Order positive and negative integers, decimals and fractions; use the four operations with whole numbers, decimals and directed numbers; and apply the correct order of operations (BIDMAS), including brackets, powers and roots.

What this dot point is asking

The Eduqas number content opens with the structure of the number system and calculation: ordering integers, decimals and fractions, calculating with the four operations including directed (signed) numbers, and applying the order of operations. This is the bedrock of the whole qualification. Both components test it, and because Component 1 is non-calculator, fluent written and mental arithmetic is essential. A sign slip or an order-of-operations error in the first line of working carries through every later step, so accuracy here protects marks across the entire paper.

Ordering numbers

To order a mixed list of integers, decimals and fractions, put them all in one form first.

For decimals, line up the decimal points and pad with trailing zeros so each has the same number of places: $0.3, 0.305, 0.35$ become $0.300, 0.305, 0.350$, which order easily. For fractions, rewrite them over a common denominator: $\tfrac{2}{3}, \tfrac{3}{4}, \tfrac{5}{8}$ over $24$ are $\tfrac{16}{24}, \tfrac{18}{24}, \tfrac{15}{24}$, so the order is $\tfrac{5}{8} < \tfrac{2}{3} < \tfrac{3}{4}$. With negative numbers, remember the number line: $-7$ is smaller than $-3$, because it lies further left.

The four operations and directed numbers

Adding and subtracting directed numbers is where most marks are lost.

So $-4 \times 6 = -24$ (unlike signs), $-20 \div (-5) = 4$ (like signs), and $-7 - (-10) = -7 + 10 = 3$. A number line helps with the additions and subtractions: start at the first number and step right for $+$ or left for $-$. Distinguishing position (which can be negative) from distance (which cannot) is a recurring exam theme, as in temperature, depth and bank-balance problems.

The order of operations (BIDMAS)

When an expression mixes operations, the order is fixed.

So $5 + 2 \times 3^2 = 5 + 2 \times 9 = 5 + 18 = 23$: the power, then the multiplication, then the addition. Division and multiplication share a level, so $12 \div 2 \times 3$ is worked left to right as $6 \times 3 = 18$, not $12 \div 6$. Treating a fraction bar as a bracket matters: $\dfrac{8 + 4}{2 + 1} = \dfrac{12}{3} = 4$, evaluating top and bottom before dividing.

Why this matters

Calculation underpins every other area of the Eduqas course, from compound measures to probability to solving equations. Because AO1 (using standard techniques) is half of the marks and AO2 and AO3 reward clear reasoning, accurate signed arithmetic and a correct order of operations are constantly assumed rather than re-tested in isolation. Securing them frees attention for the harder reasoning that earns the top grades.