WJEC GCSE Mathematics and Numeracy

## Place value and directed numbers Each digit in a number is worth a power of ten that depends on its position. In $4\,805.27$ the 8 is worth 800, the 5 is worth 5 and the 7 is worth $\frac{7}{100}$. Whole numbers of any size are read and written in groups of three digits, so $3\,200\,450$ is three million, two hundred thousand, four hundred and fifty. **Directed numbers** are numbers with a sign, positive or negative. On a number line the larger number is always the one further right, so $-2 > -7$, and ordering a list such as $-3,\ 4,\ -8,\ 0,\ -1$ gives $-8,\ -3,\ -1,\ 0,\ 4$. Adding a negative number moves left and subtracting a negative number moves right, because subtracting takes away a debt. $$ \begin{aligned} 5 + (-8) &= -3 \\ -3 - (-8) &= -3 + 8 = 5 \\ -6 - 4 &= -10 \end{aligned} $$ When multiplying or dividing, two numbers with the same sign give a positive answer and two with different signs give a negative one. $$ \begin{aligned} (-4) \times 6 &= -24 \\ (-4) \times (-6) &= 24 \\ -18 \div (-3) &= 6 \\ 20 \div (-5) &= -4 \end{aligned} $$ ## Order of operations and inverse operations A calculation with several operations is worked in a fixed order so that everyone gets the same answer: brackets first, then indices (powers and roots), then multiplication and division from left to right, then addition and subtraction from left to right. A fraction bar works like a bracket round the top and round the bottom. $$ \begin{aligned} 24 - 3 \times (2 + 4)^2 \div 9 &= 24 - 3…