VA ClassesAdding and Subtracting Fractions With the Same Denominator
When the bottom numbers already match there is almost nothing to do, which is why the mistake children make here is so revealing: they add the bottoms as well, and the answer comes out smaller than what they started with.
The one idea
Read the fractions out loud rather than looking at the digits. 38 is "three eighths" and 28 is "two eighths", and hearing them said properly does more work than any rule on this page.
Three eighths plus two eighths is five eighths, for exactly the reason three apples plus two apples is five apples. Nobody has ever answered that question with "five apple-apples", and yet 516 is the single most common answer children give here, because the digits are sitting there in pairs asking to be added.
The rule
When the denominators match, add or subtract the numerators and keep the denominator exactly as it is.
The bottom number is the size of the pieces. You are not changing the pieces, only counting them.
Adding
So 38 + 28 = 58, and the 8 sits there untouched throughout, because nothing in the picture ever cut the bar again.
Subtracting
Subtraction is the same picture read backwards: start with what you have, take some pieces away, count what survives.
So 78 minus 38 = 48, which tidies to 12.
Tidying the answer
48 is a correct answer to the arithmetic and an incomplete answer to the question, because almost every mark scheme wants the simplest form and will not award the mark without it.
- If the top and bottom share a factor, simplify. 48 becomes 12.
- If the top ends up equal to the bottom, the answer is 1. 55 is one whole.
- If the top ends up bigger than the bottom, that is an improper fraction and it is a perfectly good answer, though some questions ask for it as a mixed number.
Worked examples
A straightforward sum
- Check the bottom numbers. Both are 9, so no rewriting is needed.
- Add the top numbers only. 2 + 5 = 7.
- Keep the denominator as 9.
- Can 79 be simplified? 7 is prime and does not divide into 9, so no.
An answer that needs tidying
- Denominators match at 12, so add the tops. 5 + 3 = 8, giving 812.
- Now check whether it simplifies. Both 8 and 12 are even, so it does.
- The highest common factor is 4. 8 ÷ 4 = 2 and 12 ÷ 4 = 3.
- Finished check: 2 and 3 share nothing but 1.
A subtraction word problem
- Both amounts are in tenths, so the pieces are the same size.
- Subtract the top numbers. 9 − 4 = 5.
- The denominator stays 10, giving 510 of a litre.
- Simplify: both divide by 5, giving 12.
Common mistakes
1. Adding the bottom numbers as well
38 + 28 comes out as 516. Almost every child does this at least once, and telling them the rule again rarely helps. Send them back to the picture instead and ask when the bar was ever cut into sixteen pieces. It never was. Then ask whether an answer can be smaller than what you started with after adding something to it, and let them work out that their own answer fails that test.
2. Leaving the answer unsimplified
The working stops at 812 instead of going on to 23. Every step of the arithmetic was right and the mark still goes, which children find genuinely unfair until somebody explains that simplifying is not a bonus, it is the last step of the question.
3. Using this rule when the denominators do not match
Writing 12 + 13 = 25. The pieces are different sizes, so they cannot be counted together yet. That case needs a common denominator first, which is the next topic.
Practice questions
Seven questions. One attempt each, and the explanation appears once the answer is in.
Check yourself
No sign up. Nothing is sent anywhere, the score stays on this device.
For parents
When your child adds the bottom numbers, resist the urge to correct it straight away. Ask instead whether the answer ought to come out bigger or smaller than what they began with. They will say bigger without hesitating, because that part is obvious to them, and then they will look back at their own answer and see that it is smaller. A child who catches their own mistake that way tends not to repeat it, which is not something you can say for being told.
Keep going
Still stuck on this?
Send us the question and a teacher will answer it. No charge, and you do not have to be a student here.
What to learn next
Everything in the Learning Hub
Every topic is free and every one ends with practice questions. Start anywhere.
Fractions
Math · 9 topics
What Is a Fraction?Equivalent FractionsSimplifying FractionsComparing FractionsAdding and Subtracting Fractions With the Same DenominatorAdding Fractions With Different DenominatorsFinding a Fraction of a NumberMixed Numbers and Improper FractionsFractions to DecimalsDecimals and percentages
Math · 7 topics
What Are Decimals?Comparing and Ordering DecimalsAdding and Subtracting DecimalsRounding DecimalsWhat Are Percentages?Finding a Percentage of a NumberFractions, Decimals and PercentagesScience: matter and the water cycle
Science · 5 topics
What Is Matter?Solids, Liquids and GasesChanging StateThe Water CycleMixtures and SolutionsWhole numbers
Math · 10 topics
Place Value to 1,000,000Rounding Whole NumbersAdding and Subtracting With RegroupingTimes Tables That Actually StickMultiplying by 10, 100 and 1000Long Multiplication, Step by StepShort DivisionLong Division, Step by StepFactors, Multiples and PrimesOrder of OperationsForces and energy
Science · 6 topics
Forces and MotionFrictionGravity, Mass and WeightLevers and Simple MachinesEnergy and Its FormsSimple CircuitsEnglish: words and sentences
English · 6 topics
Nouns, Verbs and AdjectivesWhat Makes a Sentence, and What Does NotCapital Letters, Full Stops and CommasApostrophesVerb TensesSubject and Verb AgreementStuck on this topic? Get one class, free.
A tutor works through it live with your child, one on one, and sends you a short written report afterwards. No card needed.