A wrong answer can give you something useful: a chance to figure out what the numbers actually mean.
Someone wrote 3/4 + 1/2 = 4/6. Before you fix it, pause. Why might that answer seem reasonable? What was the student treating as if it worked the same way as whole-number addition?
I want you to do more than replace the answer. Your job is to explain the mistake in a way that helps another student understand it. Use a sketch, words, or a number line, and keep the same-sized whole throughout.
I can use equal-sized parts to add fractions and explain why adding the denominators does not work.
- I name the mistake.
- I represent both fractions using the same-sized parts.
- I check whether my sum is reasonable.
Notice before you calculate
Three-fourths is already greater than one-half. Adding another one-half should give a total greater than three-fourths. But 4/6 equals 2/3, which is less than 3/4. That tells us the proposed answer cannot be correct.
The denominator tells you the size of the equal parts: fourths, halves, sixths. Adding the denominators changes the size of the pieces. It does not combine the pieces you started with.
Your turn: Fix the fraction mistake
Big question: Why can’t you add fraction denominators the same way you add numerators?
Answer two questions: (1) Correct 3/4 + 1/2 by rewriting both fractions in fourths. Show your steps. (2) Explain why the original method is wrong and why your answer makes sense.
Help: One-half is the same amount as two-fourths. “I changed ___ to ___ because ___.”
Optional stretch challenge
Try 2/3 + 1/6 using sixths, and explain why the result is less than 1.
Check a new problem
A student writes 2/3 + 1/6 = 3/9. Use sixths to correct the answer. Then explain why your result is less than 1.
Check your reasoning
2/3 = 4/6, so 4/6 + 1/6 = 5/6. Five sixths is one sixth short of a whole. If you got 3/9, return to the size of the pieces before adding.
Record your work in your notebook or the response space your teacher assigns. Before submitting, check that your model and equation agree. You can practice other number relationships in the Math Arcade or use a lesson in the math learning pathways.
17 Responses
“The denominator tells us that it doesnt change. I rewrote as 9/2 so I could count all of the numbers. My answer makes sense because 3/4,1/2,46 equals 9/2.”
It must be greater than 1 because 2:4 is exactly half of a whole, and 3:4 is more than half of a whole. When you combine two amounts that are each at least half, their total will always cross over into more than one full whole.
The size of the equal parts is in a denominator.
I changed on to1/2 into 2/4 so I could add 3/4 + 2/4 = 5/4 = 1 1/4
My answer makes sense since 3/4 + 1/2 is greater than 1.
The denominator tells us that it doesn’t change. I rewrote as 5/4 so I could count the numbers. My answer makes sense because 2/4 + 3/4=5/4.
I think it is greater than 1 because 2:4 is exactly half of a whole, and 3:4 is more than half of a whole. when you combine two amounts that are each at least half, their will always cross over into more than one full whole.
The person wrote 3/4 + 1/2 = 4/6. The first mistake they made is not fact checking if their rewrite of 1/2 was right. It’s supposed to be 2/4. The second mistake is when they changed the denominator to a 6 because they can still match the two fractions while keeping it at a 4. The last mistake they made is when they added the fractions together. 3/4 + 2/4 is 5/4.
The denominator tells us that it doesn’t change. I rewrote as 9/2 so I could count all of the numbers. My answer makes sense because 3/4,1/2,46 equals 9/2
The denominator tells me the size of the equal parts I am counting. I wrote 1/2 as 2/4 so I could count how many fourths there are. My answer is correct because 3/4 only needs 1/4 more to make a whole, so adding 2/4 must give a total bigger than one I think.
The denominator tells me the size of the equal parts I am counting. I wrote 1/2 as 2/4 so I could count how many fourths there are. My answer is correct because 3/4 only needs 1/4 more to make a whole, so adding 2/4 must give a total bigger than one I think.
The size of the equal parts is in a denominator.
I changed on to 1/2 into 2/4 so I could add 3/4 + 2/4 = 5/4 = 1 1/4
My answer makes sense since 3/4 + 1/2 is greater than 1.
The denominator tells us it doesn’t change I rewrote 1/2 as 2/4 so It would be more accurate and sense. My answer makes sense because 2/4+3/4=5/4 which would be the correct answer.It would be more than 1 because 5/4= 1 1/4 which is more than 1.
The denominator tells us the size of the pieces. I rewrote 2/3 as 4/6 so I could count the total number of sixths. My answer makes sense because 5 sixths is less than a complete whole.
The denominator tells us it doesn’t change I rewrote 1/2 as 2/4 so It would be more accurate and sense. My answer makes sense because 2/4+3/4=5/4 which would be the correct answer.It would be more than 1 because 5/4= 1 1/4 which is more than 1.
The mistake was adding the top and bottom numbers instead of making the fractions have the same denominator. I changed 1/2 to 2/4 because they are equal. Then I added 3/4 + 2/4 and got 5/4, which is 1 1/4. I know my answer is right because its more than one whole and the fractions add up to more than 1.
The denominator tells us that it doesn’t change at all. I rewrote 1/2 as 2/4 so I could count the numbers and so that it would make more sense. My answer makes sense because 2/4+3/4 I think it would be 5/4.
The person wrote 3/4 + 1/2 = 4/6 . The mistake that this person made first was adding the bottom and the top numbers and not making the fractions have the have bottom number or and denominator so what I did to fix there mistake was re write the problem with the correct and same denominators those new numbers would be 2/4 instead of 1/2 , 3/4 and then I added those together and got the number 5/4 which is the correct answer to this problem .
Convert 2/3 to sixths: To change the denominator from 3 to 6, multiply both the top and bottom numbers by 2.
Add the fractions: Now that both parts are measured in sixths, you can add their numerators together while keeping the denominator the same.
Why the Result is Less Than 1
The sum 5/6 is less than 1 because a complete whole requires 6 out of 6 equal parts (6/6). Having 5 parts means your result is exactly 1/6 short of reaching 1.
The original student added both top and bottom numbers directly (2+1=3 and (3+6=9), which mistakenly changes the size of the pieces rather than combining the parts you actually have.