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Course: Algebra (all content) > Unit 1
Lesson 3: Substitution and evaluating expressionsEvaluating expressions
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
$1\text{}3/4$  an exact decimal, like
$0.75$  a multiple of pi, like
or$12\text{}\text{pi}$ $2/3\text{}\text{pi}$
Let's study another example.
Evaluate $10{\displaystyle \frac{m}{n}}+n$ when $m=6$ and $n=3$ .
$\phantom{=}10{\displaystyle \frac{{m}}{{n}}}+{n}$
$=10{\displaystyle \frac{{6}}{{3}}}+{3}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{Replace}{m}\text{with}{6}\text{and}{n}\text{with}{3}$
$=102+3$
$=11$
Let's try some practice problems!
Evaluate $10a$ 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
$1\text{}3/4$  an exact decimal, like
$0.75$  a multiple of pi, like
or$12\text{}\text{pi}$ $2/3\text{}\text{pi}$
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
$1\text{}3/4$  an exact decimal, like
$0.75$  a multiple of pi, like
or$12\text{}\text{pi}$ $2/3\text{}\text{pi}$
Evaluate $7c4$ 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
$1\text{}3/4$  an exact decimal, like
$0.75$  a multiple of pi, like
or$12\text{}\text{pi}$ $2/3\text{}\text{pi}$
Evaluate $\frac{8}{d}}+3$ 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
$1\text{}3/4$  an exact decimal, like
$0.75$  a multiple of pi, like
or$12\text{}\text{pi}$ $2/3\text{}\text{pi}$
Evaluate $6a+4b6$ 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
$1\text{}3/4$  an exact decimal, like
$0.75$  a multiple of pi, like
or$12\text{}\text{pi}$ $2/3\text{}\text{pi}$
Khan Academy video wrapper
Evaluating expressions with two variablesSee video transcript
Evaluate $5x{\displaystyle \frac{x}{y}}$ 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
$1\text{}3/4$  an exact decimal, like
$0.75$  a multiple of pi, like
or$12\text{}\text{pi}$ $2/3\text{}\text{pi}$
Evaluate $\frac{3}{2}}y3+{\displaystyle \frac{5}{3}}z$ 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
$1\text{}3/4$  an exact decimal, like
$0.75$  a multiple of pi, like
or$12\text{}\text{pi}$ $2/3\text{}\text{pi}$
Khan Academy video wrapper
Evaluating expressions with two variables: fractions & decimalsSee video transcript
Evaluate $130.5w+6x$ when $w=10$ and $x={\displaystyle \frac{1}{2}}$ .
 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
$1\text{}3/4$  an exact decimal, like
$0.75$  a multiple of pi, like
or$12\text{}\text{pi}$ $2/3\text{}\text{pi}$
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
$1\text{}3/4$  an exact decimal, like
$0.75$  a multiple of pi, like
or$12\text{}\text{pi}$ $2/3\text{}\text{pi}$
Khan Academy video wrapper
Evaluating an expression with one variableSee video transcript
Challenge problem 1
Complete the table to evaluate $2x$ at different values of $x$ .
 
 

Khan Academy video wrapper
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  Cost  

 

The cost of $6$ roses
To find the cost of $6$ roses, we need to evaluate the expression $2+5r$ when $r=6$ :
$\phantom{=}2+5{r}$
$=2+5\cdot {6}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}{\text{Replace}{r}\text{with}{6}\text{.}}$
$=2+30\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}{\text{Multiply first because of order of operations}}$
$=32$
The cost of $6$ roses is $32$ dollars.
The cost of $9$ roses
To find the cost of $9$ roses, we need to evaluate the expression $2+5r$ when $r=9$ :
$\phantom{=}2+5{r}$
$=2+5\cdot {9}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}{\text{Replace}{r}\text{with}{9}\text{.}}$
$=2+45\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}{\text{Multiply first because of order of operations}}$
$=47$
The cost of $9$ roses is $47$ dollars.
The answer
Here is the completed table:
Number of roses  Cost  

Cam has $32$ dollars. How many roses can he afford to buy?
Assume that he wants to buy as many roses as he can.
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
$1\text{}3/4$  an exact decimal, like
$0.75$  a multiple of pi, like
or$12\text{}\text{pi}$ $2/3\text{}\text{pi}$
Cam can buy $6$ roses with $32$ dollars.
Extra challenge
Explain to a family member, friend, or classmate why the cost of $6$ roses is not double the cost of $3$ roses.
Think about the expression for cost $2+5r$ .
What if the expression for cost was just $5r$ instead?
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