A girl and her brother admire a fresh pan of cornbread

Joining and Separating Fractions

Maya baked a pan of cornbread and cut it into equal pieces. How can she share it fairly with her brother?

4th Grade Math

Step 1: Read the Model

Maya cut her cornbread into 8 equal parts. The shaded parts are the pieces she wants to eat. What fraction of the pan is shaded?

The denominator 8 counts the equal parts in the whole. The numerator 3 counts the shaded parts. The model shows 3/8.

Step 2: Join the Parts

Maya eats 3/8 of the pan. Her brother Leo eats 2/8 of the same pan. How much did they eat together?

Adding fractions means joining parts of the same whole. Add the numerators: 3 + 2 = 5. The pieces are still eighths, so 3/8 + 2/8 = 5/8.

The Big Idea

Adding Fractions = Joining Parts

          Step 1: Check that both fractions refer to the same whole.

          Step 2: Add the numerators.

          Step 3: Keep the denominator the same.

Maya says: Eighths plus eighths always makes eighths. The size of the pieces never changes when we join them!

Step 3: Separate the Parts

The next day, 7/8 of a new pan is left. Maya gives 4/8 to her neighbor. How much cornbread is left now?

Subtracting means separating parts from the whole. Take 4 eighths away: 7 - 4 = 3. The pieces are still eighths, so 7/8 - 4/8 = 3/8.

Watch Out!

A Common Mistake

          3/8 + 2/8 does NOT equal 5/16!

          The denominator names the size of the parts.

          Joining parts never changes their size.

          Only the numerator changes.

If you add the denominators, your pieces suddenly shrink. That would not be fair to anyone!

Solve It!

2/6 + 3/6 = ?

The parts are sixths. Join them by adding the numerators: 2 + 3 = 5. So 2/6 + 3/6 = 5/6. The denominator stays 6.

Word Problem

Nia painted 4/10 of a fence. Her cousin Theo painted 3/10 of the same fence. Determine how much of the fence they painted together.

Both fractions refer to the same fence, so we can join the parts. 4 + 3 = 7 tenths. Together they painted 7/10 of the fence.

What Goes in the Blank?

3/6 + ? = 5/6

Think: 3 sixths plus how many sixths makes 5 sixths? 5 - 3 = 2, so the missing fraction is 2/6. Check: 3/6 + 2/6 = 5/6.

Word Problem

Sam's water bottle was 7/8 full. On his hike, he drank 3/8 of the bottle. What fraction of the bottle is left?

Drinking separates parts from the whole, so we subtract. 7 - 3 = 4 eighths. That means 7/8 - 3/8 = 4/8 of the bottle is left.

Match the Model

Analyze the model. Both bars show parts of the same whole. Which equation does the model show?

Each bar shows 2/6 shaded. Joining them gives 2 + 2 = 4 sixths. So the model shows 2/6 + 2/6 = 4/6.

Challenge!

A hiking trail is split into 12 equal sections. Ava hiked 5/12 in the morning and 4/12 after lunch. What fraction of the trail is left to hike?

First join the hiked parts: 5/12 + 4/12 = 9/12. The whole trail is 12/12. Now separate: 12/12 - 9/12 = 3/12 of the trail is left.

When might you join or separate parts of a whole in your own life? Think of one example with food and one without.

Great Work!

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correct

fraction numerator denominator determine analyze