Ordering integers, decimals and fractions

This is foundational for the whole WJEC GCSE — every Foundation paper opens with an ordering question worth 2–3 marks.

Ordering integers (positive and negative)

On a number line, numbers increase as you move right. So -7 < -3 < 0 < 4 < 11. The bigger the magnitude of a negative number, the smaller it is: -100 is less than -1.

Ordering decimals

Compare digit by digit, from the left:

1. Match decimal places by adding trailing zeros: 0.7, 0.65, 0.703 → 0.700, 0.650, 0.703.
2. Compare like whole numbers: 650 < 700 < 703.
3. So 0.65 < 0.7 < 0.703.

WJEC trap: students assume "more digits after the point = larger". 0.45 is smaller than 0.5. Always pad with zeros first.

Ordering fractions

Three reliable methods:

Method 1 — Common denominator. For 2/3, 3/5, 7/10:

• LCM(3, 5, 10) = 30. So 20/30, 18/30, 21/30. Order: 18/30 < 20/30 < 21/30, i.e. 3/5 < 2/3 < 7/10.

Method 2 — Convert to decimals (calculator paper). 2/3 = 0.667, 3/5 = 0.6, 7/10 = 0.7. Order: 0.6, 0.667, 0.7.

Method 3 — Cross-multiplication for two fractions only. To compare a/b and c/d, compare ad with bc. If ad > bc then a/b > c/d.

Mixed lists (the typical WJEC question)

"Place these in order, smallest first: 0.45, 1/2, 0.5, 3/8, 40%."

Convert everything to one form (decimals are easiest with a calculator):

• 0.45 = 0.45
• 1/2 = 0.5
• 0.5 = 0.5
• 3/8 = 0.375
• 40% = 0.4

Order: 0.375, 0.4, 0.45, 0.5, 0.5 → 3/8, 40%, 0.45, 0.5 = 1/2.

WJEC exam tip

Always re-write the answer using the original notation the question asked for, not your converted decimals. The B1 mark requires the original list ordered correctly.