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Can you use the order of operations? What's the value of a ? In this concept, we will learn to use the order of operations.

(3 + 5) \div 2 + 4 \times 6 = a

Guidance

The order of operations tells us the correct order of evaluating math expressions. We always do parenthesis first . Then we do multiplication and division (from left to right) and finally addition and subtraction (from left to right) .

In order to evaluate expressions using the order of operations, we can use the problem solving steps to help.

  • First, describe what you see in the problem. What operations are there?
  • Second, identify what your job is. In these problems, your job will be to solve for the unknown.
  • Third, make a plan . In these problems, your plan should be to use the order of operations.
  • Fourth, solve .
  • Fifth, check .

Example A

Figure out the value of the variable. Follow the order of operations.

8-(3-1)+6\times 2=e

Solution:

We can use the problem solving steps to help.

Describe: The equation has parenthesis, multiplication, addition and subtraction.

My Job: Do the operations to figure out the value of e .

Plan: Do the parenthesis first. Then do the multiplication. Finally, do the subtraction and addition from left to right.

Solve: First do the parenthesis: 8-(3-1)+6\times 2=8-2+6\times 2

Next do the multiplication: 8-2+6\times 2=8-2+12
Last do the subtraction and addition: 8-2+12=6+12=18
e=18

Check: 8-(3-1)+6\times 2=8-2+6\times 2=8-2+12=6+12=18

Example B

Figure out the value of the variable. Follow the order of operations.

(4 + 6) \div 5 - 3 \div 3 = a

Solution:

We can use the problem solving steps to help.

Describe: The equation has parenthesis, division, addition and subtraction.

My Job: Do the operations to figure out the value of a .

Plan: Do the parenthesis first. Then do the division. Finally, do the subtraction and addition from left to right.

Solve: First do the parenthesis: (4 + 6) \div 5 - 3 \div 3 =10\div 5-3 \div 3

Next do the division: 10\div 5-3 \div 3=2-1
Last do the subtraction: 2-1=1
a=1

Check: (4 + 6) \div 5 - 3 \div 3 =10\div 5-3 \div 3=2-1=1

Example C

Figure out the value of the variable. Follow the order of operations.

6 \times 7 \div 6 + 8 = c

Solution:

We can use the problem solving steps to help.

Describe: The equation has multiplication, division and addition.

My Job: Do the operations to figure out the value of c .

Plan: Do the multiplication and division first from left to right. Then do the addition.

Solve: First do the multiplication and division: 6 \times 7 \div 6 + 8=42 \div 6+8=7+8

Last do the addition: 7+8=15
c=15

Check: 6 \times 7 \div 6 + 8=42 \div 6 +8=7+8=15

Concept Problem Revisited

(3 + 5) \div 2 + 4 \times 6 = a

We can use the problem solving steps to help.

Describe: The equation has parenthesis, division, multiplication and addition.

My Job: Do the operations to figure out the value of a .

Plan: Do the parenthesis first. Then, do the multiplication and division from left to right. Finally do the addition.

Solve: First do the parenthesis: (3 + 5) \div 2 + 4 \times 6=8 \div 2 +4 \times 6

Next do the multiplication and division from left to right: 8 \div 2 +4 \times 6=4+24
Last do the addition: 4+24=28
a=28

Check: (3 + 5) \div 2 + 4 \times 6=8 \div 2 +4 \times 6 = 4+24=28

Vocabulary

Order of operations tell us the correct order of evaluating math expressions. We always do Parenthesis first . Then we do multiplication and division (from left to right) and finally addition and subtraction (from left to right) .

Guided Practice

Figure out the value of the variables. Follow the order of operations.

1. (10 - 2) \div 2 + 5 \times 3 = b

2. 4 + (9 + 6) \div 3 = d

3. 12 + 2 \times 3 \div 6 + (7 - 4) = q

Answers:

1. b = 19

2. d = 9

3. q = 16

Practice

Figure out the value of the variables. Follow the order of operations.

  1. 4 \times (6 - 2) \div 2 \times 3 = t
  2. 2 \times (11 - 1) \div 2 = g
  3. 3 \times (12 - 4) - (5 - 2) = m
  4. 6 \times (7 + 3) \div 4 \times 2 = n
  5. 3 \times (5-2) - (3 -2) = p
  6. 2 \times (6+1) \div 2 \times 3 = q
  7. 5 \times (4-1) + 3 \times 8 = r
  8. 8 \times (5-4) \div 2 \times 5 = s
  9. 7 \times (7 - 3) \div 2 + 1 = u
  10. 5 \times (3+4) + 2 \times 3 = w

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Date Created:

Jan 18, 2013

Last Modified:

May 27, 2014
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