousandths and so on. In 0.472 the 7 is in the second decimal place, meaning hundredths.

A fraction or ratio expressed out of 100, written with the percent sign. 45% means 45 parts in every 100, or 45/100.

The increase or decrease in a quantity expressed as a percentage of its original value, found by dividing the change by the original amount and multiplying by 100.

A part of a quantity found by converting the percentage to a decimal or fraction and multiplying, for example 15% of 240 is 0.15 x 240 = 36.

A comparison of two or more quantities of the same kind, written with a colon such as 3:2, or as a fraction. It shows relative size, not the actual amounts.

A statement that two ratios or fractions are equal, or the relationship of one part to the whole. Problems often require sharing an amount in a given ratio.

A technique for ratio and proportion problems in which you first find the value of one unit, then multiply to find the required quantity.

A letter or symbol standing for an unknown or changing number in an expression or equation, such as x in 3x + 5 = 20.

A combination of numbers, variables and operations without an equals sign, such as 4y - 7. It can be evaluated or simplified but not solved.

A mathematical statement that two expressions are equal, shown by an equals sign, for example 2x + 3 = 11. Solving it means finding the value of the variable.

Replacing a variable in an expression or formula with a given number and calculating the result, for example finding 3x + 2 when x = 5.

A rule written as an equation linking quantities, such as area = length x width or distance = speed x time. Values are substituted into it to find a result.

The total distance around the outside edge of a flat shape, found by adding the lengths of all its sides.

The amount of flat surface a shape covers, measured in square units such as square centimetres or square metres.

The amount of space a solid object occupies, measured in cubic units such as cubic centimetres. For a cuboid it is length x width x height.

The amount of turn between two lines meeting at a point, measured in degrees. A right angle is 90 degrees and a straight line is 180 degrees.

The unit used to measure angles. A full turn is 360 degrees, a half turn 180 degrees and a quarter turn 90 degrees.

A three-sided flat shape whose interior angles always add up to 180 degrees. It may be equilateral, isosceles, scalene or right-angled.

In a right-angled triangle, the square of the longest side equals the sum of the squares of the other two sides, written a squared plus b squared equals c squared.

The distance around a circle, calculated as pi multiplied by the diameter, or 2 multiplied by pi multiplied by the radius.

The distance from the centre of a circle to any point on its edge. It is exactly half the diameter.

The distance across a circle through its centre, equal to twice the radius.

Changing a measurement from one unit to another of the same kind, for example 2.5 metres to 250 centimetres, by multiplying or dividing by the conversion factor.

The decimal measuring system based on prefixes such as kilo, centi and milli, used for length, mass and capacity. Each step between neighbouring prefixes is a factor of ten.

The amount a container can hold, usually measured in litres and millilitres, as distinct from the volume of the container itself.

The average of a set of values, found by adding all the values and dividing by how many there are.

The middle value of a set of numbers arranged in order. If there is an even count, it is the mean of the two middle values.

The difference between the largest and smallest values in a data set, showing how spread out the data is.

A graph using rectangular bars whose heights or lengths represent the frequency of each category, making comparisons between categories easy to read.

A table listing values or categories alongside how often each occurs, often used to calculate totals, means and other statistics.

A number that, when multiplied by itself, gives the original number. The square root of 49 is 7 because 7 x 7 = 49.