Adding and subtracting fractions with a common denominator — 11–13
When neither denominator divides the other, find a new size of part that fits both, then add or subtract the numerators.
Same-size parts, a new common size
To add or subtract fractions you need parts of the same size. If the denominators are different, rewrite each fraction as an equivalent one, all with the same denominator: a common multiple of the denominators, and the smallest one (the lowest common multiple) keeps the numbers small. Then add or subtract only the numerators, and the denominator stays. Example: 1/4 + 1/6. The lowest common multiple of 4 and 6 is 12, so 3/12 + 2/12 = 5/12.
Why a new size of part
Last year one denominator was a multiple of the other, so you could bring the smaller one up to the larger one. With 1/4 and 1/6 that fails: 6 is not a multiple of 4. So you look for a new size of part that fits a whole number of times in both. The twelfth does: it fits 3 times in a quarter and 2 times in a sixth. Any common multiple works (24 too), but then you may need to shorten the result at the end.
Calculating 5/6 − 3/8 and 1/6 + 3/10
5/6 − 3/8. Step 1: the lowest common multiple of 6 and 8 is 24. Step 2: 5/6 = 20/24 (× 4) and 3/8 = 9/24 (× 3). Step 3: 20/24 − 9/24 = 11/24; 11 and 24 share only 1, so it is irreducible. Now 1/6 + 3/10: the lowest common multiple is 30, so 5/30 + 9/30 = 14/30. Both numbers are even: 14/30 = 7/15, and 7 and 15 share only 1.
Adding tops and bottoms
The most common slip is to add numerators and denominators separately: 1/4 + 1/6 = 2/10. It feels natural, because you did the same thing above and below. But check it: 2/10 is 0.2 and 1/4 is 0.25, so the “sum” would be smaller than one of the parts you added. With positive numbers that cannot happen. The denominator is the size of the part; it is not something to add. Bring both to twelfths first: 3/12 + 2/12 = 5/12.
Fractions of an hour, cups in a recipe
Fractions of an hour are added this way. One task takes 1/4 of an hour and another takes 1/6 of an hour. Together, 1/4 + 1/6 = 3/12 + 2/12 = 5/12 of an hour. Check it with minutes: 1/4 of 60 min is 15 min, 1/6 of 60 min is 10 min, and 15 + 10 = 25 min, which is 5/12 of 60. A recipe works the same way when you pour together 3/4 of a cup and 2/3 of a cup: 9/12 + 8/12 = 17/12 of a cup.
Keep exploring
Other languages
Loading MyLeoNes™…