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# 7.1: Solve for the Unknown

Difficulty Level: At Grade Created by: CK-12

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

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. $5 \times (3+4) + 2 \times 3 = w$

Jan 18, 2013