Integers and rational numbers worksheet for Pre-Algebra

Pre-Algebra uses this sheet to make signed numbers and fractions automatic: adding and subtracting integers with different signs, and adding, subtracting, multiplying and dividing fractions. These skills come up in every equation after this, so they need to be quick and reliable. Multiplying and dividing negatives is a separate kind you can turn on.

Also taught in Algebra 1, at its own level and with its own examples.

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Sigma Prep · sigmaprep.io/worksheets Name Integers and Rational Numbers Date Period Simplify. Add and subtract signed numbers $- 4 + 11$ $- 2 - 12$ $8 - 2$ $5 + 10$ $1 + 12$ $9 - 11$ $- 12 + 7$ Add and subtract fractions $\frac{3}{4} - \frac{1}{4}$ $\frac{2}{3} + \frac{1}{2}$ $\frac{4}{5} + \frac{8}{15}$ $\frac{1}{2} - \frac{4}{9}$ $\frac{1}{4} + \frac{1}{2}$ $\frac{2}{3} - \frac{1}{12}$ $\frac{4}{5} + \frac{1}{2}$ Multiply and divide fractions $\frac{1}{2} \div \frac{1}{6}$ $\frac{1}{5} \cdot \frac{1}{5}$ $\frac{2}{5} \cdot \frac{4}{5}$ $\frac{1}{3} \div \frac{1}{3}$ $\frac{5}{6} \cdot \frac{1}{2}$ $\frac{1}{2} \div \frac{1}{3}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Integers and Rational Numbers

Date Period

Simplify.

Add and subtract signed numbers
$- 4 + 11$
$- 2 - 12$
$8 - 2$
$5 + 10$
$1 + 12$
$9 - 11$
$- 12 + 7$

Add and subtract fractions
$\frac{3}{4} - \frac{1}{4}$
$\frac{2}{3} + \frac{1}{2}$
$\frac{4}{5} + \frac{8}{15}$
$\frac{1}{2} - \frac{4}{9}$
$\frac{1}{4} + \frac{1}{2}$
$\frac{2}{3} - \frac{1}{12}$
$\frac{4}{5} + \frac{1}{2}$

Multiply and divide fractions
$\frac{1}{2} \div \frac{1}{6}$
$\frac{1}{5} \cdot \frac{1}{5}$
$\frac{2}{5} \cdot \frac{4}{5}$
$\frac{1}{3} \div \frac{1}{3}$
$\frac{5}{6} \cdot \frac{1}{2}$
$\frac{1}{2} \div \frac{1}{3}$



Sigma Prep · sigmaprep.io/worksheets Name Integers and Rational NumbersAnswer keyVersion 2 Date Period Simplify. Add and subtract signed numbers $- 4 + 11$ $7$ $- 2 - 12$ $- 14$ $8 - 2$ $6$ $5 + 10$ $15$ $1 + 12$ $13$ $9 - 11$ $- 2$ $- 12 + 7$ $- 5$ Add and subtract fractions $\frac{3}{4} - \frac{1}{4}$ $\frac{1}{2}$ $\frac{2}{3} + \frac{1}{2}$ $\frac{7}{6}$ $\frac{4}{5} + \frac{8}{15}$ $\frac{4}{3}$ $\frac{1}{2} - \frac{4}{9}$ $\frac{1}{18}$ $\frac{1}{4} + \frac{1}{2}$ $\frac{3}{4}$ $\frac{2}{3} - \frac{1}{12}$ $\frac{7}{12}$ $\frac{4}{5} + \frac{1}{2}$ $\frac{13}{10}$ Multiply and divide fractions $\frac{1}{2} \div \frac{1}{6}$ $3$ $\frac{1}{5} \cdot \frac{1}{5}$ $\frac{1}{25}$ $\frac{2}{5} \cdot \frac{4}{5}$ $\frac{8}{25}$ $\frac{1}{3} \div \frac{1}{3}$ $1$ $\frac{5}{6} \cdot \frac{1}{2}$ $\frac{5}{12}$ $\frac{1}{2} \div \frac{1}{3}$ $\frac{3}{2}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Integers and Rational NumbersAnswer keyVersion 2

Date Period

Simplify.

Add and subtract signed numbers
$- 4 + 11$ $7$
$- 2 - 12$ $- 14$
$8 - 2$ $6$
$5 + 10$ $15$
$1 + 12$ $13$
$9 - 11$ $- 2$
$- 12 + 7$ $- 5$

Add and subtract fractions
$\frac{3}{4} - \frac{1}{4}$ $\frac{1}{2}$
$\frac{2}{3} + \frac{1}{2}$ $\frac{7}{6}$
$\frac{4}{5} + \frac{8}{15}$ $\frac{4}{3}$
$\frac{1}{2} - \frac{4}{9}$ $\frac{1}{18}$
$\frac{1}{4} + \frac{1}{2}$ $\frac{3}{4}$
$\frac{2}{3} - \frac{1}{12}$ $\frac{7}{12}$
$\frac{4}{5} + \frac{1}{2}$ $\frac{13}{10}$

Multiply and divide fractions
$\frac{1}{2} \div \frac{1}{6}$ $3$
$\frac{1}{5} \cdot \frac{1}{5}$ $\frac{1}{25}$
$\frac{2}{5} \cdot \frac{4}{5}$ $\frac{8}{25}$
$\frac{1}{3} \div \frac{1}{3}$ $1$
$\frac{5}{6} \cdot \frac{1}{2}$ $\frac{5}{12}$
$\frac{1}{2} \div \frac{1}{3}$ $\frac{3}{2}$

How to do these

$- 7 + 12 - (- 4)$

Subtracting -4 is the same as adding 4.
-7 + 12 = 5, then 5 + 4 = 9.

The answer is $9$ .

Where students go wrong

Using the multiplication rule for addition. -8 + (-3) is -11, not 11: two negatives make a positive only when you multiply or divide.

Also called adding integers, subtracting negative numbers, signed numbers, adding and subtracting rational numbers or multiplying and dividing rational numbers.

What you can put on this worksheet

Adding and subtracting signed numbers: $9 - 6$ → $3$
Adding and subtracting fractions: $\frac{3}{4} + \frac{1}{8}$ → $\frac{7}{8}$
Multiplying and dividing fractions: $\frac{3}{4} \cdot \frac{1}{8}$ → $\frac{3}{32}$
Multiplying and dividing signed numbers: $7 \times (- 5)$ → $- 35$
Three or more factors: $(4) (- 3) (2)$ → $- 24$
Division written as a fraction: $\frac{16}{8}$ → $2$
Adding and subtracting negative decimals: $(- 14.7) - (- 11.3)$ → $- 3.4$
Mixed formats: adding and subtracting: $\frac{1}{2} + 3.5$ → $4$
Mixed formats: multiplying and dividing: $\frac{1}{2} \times 3.5$ → $\frac{7}{4}$
Four numbers in a row: $7 + 1 - (- 7) + (- 12)$ → $3$

Questions about these worksheets

Yes. Every integers and rational numbers sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Pre-Algebra is usually taken around 7th or 8th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the integers and rational numbers questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 10: adding and subtracting signed numbers, adding and subtracting fractions, multiplying and dividing fractions, multiplying and dividing signed numbers, three or more factors, division written as a fraction, adding and subtracting negative decimals, mixed formats: adding and subtracting, mixed formats: multiplying and dividing and four numbers in a row. Tick as many as you want and set how many of each, or let it spread them evenly.

Adding the tops and the bottoms. Two thirds plus one quarter is not three sevenths. Only the tops get added, and only once the bottoms match.

Integers and rational numbers worksheet for Pre-Algebra

Select your difficulty

Add and subtract signed numbers

Add and subtract fractions

Multiply and divide fractions

Add and subtract signed numbers

Add and subtract fractions

Multiply and divide fractions

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these integers and rational numbers worksheets free?+

Do the integers and rational numbers worksheets come with an answer key?+

Are these integers and rational numbers worksheets printable?+

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Can I get a different version of the same integers and rational numbers worksheet?+

Is this a free alternative to Kuta Software for integers and rational numbers?+

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What do students get wrong with integers and rational numbers?+