Adding and Subtracting Rational Numbers
Free printable adding and subtracting rational numbers worksheets: negative decimals and fractions, -3.25 + 1.75 and -3/4 - 1/6, with an answer key.
Each problem adds or subtracts two signed numbers that are not whole: decimals such as -3.25 + 1.75 = -1.5, or fractions such as -3/4 - 1/6 = -11/12. At least one number in every problem is negative, so the sign rules from integers are always in play.
Each problem is all decimals or all fractions, never a mix, and a sheet has the two kinds as evenly as its count allows unless the setting picks one. Fractions are drawn stacked, with denominators up to 12, and every fraction answer is in lowest terms. Decimal answers are exact and written without extra zeros.
What this worksheet covers
- Add and subtract positive and negative decimals
- Add and subtract positive and negative fractions
Common Core standards
- 7.NS.A.1 Add and subtract rational numbers, including negative numbers.
Frequently asked questions
What is a rational number?
Any number that can be written as a fraction of two integers: -3/4, 0.75 (which is 3/4), -2.5 (which is -5/2), and every integer as well. The numbers in these problems are the ones that are not whole, because the integer worksheets already cover those.
Do the integer rules still work?
Yes, exactly. Subtracting a negative is adding, so -3/4 - (-1/6) is -3/4 + 1/6. With different signs, subtract the sizes and keep the sign of the larger: -3.25 + 1.75 is -1.5, because 3.25 is the bigger size and it is the negative one.
How are the fraction answers written?
In lowest terms, with a mixed number when the answer is bigger than 1 either way: -3/4 - 1/2 is -5/4, which the key writes as -1 1/4. The fractions in the questions start in lowest terms too.
What grade is adding and subtracting rational numbers?
Seventh grade, where adding and subtracting extends from integers to every rational number. The adding and subtracting integers worksheets are the step before.