Adding fractions (different denominators)
Add and subtract fractions when one denominator is a multiple of the other by rewriting with a common denominator.
What a learner can do afterwards
- Calculate 1/3 + 1/6 by converting to sixths: 2/6 + 1/6 = 3/6 = 1/2
- Calculate 3/4 − 1/8 by converting to eighths
- Add 2/5 + 3/10 and simplify the answer
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The denominator is the bottom number. The numerator is the top number. To change thirds into sixths, count groups of 3 in 6. Since 3 + 3 = 6, there are 2 groups: 3 times 2 is 6, and 6 / 3 = 2. Multiply the top number by 2 too: 2/3 becomes 4/6. Each third splits into two sixths. The amount stays the same.
Start with two thirds of a whole.
Before adding, make the bottom numbers match so the pieces have the same size. Check whether the larger bottom number is in the smaller one's times table. If it is, use the larger number. Change the fraction with the smaller bottom number, even if that fraction has the larger value.
Equivalent fractions name the same amount of the same whole. To split pieces into smaller pieces, multiply both numbers by the same whole number. To group pieces into larger pieces, divide both numbers by the same common factor greater than 1. Changing only one number changes the amount.
Find 11/12 - 1/6. Use twelfths because 6 times 2 is 12. Multiply both numbers of 1/6 by 2: 1/6 = 2/12. Now take two twelfth-pieces from eleven. 11 - 2 = 9, so 9/12 remains. Divide both numbers by 3 to write the same remainder as 3/4.
Find 1/2 + 3/8. Use eighths because 2 times 4 is 8. Multiply both numbers of 1/2 by 4: 1/2 = 4/8. Join four eighth-pieces and three more. 4 + 3 = 7, so the sum is 7/8. To simplify a result, divide both numbers by a common factor greater than 1. Seven and eight have none, so keep 7/8.
Check an addition error by looking at the bottom number first. Adding the bottom numbers names a different piece size. Instead, use the larger bottom number when it is in the smaller one's times table. Multiply both numbers of the fraction you change by the same number. Then add only the matching piece counts.
To find a piece count before simplifying, first make the bottom numbers match. Use the larger bottom number when it is in the smaller one's times table. Divide the larger by the smaller to find what to multiply by. Multiply the changed fraction's top by that number too. Add the tops and report that count, keeping the stated piece size.
Find 7/9 - 1/3 in simplest form. Use ninths: 3 times 3 is 9, so multiply both numbers of 1/3 by 3 to get 3/9. Subtract 7 - 3 = 4, giving 4/9. A common factor divides both numbers exactly. Four and nine share no factor greater than 1, so 4/9 is already simplest. Its numerator is 4.
For two cuts, first name every length with the same bottom number. Keep the same unit, such as meters. Subtract the first cut from the starting length. Subtract the second cut from what remains. Then simplify by dividing both numbers by a common factor greater than 1, if they have one.
Match the denominators first, then add or subtract the numerators.
Practice questions and readings written for this learning dataset. Referenced videos by Khan Academy.
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