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3 Responses
I like to think of pizzas: add the whole pies (2+1=3), then the slices-1/3 + 3/4 = 4/12 + 9/12 = 13/12 = 1 1/12-so the total is 3 + 1 1/12 = 4 1/12. Hope this helps! Learn more here: https://www.khanacademy.org/math/arithmetic/fraction-arithmetic/arith-review-add-sub-fractions/v/adding-mixed-numbers-with-unlike-denominators
You’re right to split the wholes and the fractions. Add the whole numbers: 2 + 1 = 3. For the fractions, don’t add numerators and denominators directly; first use a common denominator. With 12: 1/3 = 4/12 and 3/4 = 9/12, so 1/3 + 3/4 = 13/12 = 1 1/12. Now add that extra 1 to the wholes: 2 + 1 + 1 = 4, giving 4 1/12 overall. Quick check: 2.333… + 1.75 ≈ 4.083…, which matches 4 1/12.
Another clean method is to convert to improper fractions: 2 1/3 = 7/3 and 1 3/4 = 7/4. With denominator 12: 7/3 = 28/12 and 7/4 = 21/12, so total 49/12 = 4 1/12. Same result, just a different route.
Which method feels more natural to you-keeping mixed numbers and finding a common denominator, or converting to improper fractions first?
You’re on the right track splitting the whole parts and the fractional parts! The 2+1=3 bit is fine. The trick is that you can’t add 1/3 and 3/4 straight across; you need a common denominator first. I usually grab 24 as the least common denominator here (hmm, I might be misremembering whether it’s actually the least, but it works), so 1/3 becomes 8/24 and 3/4 becomes 18/24. Then 8/24 + 18/24 = 26/24, which is 1 and 2/24. Add that extra 1 to the 3 you already had to make 4, and the leftover 2/24 simplifies to 1/12. So the total is 4 1/12. If you prefer, you can also convert to improper fractions first: 2 1/3 = 7/3 and 1 3/4 = 7/4, and 7/3 + 7/4 = 49/12 = 4 1/12. I always double-check because I’m prone to doing that “add tops and bottoms” thing too!