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Section 7.2 · Number

Adding and subtracting fractions

Add and subtract fractions and mixed numbers, using a common denominator and simplifying the answer.

6 teaching slides 50 practice questions Worked answers for every question

1 · Teaching slidesuse ← → keys

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2 · Key words

common denominatorThe same denominator for both fractions.
lowest common denominatorThe LCM of the two denominators.
equivalent fractionThe same value written with a different denominator.
mixed numberA whole number and a fraction together.
simplifyDivide numerator and denominator by their HCF.

3 · Summary of the sectionrevise from this

  • You can only add or subtract fractions when the denominators match — the parts must be the same size.
  • Find the lowest common denominator: the LCM of the two denominators.
  • Rewrite each fraction over that denominator, then add or subtract the numerators only.
  • The denominator does not change when you add. 2/7 + 3/7 = 5/7, not 5/14.
  • Simplify the answer, and write an improper answer as a mixed number if the question is in mixed numbers.
  • For mixed numbers, either add the parts separately or convert to improper fractions first.
  • For subtracting mixed numbers, converting to improper fractions avoids borrowing — it is the safer route.
  • Estimate first: 1/2 + 1/3 must be more than 1/2, so an answer of 2/5 is wrong before you check anything else.
PDFPrintable worksheet All 50 questions, space to work PDFWorked answers Full solutions, not just the answer

Video lessons1 videos

Math Antics - Adding and Subtracting Fractions

American mathantics

The common-denominator method, built up from what the parts actually mean.

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4 · Practice50 questions, easiest first

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7.1 Fractions and equivalence
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7.3 Multiplying fractions