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### Course: Algebra (all content)>Unit 1

Lesson 3: Substitution and evaluating expressions

# Evaluating expressions

Learn to evaluate all sorts of expressions: expressions with one variable, two variables, fractions and decimals, and even expressions in word problems.
Evaluating expressions with two variablesSee video transcript

#### Try it yourself

Evaluate $2c+1$ when $c=4$.

## Let's study another example.

Evaluate $10-\frac{m}{n}+n$ when $m=6$ and $n=3$.
$\phantom{=}10-\frac{m}{n}+n$
$=10-2+3$
$=11$

## Let's try some practice problems!

Evaluate $10-a$ when $a=1$.

Evaluate $6b$ when $b=2$.

Evaluate $7c-4$ when $c=3$.

Evaluate $\frac{8}{d}+3$ when $d=4$.

Evaluate $6a+4b-6$ when $a=1$ and $b=3$.

Evaluate $5x-\frac{x}{y}$ when $x=4$ and $y=2$.

Evaluate $\frac{3}{2}y-3+\frac{5}{3}z$ when $y=4$ and $z=3$.

Evaluate $13-0.5w+6x$ when $w=10$ and $x=\frac{1}{2}$.

## Let's try a word problem

The expression $2m+10c$ gives the amount of money (in dollars) a dessert store makes from selling $m$ muffins and $c$ cakes.
How much money does the dessert store make from selling $3$ muffins and $4$ cakes?
dollars

## Challenge problem 1

Complete the table to evaluate $2x$ at different values of $x$.
$x$$2x$
$1$$2$
$2$$4$
$3$$6$
$4$
$5$
$6$

## Challenge problem 2

A flower store uses the expression $2+5r$ to determine the cost (in dollars) of $r$ roses.
Complete the table to find the cost of different numbers of roses.
Number of roses $\left(r\right)$Cost $\left(2+5r\right)$
$3$$17$
$6$
$9$

Cam has $32$ dollars. How many roses can he afford to buy?
Assume that he wants to buy as many roses as he can.

#### Extra challenge

Explain to a family member, friend, or classmate why the cost of $6$ roses is not double the cost of $3$ roses.

## Want to join the conversation?

• Cam has 32 dollars. How many roses can he afford to buy?
Assume that he wants to buy as many roses as he can.

how do you solve this and come out with the answer 6. Can you please explain?
• The expression 2+5r equals the cost of the roses, which is 36. So you can replace "cost of roses" with 36 and get the expression 2+5r=36. Now you have an equation that you have to solve. Solving this algebraically requires knowledge of algebra higher than what you've got now, so try using the guess-and-check method. Make a chart of amounts of roses and the price that each one of them would cost. 2 roses cost 12 dollars, 3 roses cost 17 dollars, 4 roses cost 22 dollars, 5 roses cost 27 dollars, and 6 roses cost 32 dollars. And that's your answer!
If you want to find out how to solve the equation algebraically, head over to these videos: https://www.khanacademy.org/math/algebra-home/alg-basic-eq-ineq
(1 vote)
• What is PEMDAS? Why do we have to follow it?
• Good question!
PEMDAS is an acronym for:
P – Parentheses
E – Exponents
M – Multiplication
D – Division
S – Subtraction
Note that you do M and D at the same time, and A and S at the same time. When you have a complicated expression, this is the order of which you solve the operations.
For example, let's take the expression:
5 - 2 * 8^2 + (5 - 3 / 3)

Now, if you were to do it left to right, you would do:
3 * 8 ^ 2 + (5 - 3 / 3)
24 ^ 2 + (5 - 3 / 3)
576 + (5 - 3 / 3)
581 - 3 / 3
578 / 3
192.66666667
But, if you use PEMDAS, you get:
5 - 2 * 8^2 + (5 - 3 / 3)  //1st: Parentheses5 - 2 * 8^2 + (5 - 1)  //Division is done first5 - 2 * 8^2 + 4  //2nd: Exponents5 - 2 * 64 + 4  //3rd: Multiplication5 - 128 + 4  //4th: Addition/Subtraction-123 + 4-119  //Answer!

So why do we use PEMDAS? Well, without it, there would be no guidelines on what to do first.
• I don't want to go to a flower store where I can get charged 2$for buying 0 roses. (6 votes) • Well, maybe you can buy infinite number of flowers and get the most out of that$2.
(1 vote)
• the value of the constant is the same regardless of the number of roses.
• I saw a question about PEMDAS and Its very good explanation, What is BOADMASS and when is that used?
• It is spelled: BODMAS. It is exactly the same as PEMDAS. There are also BEDMAS and BIDMAS. They just use different words to represent the same exact rules for order of operations.
B = Brackets or P = Parentheses
O = Orders, or E = Exponents; or I = Indices.
MD = Multiplication & Division; or DM = Division & Multiplicaton
• In the question it asks us to solve, "how much money do you get from selling 3 muffins and 4 cakes,"and it tells us that the price of muffins is 2$, and the cakes are 10$.So now the equation is 2 times 3 + 10 times 4. First we multiply which then gives us 6+40 with will give us 46$(1 vote) • How many dollars in one pound? (0 votes) • Currency exchange rates vary daily. You would need to look it up on the internet for the current exchange rate. (4 votes) • On the 8th problem from the top, I cannot seem to get the answer right. The problem is 3/2y-3+5/3z y=4 z=3. I converted the fractions to decimals before multiplying them, and I keep coming up with 10.8. I know I'm probably doing something stupidly wrong, but can you please tell me what? (2 votes) • The error is from converting the fractions to decimals. 5/3 is a repeating decimal (1.666...). You likely changed it into 1.6 or 1.7. Neither one is equal to 5/3. Unless the fraction creates a terminating decimal, you are better off using the fraction to maintain its entire value. By rounding / truncating repeating decimals, you no longer have the same value and you get incorrect answers when exact answers are needed. 3/2 (4/1) + 5/3 (3/1) Cancel common factors 3/1 (2/1) + 5/1 (1/1) Multiply, then add 6 + 5 = 11 Hope this helps. (0 votes) • If he wants to cut the money and then if the cost of a tulip is 1 dollar dollar then how if you have to spend only$31 then how much money should he pay