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Course: Algebra (all content) > Unit 1

Lesson 3: Substitution and evaluating expressions
Math
Algebra (all content)
Introduction to algebra
Substitution and evaluating expressions
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Evaluating expressions

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

Try it yourself

Evaluate 2c+1 when c=4.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Let's study another example.

Evaluate 10−mn+n when m=6 and n=3.
=10−mn+n
=10−63+3        Replace m with 6 and n with 3
=10−2+3
=11

Let's try some practice problems!

Evaluate 10−a when a=1.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Evaluate 6b when b=2.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Evaluate 7c−4 when c=3.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Evaluate 8d+3 when d=4.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Evaluate 6a​​+4b−6 when a=1 and b=3.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Evaluate 5x−xy when x=4 and y=2.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Evaluate 32y−3+53z when y=4 and z=3.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Evaluate 13−0.5w+6x when w=10 and x=12.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

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?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
dollars

Challenge problem 1

Complete the table to evaluate 2x at different values of x.
x2x
12
24
36
4
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
5
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
6
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

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 (r)Cost (2+5r)
317
6
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
9
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Cam has 32 dollars. How many roses can he afford to buy?
Assume that he wants to buy as many roses as he can.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

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?

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  • aqualine seed style avatar for user Ana Chavarria
    Posted 8 years ago. Direct link to Ana Chavarria's post “Cam has 32 dollars. How m...”
    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?
    (10 votes)
    Default Khan Academy avatar avatar for user
    • purple pi purple style avatar for user StarryNight
      Posted 8 years ago. Direct link to StarryNight's post “The expression 2+5r equal...”
      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)
  • blobby green style avatar for user Darpan Rastogi
    Posted 7 years ago. Direct link to Darpan Rastogi's post “What is PEMDAS? Why do we...”
    What is PEMDAS? Why do we have to follow it?
    (5 votes)
    Default Khan Academy avatar avatar for user
    • hopper cool style avatar for user cheese33
      Posted 7 years ago. Direct link to cheese33's post “Good question! PEMDAS is...”
      Good question!
      PEMDAS is an acronym for:
      P – Parentheses
      E – Exponents
      M – Multiplication
      D – Division
      A – Addition
      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: Parentheses
      5 - 2 * 8^2 + (5 - 1)  //Division is done first
      5 - 2 * 8^2 + 4  //2nd: Exponents
      5 - 2 * 64 + 4  //3rd: Multiplication
      5 - 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.
      Learn more here: http://study.com/academy/lesson/what-is-pemdas-definition-rule-examples.html
      (6 votes)
  • aqualine tree style avatar for user ojinkins
    Posted 7 years ago. Direct link to ojinkins's post “I don't want to go to a f...”
    I don't want to go to a flower store where I can get charged 2$ for buying 0 roses.
    (6 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user Mehboob Rehan
    Posted 7 years ago. Direct link to Mehboob Rehan's post “I saw a question about PE...”
    I saw a question about PEMDAS and Its very good explanation, What is BOADMASS and when is that used?
    (2 votes)
    Default Khan Academy avatar avatar for user
    • stelly blue style avatar for user Kim Seidel
      Posted 7 years ago. Direct link to Kim Seidel's post “It is spelled: BODMAS. ...”
      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
      AS = Addition & Subtraction

      Here are some examples of where these are used according to Wikipedia: PEMDAS is used in the US. BODMAS is used in the UK & Australia. BEDMAS is used in Canada & New Zealand. BIDMAS is used in some African countries.
      (2 votes)
  • blobby green style avatar for user Md. Durjoy Mia
    Posted 5 months ago. Direct link to Md. Durjoy Mia's post “the value of the constant...”
    the value of the constant is the same regardless of the number of roses.
    (2 votes)
    Default Khan Academy avatar avatar for user
  • duskpin ultimate style avatar for user nurali
    Posted 8 years ago. Direct link to nurali's post “I don't understand the wo...”
    I don't understand the word problem with muffins and cakes
    can someone explain it.
    (2 votes)
    Default Khan Academy avatar avatar for user
    • male robot johnny style avatar for user Math Enjoyer
      Posted a year ago. Direct link to Math Enjoyer's post “In the question it asks u...”
      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)
  • female robot grace style avatar for user Aaryan Paul
    Posted 7 years ago. Direct link to Aaryan Paul's post “How many dollars in one p...”
    How many dollars in one pound?
    (0 votes)
    Default Khan Academy avatar avatar for user
  • aqualine ultimate style avatar for user Aubrey Carr
    Posted 8 years ago. Direct link to Aubrey Carr's post “On the 8th problem from t...”
    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)
    Default Khan Academy avatar avatar for user
    • stelly blue style avatar for user Kim Seidel
      Posted 8 years ago. Direct link to Kim Seidel's post “The error is from convert...”
      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)
  • male robot donald style avatar for user Sree Chaitanya. B
    Posted 7 years ago. Direct link to Sree Chaitanya. B's post “If he wants to cut the mo...”
    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
    (0 votes)
    Default Khan Academy avatar avatar for user
  • mr pink red style avatar for user prince_eg17
    Posted 7 years ago. Direct link to prince_eg17's post “it is not the double cost...”
    it is not the double cost of three roses because it builds up a different price
    (0 votes)
    Default Khan Academy avatar avatar for user