PSLCE Mathematics key terms

The value a digit has because of the position it occupies in a number. In 4,072 the 4 is worth four thousands, the 7 is worth seven tens, and the 2 is worth two ones.

Any one of the ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 used to write numbers. A numeral such as 583 is made of three digits placed in different positions.

A written symbol or group of symbols that stands for a number, such as 47 or 3.5. The numeral is the written form; the number is the amount it represents.

A way of writing a number as the sum of the values of each of its digits. For example, 3,506 in expanded form is 3,000 + 500 + 0 + 6.

The usual way of writing a number using digits in their correct positions, such as 8,204. It contrasts with expanded form and with word form.

Replacing a number with a nearby value that has fewer non-zero digits, chosen by looking at the next digit. 738 rounded to the nearest ten is 740 because the ones digit 8 is 5 or more.

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

The result of multiplying a whole number by another whole number. The multiples of 5 are 5, 10, 15, 20 and so on, without end.

A whole number greater than 1 whose only factors are 1 and itself. Examples are 2, 3, 5, 7 and 11; 1 is not prime and 9 is not prime because 3 divides it.

A whole number greater than 1 that has at least one factor other than 1 and itself. 15 is composite because it can be written as 3 × 5.

The largest whole number that divides two or more given numbers exactly. The HCF of 18 and 24 is 6, since 6 is the biggest number dividing both.

The smallest whole number that is a multiple of two or more given numbers. The LCM of 4 and 6 is 12, the first number appearing in both multiplication tables.

The agreed sequence for working out an expression with several operations: brackets first, then powers, then multiplication and division left to right, then addition and subtraction left to right.

Symbols ( ) used to group part of an expression so that it is calculated first. In 3 × (4 + 5) the addition inside the brackets is done before multiplying.

The answer obtained when two or more numbers are multiplied together. In 7 × 8 = 56, the product is 56.

The answer obtained when one number is divided by another. In 45 ÷ 9 = 5, the quotient is 5.

The amount left over when a whole number does not divide exactly into another. 23 ÷ 5 gives a quotient of 4 and a remainder of 3.

Finding a sensible approximate answer by rounding numbers to convenient values before calculating. Estimating 198 × 21 as 200 × 20 = 4,000 checks whether a full answer is reasonable.

The top number of a fraction. It states how many equal parts of the whole are being counted or taken. In 3/8 the numerator is 3.

The bottom number of a fraction. It states the total number of equal parts the whole has been divided into. In 3/8 the denominator is 8.

Fractions that look different but represent the same amount of a whole. 1/2, 2/4 and 5/10 are equivalent because each covers the same portion.

A fraction written with the smallest possible whole numbers, achieved by dividing numerator and denominator by their highest common factor. 12/18 simplifies to 2/3.

A fraction in which the numerator is smaller than the denominator, so its value is less than one whole. 3/5 is proper, while 7/5 is not.

A fraction in which the numerator is equal to or greater than the denominator, so its value is one or more wholes. 9/4 is improper and equals 2 1/4.

A number written as a whole number together with a proper fraction, such as 2 1/3. It can be changed into an improper fraction for calculating.

The position of a digit after the decimal point, counting from the left. In 0.472 the digit 7 is in the second decimal place and represents seven hundredths.

The dot separating the whole-number part of a decimal from the part less than one. In 12.75 it separates twelve wholes from seventy-five hundredths.

A way of expressing a fraction or part as an amount out of one hundred, written with the % sign. 45% means 45 out of every 100, or 0.45.

The total distance around the outside edge of a closed shape. For a rectangle it is twice the length plus twice the width.

The amount of flat surface a shape covers, measured in square units such as square centimetres. The area of a rectangle is length multiplied by width.

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

The amount a container can hold when full, usually measured in litres or millilitres. A bottle holding 2 litres has a capacity of 2 litres.

The amount of matter in an object, measured in grams and kilograms. Mass stays the same wherever the object is, unlike weight.

Changing a measurement from one unit to another without changing the amount. For example, 2.5 metres becomes 250 centimetres by multiplying by 100.

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

An angle of exactly 90 degrees, formed when two lines meet squarely. It is often marked with a small square and appears in every corner of a rectangle.

Two straight lines that meet or cross at a right angle. The adjacent sides of a square are perpendicular to each other.

Straight lines in the same plane that never meet, however far they are extended, because they stay the same distance apart. The opposite sides of a rectangle are parallel.

A closed flat shape with exactly three straight sides and three angles. Its angles always add up to 180 degrees.

Any closed flat shape with four straight sides and four angles. Squares, rectangles, parallelograms and trapeziums are all quadrilaterals, and their angles total 360 degrees.

The property of a shape that can be folded along a line so that one half fits exactly onto the other. A square has four lines of symmetry.

A single value found by adding all the amounts and dividing by how many there are. The mean of 4, 6 and 11 is 21 ÷ 3 = 7.

The difference between the largest and smallest values in a set of data. For the values 3, 8 and 14 the range is 14 − 3 = 11.

A table that records how often each value or category occurs in a set of data, usually using tally marks and then totals. It makes large sets of results easier to read and compare.

A diagram in which rectangular bars of equal width show how often each category occurs. The height of each bar represents its frequency.

A chart that uses small repeated pictures or symbols to show amounts, with a key stating what one symbol stands for. Half a symbol may be used to show half the key value.

A table showing the times at which events such as buses, trains or lessons take place. Reading one requires comparing start and finish times to work out durations.

The length of time between a start and an end point. A lesson beginning at 9:40 and ending at 10:25 has a duration of 45 minutes.

A way of writing time that counts hours from 00 to 23 instead of using a.m. and p.m. So 3:15 in the afternoon is written as 15:15.

The money gained when an item is sold for more than it cost to buy or make. Selling at 15 kwacha something that cost 11 kwacha gives a profit of 4 kwacha.

The money lost when an item is sold for less than it cost to buy or make. Selling at 9 kwacha something that cost 12 kwacha gives a loss of 3 kwacha.

The amount of money a customer pays for an item. Profit or loss is found by comparing this with the cost price.

Money paid for the use of borrowed or saved money, calculated only on the original amount. It equals principal × rate × time, with the rate written as a percentage per year.

The fixed step used to get from one term to the next in a sequence. In 3, 7, 11, 15 the rule is add 4 each time.

An ordered list of numbers or objects that follows a pattern. Each item is called a term, and the pattern may be made by adding, subtracting, multiplying or dividing.

One single number or item in a sequence, identified by its position. The fourth term of 2, 6, 18, 54 is 54.

A quantity in a problem or equation whose value is not yet known, often shown by a letter such as x or n. Finding its value is called solving.

A mathematical statement that two expressions are equal, joined by an equals sign. An equation such as x + 7 = 12 is solved by finding the value that makes it true.

Replacing a letter in an expression or formula with a given number and working out the result. If a = 4, then 3a + 1 becomes 3 × 4 + 1 = 13.