Signed Numbers — Practice Problems and Worked Solutions

The formulas you need here

16 worked problems

Every step is generated and checked by a computer algebra system.

1. 1.

   Evaluate the signed-number expression.

   $$-3+5$$

   Answer: $2$

   Step-by-step solution

   1. $$\text{Keep each sign attached to its number.}$$
   2. $$\text{Apply multiplication or division before addition or subtraction.}$$
   3. $$=2$$
2. 2.

   Evaluate the signed-number expression.

   $$4-7$$

   Answer: $-3$

   Step-by-step solution

   1. $$\text{Keep each sign attached to its number.}$$
   2. $$\text{Apply multiplication or division before addition or subtraction.}$$
   3. $$=-3$$
3. 3.

   Evaluate the signed-number expression.

   $$(-3)(4)$$

   Answer: $-12$

   Step-by-step solution

   1. $$\text{Keep each sign attached to its number.}$$
   2. $$\text{Apply multiplication or division before addition or subtraction.}$$
   3. $$=-12$$
4. 4.

   Evaluate the signed-number expression.

   $$(-5)(-2)$$

   Answer: $10$

   Step-by-step solution

   1. $$\text{Keep each sign attached to its number.}$$
   2. $$\text{Apply multiplication or division before addition or subtraction.}$$
   3. $$=10$$
5. 5.

   Evaluate the signed-number expression.

   $$-18÷3+4$$

   Answer: $-2$

   Step-by-step solution

   1. $$\text{Keep each sign attached to its number.}$$
   2. $$\text{Apply multiplication or division before addition or subtraction.}$$
   3. $$=-2$$
6. 6.

   Evaluate the signed-number expression.

   $$3-2(-4)$$

   Answer: $11$

   Step-by-step solution

   1. $$\text{Keep each sign attached to its number.}$$
   2. $$\text{Apply multiplication or division before addition or subtraction.}$$
   3. $$=11$$
7. 7.

   Evaluate the signed-number expression.

   $$-6+2$$

   Answer: $-4$

   Step-by-step solution

   1. $$\text{Keep each sign attached to its number.}$$
   2. $$\text{Apply multiplication or division before addition or subtraction.}$$
   3. $$=-4$$
8. 8.

   Evaluate the signed-number expression.

   $$5-9$$

   Answer: $-4$

   Step-by-step solution

   1. $$\text{Keep each sign attached to its number.}$$
   2. $$\text{Apply multiplication or division before addition or subtraction.}$$
   3. $$=-4$$
9. 9.

   Evaluate the signed-number expression.

   $$(-2)(6)$$

   Answer: $-12$

   Step-by-step solution

   1. $$\text{Keep each sign attached to its number.}$$
   2. $$\text{Apply multiplication or division before addition or subtraction.}$$
   3. $$=-12$$
10. 10.

    Evaluate the signed-number expression.

    $$(-4)(-3)$$

    Answer: $12$

    Step-by-step solution

    1. $$\text{Keep each sign attached to its number.}$$
    2. $$\text{Apply multiplication or division before addition or subtraction.}$$
    3. $$=12$$
11. 11.

    Evaluate the signed-number expression.

    $$-20÷4+3$$

    Answer: $-2$

    Step-by-step solution

    1. $$\text{Keep each sign attached to its number.}$$
    2. $$\text{Apply multiplication or division before addition or subtraction.}$$
    3. $$=-2$$
12. 12.

    Evaluate the signed-number expression.

    $$2-3(-5)$$

    Answer: $17$

    Step-by-step solution

    1. $$\text{Keep each sign attached to its number.}$$
    2. $$\text{Apply multiplication or division before addition or subtraction.}$$
    3. $$=17$$
13. 13.

    Evaluate the signed-number expression.

    $$-7+7$$

    Answer: $0$

    Step-by-step solution

    1. $$\text{Keep each sign attached to its number.}$$
    2. $$\text{Apply multiplication or division before addition or subtraction.}$$
    3. $$=0$$
14. 14.

    Evaluate the signed-number expression.

    $$(-1)(-1)(-1)$$

    Answer: $-1$

    Step-by-step solution

    1. $$\text{Keep each sign attached to its number.}$$
    2. $$\text{Apply multiplication or division before addition or subtraction.}$$
    3. $$=-1$$
15. 15.

    Evaluate the signed-number expression.

    $$-15÷(-3)$$

    Answer: $5$

    Step-by-step solution

    1. $$\text{Keep each sign attached to its number.}$$
    2. $$\text{Apply multiplication or division before addition or subtraction.}$$
    3. $$=5$$
16. 16.

    Evaluate the signed-number expression.

    $$8-2(3-7)$$

    Answer: $16$

    Step-by-step solution

    1. $$\text{Keep each sign attached to its number.}$$
    2. $$\text{Apply multiplication or division before addition or subtraction.}$$
    3. $$=16$$

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• Ratios and Percentages
• Exponents and Roots
• Algebraic Expressions
• Linear Equations
• Polynomial Basics
• Inequalities
• Coordinate Plane
• Reading Graphs
• Function Machines
• Substitution
• Factoring Basics