Adding fractions with the same denominator

A quarter plus a quarter

Two chocolate squares plus three squares = five squares. That makes sense. And that is exactly how adding fractions with the same denominator works: 2/8 + 3/8 = 5/8.

The key is that the parts are the same size. Eighths plus eighths — like squares plus squares. You only add the counts of parts (the numerators) and you leave the name of the part (the denominator) alone.

So the rule is: add the numerators, copy the denominator. Never add the denominators! 2/8 + 3/8 is not 5/16 — that would count you towards a SMALLER piece of chocolate than you had at the start. Nonsense.

Subtracting is the same, just with minus: 5/8 − 2/8 = 3/8.

Today is a short and straight lesson. Enjoy it — it is the simplest fraction counting there is. Next lesson we step it up: what if the denominators are not the same?

Adam and Filip split a pizza cut into 8 parts. Adam ate 3/8, Filip 2/8. “How much did we scoff together?” Filip asks. Adam adds out loud: “Three pieces and two pieces is five pieces. Five eighths.” Filip tries to wind him up: “And is it not five sixteenths? Eight plus eight…” Adam points at the box: “The pizza did not get cut into more pieces by adding. The pieces are still eighths — we just have five of them together.” In the box 3/8 is left and both know exactly why: 8/8 − 5/8.

💡

When the result can be simplified, simplify it: 2/8 + 2/8 = 4/8 = 1/2. An answer in simplest form is the calling card of a good counter.

Add the counts, leave the name

Adding method (same denominators):

Check that the denominators really are the same. (When they are not, this lesson is not enough — that is next lesson’s topic.)
Add the numerators: 2 + 3 = 5.
コピー the denominator: still eighths. Result 5/8.
When you can, simplify the result to simplest form.

Subtracting works the same: 7/10 − 3/10 = 4/10 = 2/5 (simplified by two).

Why the denominator does not change: the denominator is the name of the part — it says how big the pieces you add are. Three apples + two apples = five apples, not five “apple-apples”. Three eighths + two eighths = five eighths.

What if the result overflows a whole? 5/8 + 6/8 = 11/8. A numerator bigger than the denominator means more than one whole: 11/8 = 8/8 + 3/8 = 1 whole and 3/8. That write-up is called a mixed number. Eleven eighths of pizza = one whole pizza and three pieces on top.

And a check as always: the result must make sense. Adding parts makes more of them, subtracting makes fewer — if after adding you get a smaller fraction, something is wrong.

Work out 3/10 + 4/10

Step 1: Same denominators (tenths)? Yes.

Step 2: I add the numerators: 3 + 4 = 7.

Step 3: I copy the denominator: 7/10.

Step 4: Can it be simplified? 7 and 10 have no common factor — it is already in simplest form.

Picture it: a chocolate board into 10 squares. Three squares plus four squares = seven squares out of ten.

Work out 11/12 − 5/12 and simplify

I subtract the numerators: 11 − 5 = 6. I copy the denominator: 6/12.

I simplify: 6 and 12 can both be divided by six: 6/12 = 1/2.

Does it make sense? 11/12 is almost a whole, I subtracted not quite a half — about a half should be left. It fits.

Unsimplified 6/12 is not exactly a mistake, but 1/2 is the answer everyone understands at a glance.

Does it work out for three friends at 2/8 of pizza each?

5/8 of pizza is left. Tereza, Sofie and Jonáš each want 2/8. Does it work out?

I add how much they want together: 2/8 + 2/8 + 2/8 = 6/8.

I compare with the stock: they need 6/8, 5/8 is available. And 6/8 > 5/8 — it does not work out, 1/8 is missing.

A fix? Each gets an equal share: 5/8 : 3… we will leave that for later. For now it is enough: you can add three fractions at once too, still with the same rule.

⚠️

Denominators are not added. 2/8 + 3/8 = 5/8, not 5/16. Adding two pieces of pizza does not make a pizza cut into more parts. The denominator is the name of the part — and a name does not change by adding.

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. スタート with ten. When it goes well, add more.

Add fractions with the same denominator: add the numerators, copy the denominator. Write the answer as a fraction with a slash, for example 5/8.

Practise the questions

On paper

Short questions, but write them in full — including the step “simplify?” at the end.

Work out: 2/7 + 4/7, then 5/9 + 2/9, then 3/4 + 3/4. Write the last result as a mixed number too (a whole and a remainder).
Work out and simplify: 5/12 + 1/12, then 7/10 − 3/10, then 9/8 − 3/8.
Sofie drank 3/8 of a bottle, Adam 2/8 of the same bottle. How much did they drink together and how much is left in the bottle? (A whole bottle = 8/8.)
Invent two fractions with denominator 6 whose sum is exactly 1. Then another pair whose sum is more than 1.

Now you 💪

I can add two fractions with the same denominator and I know why the denominator stays.
I automatically try to simplify the result.
I understand the write-up 11/8 = 1 whole and 3/8.

✅

Done when: You add and subtract fractions with the same denominator with the rule “add the numerators, copy the denominator” and you give the result in simplest form.

What to take from this lesson

Same denominators = parts the same size. You only add the counts of parts.
Add (subtract) the numerators, copy the denominator. 2/8 + 3/8 = 5/8.
Denominators are NEVER added — a pizza does not get cut into more pieces by adding.
Numerator bigger than denominator = more than a whole: 11/8 = 1 whole and 3/8.
Simplify the result at the end: 6/12 = 1/2.