# Keep the Unit When Adding > **Is 1/5 + 2/5 equal to 3/10?** No. 1/5 + 2/5 = 3/5. Joining one fifth and two fifths gives three fifths: the number of pieces changes, but each piece is still a fifth. 3/10 is only half as much as 3/5. - Big idea: Adding like parts changes how many parts there are, not their size: 1/5 + 2/5 = 3/5. - Common confusion: When fractions have the same denominator, add the denominators too, so 1/5 + 2/5 = 3/10. - It often sounds like this: “1/5 + 2/5 is 3/10, because five plus five is ten.” - Family: Working With Fractions (slice 17 of 20) - Try it yourself (about 3 minutes, free): https://slices.org/slices/keep-the-unit-when-adding ## In plain words The denominator names the size of the pieces. In 1/5 and 2/5, every piece is one fifth of the same whole. Adding joins the pieces: one fifth and two more fifths make three fifths. The number of pieces changes, but their size does not, so 1/5 + 2/5 = 3/5. Adding the denominators as well gives 3/10. But tenths are half the size of fifths, so 3/10 is only half of 3/5. Joining pieces can’t make each piece smaller. It helps to read the denominator as a unit, like a word: 1 apple + 2 apples = 3 apples, and 1 fifth + 2 fifths = 3 fifths. The same counting works past one whole: 4/5 + 3/5 = 7/5, which is one whole and two fifths more. ## A worked example A chocolate bar is made of 5 equal squares, so each square is 1/5 of the bar. Eat 1 square, then 2 more, and you have eaten 3 squares: 3/5 of the bar. The squares didn’t shrink into tenths along the way. ## Why this confusion is common Children who have learned to add whole numbers often add every number they can see, so 1/5 + 2/5 becomes 3/10. It usually means the denominator is being read as a count of things rather than as the name of a unit. Saying the units aloud helps: one fifth plus two fifths is three fifths, just as one apple plus two apples is three apples. ## Try this away from the screen Make a whole from 5 identical blocks or tiles, so each one is 1/5. Hand over 1 block, then 2 more, counting aloud in fifths: one fifth, two fifths, three fifths. Ask: did any block change size when we joined them? Would 3/10 mean the blocks got smaller? ## Helpful ways to talk about it - Instead of “Add the tops, but leave the bottoms alone.”, try: “What size are these pieces? When we join them, how many of those pieces do we have?” - Instead of “The bottom number stays the same because that’s the rule.”, try: “Say it in words: one fifth plus two fifths. What do you get?” ## Practice questions 1. Mia eats 2/7 of a chocolate bar and Leo eats 3/7 of it. How much of the bar do they eat altogether? **Answer:** 5/7. They eat 2 pieces and 3 pieces of the same 7-piece bar: 5 pieces. The pieces are still sevenths, so 2/7 + 3/7 = 5/7. 2. What is 3/4 + 3/4? Use the number line to help. **Answer:** 6/4. Fourths stay fourths: 3 fourths + 3 fourths = 6 fourths. Six fourths from 0 is one whole and two fourths more, so 3/4 + 3/4 = 6/4. 3. What is 1/6 + 4/6? **Answer:** 5/6. One slice and four more slices of the same 6-slice pizza make five slices. The slices are still sixths, so 1/6 + 4/6 = 5/6. 4. Ana says 3/8 + 3/8 = 6/16. Is she right? **Answer:** No. Eighths stay eighths, so 3/8 + 3/8 = 6/8. Ana’s 6/16 is the same as 3/8, which would mean adding 3/8 made no difference. 5. Use sixth pieces to build 2/6 + 4/6. **Answer:** use pieces of 1/6 to make 6/6. Two sixths and four more sixths make six sixths, which fill the whole: 2/6 + 4/6 = 6/6 = 1. Adding the bottom numbers would give 6/12, which is only one half. ## Questions people ask ### Why does the denominator stay the same when you add fractions with the same denominator? Because the denominator names the size of the pieces. One fifth plus two fifths is three pieces that are each one fifth: 3/5. Joining pieces doesn’t make them smaller, so the denominator stays the same. ### What happens when the answer is more than one whole? Keep counting the same pieces. 5/6 + 4/6 = 9/6, which is one whole (6/6) and three sixths more. You can also write it as 1 3/6, or 1 1/2. ### How do I explain this to my child? Say the unit out loud. “One fifth plus two fifths” works like “one apple plus two apples”: the answer is three of the same thing, three fifths. Then check it with paper strips or a drawn bar. ## Curriculum connections (US Common Core) - 4.NF.B.3: Understand a fraction a/b with a > 1 as a sum of fractions 1/b. - 4.NF.B.3.a: Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. - 4.NF.B.3.d: Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. ## Related slices - [Adding Different Pieces](https://slices.org/slices/adding-different-pieces): Why 1/2 + 1/4 is 3/4, not 2/6: make the pieces the same size before you count them. - [The Top Number](https://slices.org/slices/the-top-number): What the top number of a fraction counts: how many of the equal parts you have. - [The Bottom Number](https://slices.org/slices/the-bottom-number): What the bottom number of a fraction counts: all the equal parts that make one whole. - [More Than One Whole](https://slices.org/slices/more-than-one-whole): Why 6/4 makes sense: a fraction can equal one whole or go beyond it.