How to Multiply and Divide Integers

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Integer multiplication and division use the same sign rules. First decide the sign, then multiply or divide the absolute values.

Sign rules

A positive times a positive is positive: \(6\times 4=24\).
A negative times a negative is positive: \((-6)(-4)=24\).
A positive times a negative, or a negative times a positive, is negative: \(6(-4)=-24\).

Division follows the same pattern because division asks for the missing factor. For example, \((-32)\div 8=-4\), and \((-32)\div(-8)=4\).

More than two factors

For a product with several integer factors, count the negative factors. An even number of negative factors gives a positive product; an odd number gives a negative product.

ACT tip

Mark the sign first, then compute the magnitude. Also remember that division by zero is undefined, so zero cannot be a divisor.

Multiplying and Dividing Integers

Think of this lesson as more than a rule to memorize. Multiplying and Dividing Integers is about number-line meaning, signs, and distance from zero. A strong student does not rush to the first formula on the page; they pause, identify the structure of the problem, and then choose the tool that matches that structure. That pause is what prevents most mistakes.

Integers are easiest when you picture direction on a number line. Positive numbers move right, negative numbers move left, and absolute value measures distance from zero.

Here is the teacher way to approach the topic. First, read the problem slowly and underline the information that is actually given. Next, name the target: are you finding a value, simplifying an expression, comparing two quantities, solving for a variable, or interpreting a graph? Once the target is clear, the calculation becomes much less mysterious because every step has a job.

Read what is given and what is being asked.
Choose the rule that connects them.
Substitute carefully and simplify in small steps.
Check the final answer against the original question.

A helpful habit is to say what each number represents before using it. For example, if a number is a denominator, a radius, a slope, a common difference, or a coefficient, it should not be treated like an ordinary loose number. Its role tells you where it belongs in the formula. This is especially important on ACT-style questions because many wrong answer choices come from using the right numbers in the wrong places.

Another good habit is to keep the work organized vertically. Write one clean line for substitution, one line for simplifying, and one line for the final answer. If the problem has units, keep the units attached. If the problem has signs, exponents, or parentheses, copy them carefully from one line to the next. Most errors in this topic are not caused by a hard idea; they are caused by dropping a negative sign, combining unlike terms, using the wrong denominator, or skipping a check.

When you finish, ask a quick reasonableness question. Should the answer be positive or negative? Should it be larger or smaller than the original number? Does it fit the graph, table, shape, or equation? Can you plug it back into the original problem? This final check turns the lesson from a procedure into understanding.

On a test, the goal is not to write the longest solution. The goal is to write enough clear work that you can see the structure, avoid traps, and recover quickly if one line goes wrong. Practice the examples below with that mindset: identify the type of problem, choose the matching rule, show the substitution, simplify carefully, and check the answer before moving on.

Free printable Worksheets

Exercises for Multiplying and Dividing Integers

1) \((-7)(6)=\)

2) \((-8)(-5)=\)

3) \(45\div(-9)=\)

4) \((-56)\div(-7)=\)

5) \(12(-4)(-3)=\)

6) \((-9)(-2)(-5)=\)

7) \((-84)\div 12=\)

8) \(96\div(-16)=\)

9) \((-11)(13)=\)

10) \((-144)\div(-18)=\)

11) \(5(-6)(-2)(-3)=\)

12) \((-120)\div 5\div(-4)=\)

13) \((-15)(-4)\div(-6)=\)

14) \(18\div(-3)\times(-7)=\)

15) \((-2)(-3)(-4)(-5)=\)

16) \(240\div(-8)\div 3=\)

17) \((-36)(5)\div(-9)=\)

18) \((-7)(8)(-2)\div(-4)=\)

19) \(420\div(-6)\times(-3)\div 7=\)

20) \((-9)(-5)(-4)\div(-10)\times 2=\)

Answers

1) \((-7)(6)=\color{red}{-42}\)

Solution
One factor is negative, so the result is negative.
Multiply absolute values: \(7\times6=42\), so \(-42\).

2) \((-8)(-5)=\color{red}{40}\)

Solution
Two negatives make a positive.
\(8\times5=40\).

3) \(45\div(-9)=\color{red}{-5}\)

Solution
Different signs give a negative quotient.
\(45\div9=5\), so \(-5\).

4) \((-56)\div(-7)=\color{red}{8}\)

Solution
Same signs give a positive quotient.
\(56\div7=8\).

5) \(12(-4)(-3)=\color{red}{144}\)

Solution
Two negative factors give a positive product.
\(12\times4\times3=144\).

6) \((-9)(-2)(-5)=\color{red}{-90}\)

Solution
Three negative factors give a negative product.
\(9\times2\times5=90\), so \(-90\).

7) \((-84)\div 12=\color{red}{-7}\)

Solution
Different signs give a negative quotient.
\(84\div12=7\), so \(-7\).

8) \(96\div(-16)=\color{red}{-6}\)

Solution
Different signs give a negative quotient.
\(96\div16=6\), so \(-6\).

9) \((-11)(13)=\color{red}{-143}\)

Solution
One negative factor gives a negative product.
\(11\times13=143\), so \(-143\).

10) \((-144)\div(-18)=\color{red}{8}\)

Solution
Same signs give a positive quotient.
\(144\div18=8\).

11) \(5(-6)(-2)(-3)=\color{red}{-180}\)

Solution
There are three negative factors, so the product is negative.
\(5\times6\times2\times3=180\), so \(-180\).

12) \((-120)\div 5\div(-4)=\color{red}{6}\)

Solution
Work left to right: \((-120)\div5=-24\).
Then \((-24)\div(-4)=6\).

13) \((-15)(-4)\div(-6)=\color{red}{-10}\)

Solution
First \((-15)(-4)=60\).
Then \(60\div(-6)=-10\).

14) \(18\div(-3)\times(-7)=\color{red}{42}\)

Solution
Work left to right: \(18\div(-3)=-6\).
Then \((-6)(-7)=42\).

15) \((-2)(-3)(-4)(-5)=\color{red}{120}\)

Solution
Four negative factors give a positive product.
\(2\times3\times4\times5=120\).

16) \(240\div(-8)\div 3=\color{red}{-10}\)

Solution
Work left to right: \(240\div(-8)=-30\).
Then \((-30)\div3=-10\).

17) \((-36)(5)\div(-9)=\color{red}{20}\)

Solution
First \((-36)(5)=-180\).
Then \((-180)\div(-9)=20\).

18) \((-7)(8)(-2)\div(-4)=\color{red}{-28}\)

Solution
First \((-7)(8)=-56\).
Then \((-56)(-2)=112\).
Finally \(112\div(-4)=-28\).

19) \(420\div(-6)\times(-3)\div 7=\color{red}{30}\)

Solution
Work left to right: \(420\div(-6)=-70\).
Then \((-70)(-3)=210\), and \(210\div7=30\).

20) \((-9)(-5)(-4)\div(-10)\times 2=\color{red}{36}\)

Solution
First \((-9)(-5)=45\).
Then \(45(-4)=-180\), \((-180)\div(-10)=18\), and \(18\times2=36\).

How to Multiply and Divide Integers