Evaluate formulas.

To evaluate a formula, we replace its letters, called variables, with specific numbers
and evaluate the right side using the order of operations rule.

3

3.7 Order of Operations and Complex Fractions 287

SolveTo evaluate the expression, we use the order of operations rule.

Prepare to add the fractions within the parentheses:

Their LCD is 8. Build so that its denominator is 8:

.

Prepare to multiply the fractions.

Write as an improper fraction.

Simplify:.

StateThe completed wall will be 49 inches high.

CheckWe can estimate to check the result. Since one block and one layer of
mortar is about 6 inches high, eight layers of blocks and mortar would be
8  6 inches, or 48 inches high. The result of 49 inches seems reasonable.

49

 49 1  49

Multiply the numerators and multiply the

denominators. To simplify, remove the common

factor of 8 from the numerator and denominator.



8

1

 49

1  8

1

(^5 98)



8

1

a

49

8

b

Add the numerators of the fractions: 6  3 9.

5 b Write the sum over the common denominator 8.

9

8

 8 a

3

4 

2

2 

6

8

3

4

b

6

8



3

8

b 8 a 5

3

4



3

8

8 a 5

Self Check 5

The formula for the area of a

triangle is. Find the

area of a triangle whose base is

meters long and whose

height is meters.

Now TryProblems 27 and 87

(^15 13)
(^12 12)
A^12 bh
EXAMPLE (^5) The formula for the area of a trapezoid is A ,
where Ais the area,his the height, and aand bare the lengths of its bases. Find A
when h in.,a in., and b in.
Strategy In the formula, we will replace the letter hwith , the letter awith ,
and the letter bwith.
WHYThen we can use the order of operations rule to find the value of the
expression on the right side of the symbol.
Solution
This is the formula for the area of a trapezoid.
Replace h,a, and bwith the given values.
Do the addition within the parentheses:.
To prepare to multiply fractions, write as an improper
fraction and 8 as.
Write the improper fraction as a mixed number by
dividing 20 by 3.
The area of the trapezoid is 6 23 in.^2.
20
 6 2 3
3
Multiply the remaining factors in the numerator.
 (^) Multiply the remaining factors in the denominator.

20

3

To simplify, factor 8 as 2 4. Then remove the common

 (^) factor of 2 from the numerator and denominator.
1 # 5 # 2
1

4

2
1

3 # 1

Multiply the numerators.
 (^) Multiply the denominators.
1 # 5 # 8
2 # 3 # 1
8
1
(^1 23)


1

2

a

5

3

ba

8

1

b

 2 21  5 21  8

1

2

a 1

2

3

b1 82



1

2

a 1

2

3

ba 2

1

2

 5

1

2

b

A

1

2

h(ab)

(^5 12)
(^1 232 12)

1 32 2 12 5 21

1

2 h^1 ab^2

h

a

b

A trapezoid