Pre-algebra and algebraGrades 6–7
Integers worksheet with answer key
A printable sheet of integer problems in three columns. Choose adding, subtracting, multiplying, dividing or combinations, set the largest absolute value from 5 to 100, and print with an answer key.
- Fresh problems every time
- Answer key on its own page
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On this page
Working with numbers below zero
Integers are the whole numbers and their negatives: ..., −3, −2, −1, 0, 1, 2, 3, ... Sixth graders meet them through temperature, debt and elevation, and seventh graders learn the rules for combining them. Most students find sign rules the sticking point of pre-algebra, so repeated practice with instant checking is valuable.
Each line on this sheet looks like −7 − (−12) = with a blank. Negative second numbers are written in parentheses, the way a textbook does, so the two signs are never side by side. The header prints the key rule for the operation chosen: to subtract, add the opposite; for products and quotients, same signs give a positive, different signs give a negative.
Choosing settings
- Operation. Adding, subtracting or both together; multiplying, dividing or both; or all four. Isolating one operation lets you target the rule that is giving trouble.
- Largest number (absolute value). From 5 to 100 in steps of 5. Small limits keep the focus on signs. For multiplication and division the factors stop at 12, even when the limit is higher, so the facts stay within the times tables.
- Number of problems. 10 to 40, three columns across.
On add and subtract sheets, most problems include at least one negative number, since the sheet is built to exercise the rules. When two positives would be generated, the first is usually flipped to negative. So a sheet will not waste space on plain whole-number arithmetic.
A good sequence is adding with a limit of 10, then subtracting, then both with a limit of 20 (the preset), and finally multiplication and division. A number line helps at the start: the number line printable lets a student draw jumps left and right.
Worked example: two problems
−7 − (−12)
- Subtracting a negative is the same as adding its opposite. The opposite of −12 is 12.
- Rewrite: −7 + 12.
- Start at −7 on a number line and move 12 to the right. Seven steps reach 0, and five more reach 5.
- Answer: 5.
−6 × 7 and −54 ÷ (−9)
- −6 × 7: the signs are different, so the product is negative. 6 × 7 = 42, so the answer is −42.
- −54 ÷ (−9): the signs are the same, so the quotient is positive. 54 ÷ 9 = 6, so the answer is 6.
A final check for any answer is to ask whether its size and sign make sense. Adding a larger positive to a smaller negative should land above zero, as it did in the first example.
Reading the key for patterns
- Dropping a sign. An answer of 19 for −7 − (−12) is the result of 7 + 12. The student treated both minus signs as subtraction.
- Wrong sign on the product. Writing 42 for −6 × 7 means the sign step was skipped. Ask the student to count how many negatives are in the problem: an odd number gives a negative result.
- Using the larger number's sign. For −8 + 3, the answer is −5 because 8 is farther from zero than 3. A student who writes 5 or −11 needs to see it on a number line.
- Division by repeated signs. If −54 ÷ (−9) gives −6, the student applied the negative-times-positive rule to a quotient of two negatives.
Next steps
Once integer facts are secure, combine them with the order of operations worksheet or the evaluating algebraic expressions worksheet. Integers also appear as solutions in two-step equations.