Rational Numbers Worksheets
Free printable rational numbers worksheets: add, subtract, multiply and divide negative decimals and fractions on one sheet, with an answer key.
All four operations with signed decimals and fractions on one sheet: -3.25 + 1.75 = -1.5, -3/4 - 1/6 = -11/12, -3.6 × 0.5 = -1.8 and -3/4 ÷ (-1/2) = 1 1/2. The four operations and the two kinds of number are dealt as evenly as the count allows, so no one case fills the page.
Every problem has at least one negative number and no zero. Fractions are drawn stacked with denominators up to 12, and their answers are in lowest terms; decimal answers are exact, with no repeating decimals and no extra zeros. Decimals only or fractions only is one setting away.
What this worksheet covers
- Add, subtract, multiply and divide rational numbers
- Apply the sign rules to fractions and decimals
Common Core standards
- 7.NS.A.1 Add and subtract rational numbers, including negative numbers.
- 7.NS.A.2 Multiply and divide rational numbers, including negative numbers.
Frequently asked questions
Why mix all four operations?
Because the sign rules differ. For addition the sign of the answer depends on which number is bigger; for multiplication it depends only on whether the signs match. Mixed, a student has to stop and ask which rule each problem needs.
What counts as a rational number?
Any number that is a fraction of two integers, which includes decimals that end, such as -2.5, and the integers themselves. The integer worksheets cover whole numbers; these sheets bring in decimals and fractions.
Are there mixed numbers?
In the answers, yes: an answer bigger than 1 either way is written as a mixed number in lowest terms, such as -1 1/4. The fractions in the questions are proper fractions, like -5/6.
What grade are rational numbers?
Seventh grade, the end of the number system work that starts with integers. A student not yet sure of the sign rules is better starting on the integer worksheets.