Key ideas
Same denominator
Add or take away the numerators. The denominator stays the same.
27 + 37 = 57
Different denominators
Change them to equivalent fractions with the same denominator first. Use the lowest common multiple.
13 + 14 = 412 + 312 = 712
Mixed numbers
Add the whole numbers, then add the fractions.
If the fractions come to more than 1, carry the whole one over.
From a whole number
Borrow 1 whole and write it as a fraction:
3 − 25 = 2 + 55 − 25 = 235
Typing answers: fractions like 5/7, mixed numbers like 2 3/5 (a space between). Always simplify.
Same denominator
Calculate 38 + 18. Simplify your answer.(2 marks)
Add the numerators.38 + 18 = 48✓1
In plain English3 eighths and 1 eighth make 4 eighths. The denominator doesn't change.
Simplify.48 = 12 ÷ 4 top and bottom✓2
In plain English4 goes into both 4 and 8.
⚠ A common mistake: adding the denominators too: 416. The pieces are still eighths.
Different denominators
Calculate 23 + 14.(3 marks)
Find a common denominator.Multiples of 3: 3, 6, 9, 12Multiples of 4: 4, 8, 12LCM = 12✓1
In plain EnglishThe lowest common multiple of 3 and 4 is 12.
Change to twelfths.23 = 812, 14 = 312✓2
In plain English× 4 top and bottom for thirds, × 3 top and bottom for quarters.
Add.812 + 312 = 1112✓3
In plain EnglishNow the denominators match, add the numerators and keep the denominator the same. 11/12 cannot be simplified.
Calculate 56 − 14.(3 marks)
Common denominator.LCM of 6 and 4 = 12✓1
In plain EnglishThe lowest common multiple of 6 and 4 is 12, so change both fractions to twelfths.
Equivalent fractions.1012 − 312✓2
In plain English× 2 top and bottom for sixths, × 3 top and bottom for quarters.
Subtract.= 712✓3
In plain EnglishTake away the numerators and keep the denominator. 7/12 cannot be simplified.
Mixed numbers
Calculate 234 + 112.(3 marks)
Whole numbers.2 + 1 = 3✓1
In plain EnglishAdd the whole numbers first.
Fractions.34 + 24 = 54 = 114✓2
In plain EnglishChange halves to quarters. 5 quarters is 1 whole and 1 quarter.
Put them together.3 + 114 = 414✓3
In plain EnglishAdd the 1 whole from the fractions to the 3 wholes you already had.
Calculate 413 − 156.(3 marks)
Make them improper.413 = 133 = 266, 156 = 116✓1
In plain EnglishThe second fraction is bigger than the first, so it is easiest to change both to improper fractions with the same denominator.
Subtract.266 − 116 = 156✓2
In plain EnglishThe denominators are the same, so take away the numerators.
Simplify.156 = 52 = 212✓3
In plain English3 goes into 15 and 6, so simplify. Then change the improper fraction back to a mixed number: 5 halves is 2 wholes and 1 half.
Fractions from whole numbers
Calculate 3 − 25.(2 marks)
Split off one whole.3 = 2 + 55✓1
In plain EnglishOne whole is 5 fifths.
Take away.55 − 25 = 35= 235✓2
In plain EnglishTake 2 fifths away from the 5 fifths, then put the 2 wholes back.
Whole numbers and mixed numbers
Calculate (a) 5 + 38 (b) 623 − 4.(2 marks)
Adding a whole number.5 + 38 = 538✓1
In plain EnglishThe whole number and the fraction just join together.
Taking a whole number away.623 − 4 = 223✓2
In plain EnglishTake the 4 from the whole number part. The fraction stays the same.
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Your turn
Non-calculator. Type fractions like 5/7 and mixed numbers like 2 3/5. Simplify your answers. Stuck? Tap Need a hint?