Numerical Ability lesson

Fractions and Decimals: The Operations

Convert, compare, add, subtract, multiply and divide fractions and decimals with one clear procedure each, and check every answer.

30 min read · Professional and Sub-Professional

What it is

A fraction like 3/4 means 3 parts out of 4 equal parts. The top number is the numerator (how many parts you have); the bottom number is the denominator (how many equal parts make one whole). A decimal like 0.75 writes the same amount using tenths, hundredths and so on. 3/4 and 0.75 are the same amount written two ways.

Why it matters on the exam

Fractions and decimals appear in almost every numerical item: computations, percent problems, word problems about money and time, and data interpretation. If the basic operations are automatic, you save time and avoid the traps the exam builds into the choices (adding denominators, putting the decimal point in the wrong place, flipping the wrong fraction).

Rule 1 of 7Converting between fractions and decimals, and reducing
Fraction to decimal: divide the top by the bottom. Decimal to fraction: write the digits over 10, 100, 1000 (one zero per decimal place), then reduce by dividing top and bottom by their GCF.
Worked example 1 of 3Subtracting mixed numbers with borrowing
A roll had 3 1/3 meters of ribbon. A staff member cut off 1 3/4 meters. How much ribbon is left?
  1. 1 7/12 m
  2. 2 5/12 m
  3. 1 5/12 m
  4. 2 7/12 m
Step 1 · What is asked?"How much is left" means subtract: 3 1/3 − 1 3/4.
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In the full lesson

  • How to recognize it on the test
  • What to look for (5 checks)
  • All 7 rules and tools
  • 3 worked examples, every step explained
  • 6 common mistakes and how to fix them
  • 3 exam techniques
  • Remember: 5 key points
  • Practice questions with explanations, and your progress saved
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More Numerical Ability lessons

ReviewTayo has 47 lessons that follow the official scope of the exam, each with rules, worked examples, common mistakes and practice. Open one and read the first part.

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