Fraction Word Problems
Solve word problems involving addition and subtraction of fractions with unlike denominators, using visual models and benchmark fractions to estimate and assess reasonableness
What a learner can do afterwards
- Solve: 'Tara ate 2/5 of a pizza and Sam ate 1/3. How much did they eat together?'
- Recognise that 2/5 + 1/2 ≠ 3/7 because 3/7 < 1/2 but the sum should exceed 1/2
- Estimate a fraction sum using benchmarks (0, 1/2, 1) before computing exactly
The lesson
You already know how to add and subtract fractions with different denominators. Word problems just hide that same math inside a story. Read carefully, find the fractions, and rewrite them with a common denominator before you add or subtract.
Tara ate 2/5 of a pizza and Sam ate 1/3. To add them, rewrite with a common denominator of 15: 2/5 = 6/15 and 1/3 = 5/15. Together they ate 6/15 + 5/15 = 11/15 of the pizza.
Watch out for this mistake: adding numerators and denominators straight across. 2/5 + 1/2 is NOT 3/7, because 3/7 is less than 1/2, but adding a positive fraction to 1/2 must give you more than 1/2. If your answer looks too small, check your work.
Mia walks 1 and 1/2 miles to school and 3/4 of a mile to a friend's house. Estimate first: 1/2 is close to 1/2 and 3/4 is close to 1, so the fraction parts should add to a little less than one and a half. Exact answer: 1/2 + 3/4 = 2/4 + 3/4 = 5/4 = 1 and 1/4. Total distance: 1 + 1 + 1/4 = 2 and 1/4 miles, which matches the estimate.
Rewrite fractions with a common denominator to add or subtract in word problems, and use benchmarks like 0, 1/2, and 1 to check that your answer makes sense.
Watch it
Where it sits
This opens up
Nothing builds on it yet.
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.