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Section 7.1 · Number

Fractions and equivalence

Recognise equivalent fractions, simplify, compare and order fractions, and convert between improper fractions and mixed numbers.

6 teaching slides 75 practice questions Worked answers for every question

1 · Teaching slidesuse ← → keys

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2 · Key words

numeratorThe top number: how many parts you have.
denominatorThe bottom number: how many equal parts make the whole.
equivalent fractionsFractions with the same value, such as 2/4 and 1/2.
simplest formWhen the numerator and denominator share no factor except 1.
improper fractionOne whose numerator is at least its denominator, such as 7/4.
mixed numberA whole number and a fraction together, such as 1 3/4.
common denominatorThe same denominator, used so two fractions can be compared.

3 · Summary of the sectionrevise from this

  • The denominator says how many equal parts make the whole; the numerator says how many you have.
  • Multiply or divide both parts by the same number to get an equivalent fraction. Adding does not work.
  • To simplify, divide both parts by their HCF — one step, not several.
  • To compare, rewrite both over a common denominator, then compare the numerators.
  • The lowest common denominator is the LCM of the two denominators.
  • An improper fraction is at least 1; a mixed number shows the whole part separately.
  • 7/4 → 7 ÷ 4 = 1 remainder 3 → 1 3/4. Going back: 1 × 4 + 3 = 7.
  • Never compare numerators until the denominators match — that is the commonest mistake in this unit.
PDFPrintable worksheet All 75 questions, space to work PDFWorked answers Full solutions, not just the answer

Video lessons3 videos

Math Antics - Simplifying Fractions

American mathantics

Dividing top and bottom by a common factor, and why that leaves the value unchanged.

Math Antics - Comparing Fractions

American mathantics

Why a common denominator is needed before two fractions can be compared.

Math Antics - Mixed Numbers

American mathantics

Converting both ways between mixed numbers and improper fractions.

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4 · Practice75 questions, easiest first

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7.2 Adding and subtracting fractions