Simplifying Expressions With Integers

To add two numbers with the same sign, add their absolute values. The sum has the same sign as the numbers. To add two numbers with different signs, find the difference between their absolute values. The sum has the same sign as the number with the greater absolute value.

Example 1

Add.

1. − 8 + ( − 5 ) = − 13 negative 8 plus open negative 5 close equals negative 13
2. − 8 + 5 = − 3 negative 8 plus 5 equals negative 3
3. 8 + ( − 5 ) = 3 8 plus open negative 5 close equals 3

To subtract a number, add its opposite.

Example 2

Subtract.

• a.

  4 − 7 = 4 + ( − 7 )   = − 3 table with 2 rows and 3 columns , row1 column 1 , 4 minus 7 , column 2 equals , column 3 4 plus open negative 7 close , row2 column 1 , , column 2 equals , column 3 negative 3 , end table

• b.

  − 4 − ( − 7 ) = − 4 + 7   = 3 table with 2 rows and 3 columns , row1 column 1 , negative 4 minus open negative 7 close , column 2 equals , column 3 negative 4 plus 7 , row2 column 1 , , column 2 equals , column 3 3 , end table

• c.

  − 4 − 7 = − 4 + ( − 7 )   = − 11 table with 2 rows and 3 columns , row1 column 1 , negative 4 minus 7 , column 2 equals , column 3 negative 4 plus open negative 7 close , row2 column 1 , , column 2 equals , column 3 negative 11 , end table

The product or quotient of two numbers with the same sign is positive. The product or quotient of two numbers with different signs is negative.

Example 3

Multiply or divide.

1. ( − 3 ) ( − 5 ) = 15 open negative 3 close open negative 5 close equals 15
2. − 35 ÷ 7 = − 5 negative 35 divides 7 equals negative 5
3. 24 ÷ ( − 6 ) = − 4 24 divides open negative 6 close equals negative 4

Example 4

Simplify 2 2 − 3 ( 4 − 6 ) − 12 . 2 squared , minus 3 open 4 minus 6 close minus 12 .

Order of Operations

1. Perform any operation(s) inside grouping symbols.
2. Simplify any terms with exponents.
3. Multiply and divide in order from left to right.
4. Add and subtract in order from left to right.

Exercises

Simplify each expression.

1. − 4 + 5 negative 4 plus 5
2. 12 − 12 12 minus 12
3. − 15 + ( − 23 ) negative 15 plus open negative 23 close
4. 4 − 17 4 minus 17
5. − 5 − 12 negative 5 minus 12
6. 3 − ( − 5 ) 3 minus open negative 5 close
7. − 8 − ( − 12 ) negative 8 minus open negative 12 close
8. − 19 + 5 negative 19 plus 5
9. ( − 7 ) ( − 4 ) open negative 7 close open negative 4 close
10. − 120 ÷ 30 negative 120 divides 30
11. ( − 3 ) ( 4 ) open negative 3 close open 4 close
12. 75 ÷ ( − 3 ) 75 divides open negative 3 close
13. ( − 6 ) ( 15 ) open negative 6 close open 15 close
14. ( 18 ) ( − 4 ) open 18 close open negative 4 close
15. − 84 ÷ ( − 7 ) negative 84 divides open negative 7 close
16. − 2 ( 1 + 5 ) + ( − 3 ) ( 2 ) negative 2 open 1 plus 5 close plus open negative 3 close open 2 close
17. − 4 ( − 2 − 5 ) + 3 ( 1 − 4 ) negative 4 open negative 2 minus 5 close plus 3 open 1 minus 4 close
18. 20 − ( 3 ) ( 12 ) + 4 2 20 minus open 3 close open 12 close plus , 4 squared
19. − 15 − 5 − 36 − 12 + − 12 − 4 negative 15 over negative 5 . minus . 36 over negative 12 . plus . negative 12 over negative 4
20. 5 2 − 6 ( 5 − 9 ) 5 squared , minus 6 open 5 minus 9 close
21. ( − 3 + 2 3 ) ( 4 + − 42 7 ) open . negative 3 plus , 2 cubed . close . open . 4 plus , negative 42 over 7 . close

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