GCSE Maths · Number Basics · Higher · Summary

GCSE Maths Number Basics (Higher): summary and key words

Chapter summary

Skill	Method
Place value and ordering	Compare column by column from the left; give decimals the same number of decimal places; < > ≤ ≥ ≠
Adding and subtracting	Line up the place values (and decimal points); carry when adding, exchange when subtracting; check with the inverse
Multiplying	Long multiplication or the grid method; for decimals multiply as whole numbers then count total decimal places
Dividing	Short or long division (divide, multiply, subtract, bring down); for a decimal divisor multiply both numbers by 10, 100... first
Negative numbers	Number line: adding moves right, subtracting moves left; + (−) is −, − (−) is +; same signs × ÷ give +, different signs give −
Order of operations	BIDMAS: Brackets, Indices, Division/Multiplication, Addition/Subtraction (left to right); a fraction line and a root sign act like brackets
Inverse operations	+ and −, × and ÷, square and square root; undo steps in reverse order; use given facts and powers of 10
Reciprocals	Turn the fraction upside down; number × reciprocal = 1; dividing by a number = multiplying by its reciprocal; 0 has no reciprocal
Units of measure	To a smaller unit multiply, to a bigger unit divide; use the same unit throughout; time is not decimal (60 minutes = 1 hour)
Problem solving	Read, plan, calculate, check; round a remainder up if all must fit in; compare unit prices; check by estimating or the inverse

I can use place value to read, write and order whole numbers and decimals, and use the symbols =, ≠, <, >, ≤, ≥.
I can add and subtract whole numbers and decimals using column methods.
I can multiply and divide whole numbers and decimals by a written method (long multiplication and long or short division).
I can order, add, subtract, multiply and divide negative numbers.
I can use BIDMAS for brackets, powers and roots, and for fraction lines.
I can use inverse operations to check answers, find missing numbers and work backwards.
I can find the reciprocal of a number and use it to divide.
I can convert between metric units and between units of time, and use 12-hour and 24-hour clock times.
I can solve multi-step problems, deal sensibly with remainders and check my answers by estimating.

Place value: The value of a digit because of the column it is in.
Decimal place: A digit after the decimal point; the first is tenths, the second hundredths.
Integer: A whole number: positive, negative or zero.
Sum / total: The result of adding.
Difference: The result of subtracting the smaller number from the larger.
Product: The result of multiplying.
Quotient: The result of dividing.
Remainder: The amount left over after dividing.
Dividend / divisor: In 12 ÷ 4, 12 is the dividend (the number divided) and 4 is the divisor (the number you divide by).
Inverse operation: An operation that undoes another: + and −, × and ÷.
BIDMAS: The order of operations: Brackets, Indices, Division and Multiplication, Addition and Subtraction.
Index (power): A small raised number that tells you how many times to multiply a number by itself, e.g. 3² = 9.
Reciprocal: The number you multiply by to get 1. The reciprocal of 4 is 14.
Negative number: A number less than zero.
Metric unit: A unit of measure linked to others by powers of 10 (mm, cm, m, km, g, kg, ml, litre).
Speed: Distance divided by time, for example in kilometres per hour (km/h).