11+ Fractions: Five Fast Techniques Every Child Should Know Before the Exam

Many children freeze. They reach for long division. They run out of time.

But well-prepared students know something the others do not: you do not need long division every time. You need the right technique for the right situation.

Here are five fraction techniques I teach my students at Embrace Maths. Each one turns a slow, stressful question into a confident, fast one.

Technique 1: The Butterfly Method

Best for: comparing exactly two fractions

When you need to compare just two fractions, the Butterfly Method is one of the fastest tools available. Instead of finding a common denominator (which is slow), you cross-multiply diagonally.

Let's compare 7/9 and 3/4.

Write the two fractions side by side:   7/9   and   3/4

Now cross-multiply in two steps:

1. Multiply the numerator of the left fraction by the denominator of the right: 7 x 4 = 28. Write 28 above the left fraction.
2. Multiply the numerator of the right fraction by the denominator of the left: 3 x 9 = 27. Write 27 above the right fraction.

Compare the two results: 28 > 27. The fraction sitting below the bigger result is the bigger fraction. 28 is above 7/9, so 7/9 > 3/4.

Why "Butterfly"? Draw the two diagonal multiplication lines crossing between the fractions. They look exactly like butterfly wings. Children who visualise this rarely forget which way round it goes.

When to use it:

• Exactly two fractions to compare
• Awkward denominators that do not share obvious common factors
• You need a quick result without much working

For longer lists mixing fractions and decimals, Techniques 2 to 5 are the better tools.

Technique 2: Famous Fractions — Just Memorise These

Best for: instant recognition of the most common 11+ fractions

This is not a trick. It is something more valuable than a trick.

Certain fractions appear so often in 11+ papers that knowing their decimal equivalents instantly, without any calculation at all, is worth genuine marks. These are the ones worth memorising:

A child who has memorised this list is not just saving time on ordering questions. These same fractions appear in percentage questions, word problems, ratio questions and probability and often on the same paper. Knowing them instantly is not one shortcut. It is the same shortcut used ten times over across the exam. So a child who knows this list has already saved themselves a few minutes in the exam before they have even picked up their pencil.

Technique 3: The Scale Up Shortcut

Best for: fractions whose denominator scales neatly to 10 or 100

Some denominators multiply neatly up to 10 or 100. When they do, converting to a decimal takes a single multiplication with no division needed.

Scaling to 10

Denominator is 5? Multiply numerator and denominator by 2.

Example: 3/5 becomes 6/10 = 0.6

Scaling to 100

• Denominator is 25? Multiply by 4.   Example: 17/25 becomes 68/100 = 0.68
• Denominator is 50? Multiply by 2.   Example: 13/50 becomes 26/100 = 0.26
• Denominator is 20? Multiply by 5.   Example: 9/20 becomes 45/100 = 0.45

This technique works for denominators of 5, 20, 25 and 50, all of which appear regularly in 11+ papers.

Technique 4: The Magic 9s Rule

Best for: any fraction with 9 as the denominator

This is the one children love most once they see it. Fractions with 9 as the denominator follow a beautiful pattern:

The numerator simply repeats forever as long as the numerator is smaller than 9. So 7/9 = 0.777, instant, no calculation required.

Once a child sees this pattern, they never forget it.

Technique 5: Adding Zeros to Line Up Decimals

Best for: when decimals with different decimal places look confusing to compare

This one is simple but surprisingly powerful for a 10-year old.

When comparing decimals with different numbers of decimal places, add zeros to make them the same length before comparing.

0.35 looks greater than 0.4 to many children, because 35 feels greater than 4. But write 0.4 as 0.40 and the comparison becomes instantly clear:

This is not a trick so much as a habit. Teach your child to always add zeros to line up decimal places before comparing, and a whole category of careless errors simply disappears.

Putting It All Together

Let's go back to our original question and solve it using these techniques:

Common Mistakes to Avoid

Thinking a bigger denominator means a bigger fraction

3/8 is smaller than 3/4, even though 8 is bigger than 4. A bigger denominator means the pieces are smaller, so the fraction is smaller, not bigger. This is one of the most persistent misconceptions in fraction work, and one I see even in otherwise strong students.

Comparing decimals without lining up the decimal places

0.35 and 0.4 look deceptively different in length. Always add zeros first. Always.

Reaching for long division as a first instinct

Long division is reliable but dangerously slow under exam conditions. It should be a last resort, not a first instinct. The five techniques above cover the vast majority of fractions that appear in 11+ papers.

Quick Practice Challenge

Work through it before reading the solution.

Solution

• 4/5 = 0.8 (Famous Fraction — memorise this one)
• 0.78 = 0.78 (already a decimal)
• 7/10 = 0.70 (Famous Fraction — add zero to align)
• 5/8 = 0.625 — two ways to get there:
  • Short division: 5 divided by 8 = 0.625
  • Using Famous Fractions: 1/8 = 0.125, so 5/8 = 5 x 0.125 = 0.625

Notice that 5/8 needed a little more thought. Not every fraction has an instant shortcut, and part of good exam technique is knowing when to use a technique and when to simply calculate. The goal is always efficiency, not cleverness for its own sake.

Exam-Day Decision Checklist

Print this out and keep it visible during revision:

A Final Word

The 11+ rewards children who work efficiently, not just children who work hard.

These techniques are not shortcuts in the negative sense. They are exactly the kind of mathematical fluency that examiners want to see: the ability to choose a smart approach, apply it confidently, and move on to the next question.

The more your child practises these methods, the more automatic they become. And in the exam room, automatic means fast. Fast means more time for harder questions. More time means more marks.

That is not luck. That is preparation.