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Add and Subtract Fractions as Joining and Separating Parts

Students understand fraction addition as joining parts and subtraction as separating parts of the same whole. They use visual models to connect the action of combining or removing parts to the symbolic operation, with like denominators.

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Add and Subtract Fractions as Joining and Separating Parts

Grade 4 · Understanding Fraction Addition and Subtraction · question 1 of 3

0 of 20

20 rungs. A star at the top.

4/6 − 1/6 =

How it is taught

0:00 of 3:23

Adding fractions joins same-size parts.

Subtracting fractions takes same-size parts away.

The bottom stays the same.

Read it: Same pieces, a new count

A bar is cut into 6 pieces and 2 of them are shaded: 2/6. 1 more piece of the same size joins them. Now 3 pieces are shaded, and every one is still 1/6, so the bar shows 3/6.

  1. Read the bottom number first: each piece is 1/6 of the bar, and joining does not change that.
  2. Count the pieces that join or leave: here 1 piece joins the 2 that are there.
  3. Count what is shaded now and keep the bottom number: 3 pieces of 1/6 make 3/6.

Joining pieces changes how many are shaded. Nothing cuts the bar again, so every piece stays 1/6.

The bottom number says how big each piece is and the top number counts them, so only the top number changes.

Separating works the same way: take 1 piece away from 3/6 and 2 pieces of 1/6 are left, which is 2/6.

To add or subtract fractions with the same bottom number, add or subtract the top numbers and keep the bottom number.

Adding the bottom numbers too, and writing 2/6 + 1/6 = 3/12.

3/12 is 3 pieces of a bar cut into 12, only half of what is shaded here. Nothing cut the bar again, so the answer is 3/6.

2/4 + 2/4 = ___/4 — 4. 2 pieces and 2 more are 4 pieces, and every piece is still 1/4: 4/4.

2/6 + 3/6

Maya ate two sixths of a pizza. Then she ate three sixths more. How much did she eat in all?

Here's the whole pizza, split into six equal parts — sixths.

First, Maya ate two parts. Let's shade two sixths.

We write that as two over six — two sixths.

Then she joined three more parts. Let's shade three more sixths.

We add three sixths to what she had.

Now let's find the total: two sixths plus three sixths equals what?

Both fractions are sixths, so the bottom number — the denominator — stays six.

Maya's pizza: 26 then 36 moreJoining parts of the same wholejoining parts →26+36=?56Same denominator — sixths stay sixthsAdd the numerators: 2 + 3 = 5ANSWER56of the pizzaSame whole → add numerators, keep denominator
Grade 4 · Joining sixths of the same pizza

We just add the top numbers: two plus three is five.

So two sixths plus three sixths is five sixths.

Maya ate five sixths of the pizza. When we join parts of the same whole, we add the numerators!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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