Math Mistake Monday: Fix the Fraction Addition
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 challenge: explain the correction
- Write a sentence identifying the mistake without insulting the person who made it.
- Rewrite 1/2 as fourths. Show why the amount has not changed.
- Add the fourths and write the result as both an improper fraction and a mixed number.
- Explain how you know the answer should be greater than 1.
Sentence frame: “The denominator tells us ___. I rewrote ___ as ___ so I could count ___. My answer makes sense because ___.”
Compare with a model explanation after trying
The mistake was adding numerators and denominators as though they were separate whole numbers. One-half equals two-fourths, so 3/4 + 1/2 = 3/4 + 2/4 = 5/4 = 1 1/4.
Each fourth is the same size, so I can count three fourths plus two fourths. The sum is greater than 1 because 3/4 needs only 1/4 more to make a whole, and we added 1/2.
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.
