# Evaluate Expression Worksheet

Evaluate Expression Worksheet
• Page 1
1.
Find the value of the expression , for $n$ = 4.
 a. 3 b. 2 c. 1 d. 4

#### Solution:

n + 64 ÷ 45n
[Original expression.]

4+64÷45(4)
[Substitute n = 4.]

= 4+165(4)
[Do the division in the numerator: 64 by 4.]

= 20 / 20
[Simplify the terms in the numerator and the denominator.]

= 1
[Divide.]

The value of the given expression is 1.

2.
The total surface area of a cuboid is given by the formula A = 2($\mathrm{lw}$ + $\mathrm{wh}$ + $\mathrm{lh}$). Find the height of a cuboid whose length is 60 cm, width is 50 cm, and total surface area is 14800 cm2.
 a. 40 cm b. 45 cm c. 90 cm d. 100 cm

#### Solution:

A = 2(lw + lh + wh)
[Given.]

A = 2lw + 2lh + 2wh
[Distributive property.]

A - 2lw = 2lh + 2wh
[Subtract 2lw from both sides.]

A - 2lw2(l+w) = h
[Divide both sides by 2(l + w).]

The formula is solved for h.

h = A - 2lw2(l+w)

h = 14800-(2×60×50)2(60+50)
[Substitute: A = 14800, l = 60, w = 50.]

h = 14800 - 6000220

h = 8800 / 220 = 40

The height of the cuboid is 40 cm.

3.
Total surface area of a cube is given by the formula, L = 6$s$2, where $s$ is the side of the cube. Find the side of the cube, if the total surface area of the cube is known.
 a. $\sqrt{\frac{L}{2}}$ b. $\sqrt{2L}$ c. $\sqrt{\frac{L}{6}}$ d. $\sqrt{6L}$

#### Solution:

L = 6s2
[Given.]

L / 6 = s2
[Divide both sides by 6.]

L6 = s2
[Take square root on both sides.]

L6 = s

So, the side of the cube = L6

4.
Solve $\frac{1}{f}$ = $\frac{1}{u}$ + $\frac{1}{v}$ for $u$.
 a. $u$ = b. $u$ = - $\frac{1}{f}$ - $\frac{1}{v}$ c. $u$ = d. $u$ =

#### Solution:

1f = 1u + 1v

1f - 1v = 1u
[Subtract 1v from both sides.]

v - ffv = 1u
[Simplify.]

fvv - f = u

5.
Solve the formula $v$ = $u$ + $\mathrm{at}$ for $a$. Indicate any restrictions on the values of the variables.
 a. $a$ = $u$ + $\mathrm{vt}$, $t$ ≠ 0 b. $a$ = ($v$ + $u$)$t$, $v$ ≠ 0 c. $a$ = , $t$ ≠ 0 d. $a$ = , $t$ ≠ 0

#### Solution:

v = u + at
[Given.]

v - u = at
[Subtract u from both sides.]

v - ut = a
[Divide both sides by t.]

a = v - ut
[Symmetry property.]

The solution is a = v - ut, t ≠ 0
[The solution must exclude values of a variable that make the denominator zero.]

6.
Solve P = $\frac{100I}{RT}$ for I.
 a. I = 100PRT b. I = 100 + PRT c. I = $\frac{PRT}{100}$ d. I = $\frac{100}{PRT}$

#### Solution:

P = 100I / RT
[Given.]

PRT = 100I
[Multiply RT on both sides.]

PRT100 = I
[Divide both sides by 100.]

I = PRT100
[Property of Symmetry.]

7.
If ${7}^{n}$ = 49, then find the value of $n$.
 a. 5 b. 2 c. 125 d. 3

#### Solution:

7n = 49

7n = 72

n = 2
[Powers are equal, when bases are equal.]

So, the value of n is 2.

8.
Find the value of 83.
 a. 4,096 b. 512 c. 64 d. 516

#### Solution:

83 = 8 × 8 × 8
[Write exponential expression in product form.]

= 512
[Simplify.]

So, the value of 83 is 512.

9.
A bus travels at a constant speed of 98 miles per hour. Find the distance traveled by the bus in 9 hours.
 a. 3528 miles b. 882 miles c. 1764 miles d. 4410 miles

#### Solution:

Total distance traveled by the bus in x hours = 98x

Distance traveled by the bus in 9 hours = 98 × 9 = 882 miles

Jeff mows 4 lawns per day. He earns $1 mowing a lawn. How much will he earn, if he works for 4 days?  a.$16 b. $31 c.$36 d. $12 #### Solution: Total amount earned per day = Number of lawns mowed × Amount earned per lawn Amount earned per day = 4 ×$1 = $4 Amount earned in x days =$4 × x
Amount earned in 4 days = $4 × 4 =$16