Read, write and order integers and decimals, use the four operations with directed numbers and decimals, apply the order of operations (BIDMAS), and use factors, multiples, primes, the HCF and the LCM.

What this dot point is asking

This is the bedrock of the CCEA Number and Algebra strand. You must read, write and order whole numbers and decimals using place value, calculate confidently with the four operations on integers and decimals (including negatives), apply the correct order of operations, and use factors, multiples and primes to find the highest common factor and lowest common multiple. These skills appear on every module from M1 to M8, on both the non-calculator and calculator work, and weak arithmetic here leaks marks across the whole specification.

Place value and ordering

Every digit's value depends on its column. In $4205.6$ the $4$ means four thousand, the $2$ means two hundred, and the $6$ after the point means six tenths. Reading place value correctly is what lets you multiply and divide by powers of ten: multiplying by $10$ shifts every digit one column to the left, and dividing by $100$ shifts every digit two columns to the right.

To order decimals, line them up by their decimal points and compare column by column from the left. The number $0.4$ is larger than $0.39$, because $0.4 = 0.40$ and four tenths beat three tenths, even though $39$ looks bigger than $4$. Filling the shorter decimal with trailing zeros makes the comparison fair.

The four operations with directed numbers

Negative numbers (directed numbers) appear in temperature, money and algebra, so the sign rules must be automatic.

For addition and subtraction, think of a number line. Adding a negative moves left, so $5 + (-8) = -3$. Subtracting a negative moves right, so $-2 - (-6) = -2 + 6 = 4$. The shortcut is that two signs together combine: $+ -$ and $- +$ become a minus, while $- -$ becomes a plus.

For multiplication and division, like signs give a positive and unlike signs give a negative. So $(-4) \times (-3) = 12$, but $(-4) \times 3 = -12$ and $20 \div (-5) = -4$. The same rule applies however many factors there are: an even number of negatives gives a positive result and an odd number gives a negative.

The order of operations

When an expression mixes operations, the order matters. The agreed convention is BIDMAS.

So $6 + 2 \times 5 = 6 + 10 = 16$, not $40$, because the multiplication is done first. And $(6 + 2) \times 5 = 8 \times 5 = 40$, because the brackets override the order. With indices, $3 + 4^2 = 3 + 16 = 19$, since the power is evaluated before the addition.

Factors, multiples and primes

A factor divides exactly into a number; a multiple is the result of multiplying a number by an integer; a prime has exactly two factors, $1$ and itself. The number $1$ is not prime because it has only one factor.

Writing a number as a product of primes is the key technique, because it unlocks the HCF and LCM.

Why this matters

Place value drives standard form and decimal arithmetic; directed numbers underpin all of algebra; the order of operations governs how every formula is evaluated; and the HCF and LCM are exactly the tools used to add fractions and to solve problems about repeating events. CCEA writes these skills into questions across all eight modules, so fluency here is the highest-value investment in the whole course.