Ch 2: 1.1 Algebraic Expression

Algebraic Expressions

What is an Expression

 An expression is a phrase made up of numbers, operation symbols, and sometimes variables. 

A variable is a letter that represents an unknown number. When you multiply a number by a variable, you do not need a multiplication sign between the two. You can write the number directly in front of the variable.

 This number multiplied by the variable is called the coefficient.

Multiple Choice

Algebraic expressions can have a variable, operational symbols, and numbers?

• True

• False

Let's look at an expression...

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Key Words in Algebraic Expressions

Addition: sum, more, more than, plus, increased by, gain

Subtraction: difference, less, less than, minus, decreased by, loss

Multiplication: product, multiplied by, times, double, triple

Division: quotient, divided by, per, ratio, half, third, fourth, into, equal groups

Exponents: times itself, squared, cubed

Multiple Select

Finding these words in an expression means to subtract: sum, more, more than, plus, increased by, gain

• True

• False

Multiple Select

Finding these words in an expression mean to subtract: difference, less, less than, minus, decreased by, loss

• true

• false

Lets Look at some Examples

Write five plus three times itself as an expression.

Step 1. What are the key words?

Step 2. What are the terms/numbers?

Step 3. Write out the expression.

So we get 5 + 3²

The sum of five and four.

Step 1. What are the key words?
Step 2. What are the numbers/variables?
Step 3. Write out the expression.

5+4

Ten less than a number

What are the key words?

Step 1. What are the key words?

Step 2. What are the numbers/variables?

Step 3. Write out the expression

n - 10

Multiple Choice

Which phrase represents "the sum of 11 and a number".

• 11-x

• 11+x

• -11+1

• -11-x

Multiple Choice

Choose the right expression for "the difference of three and a number".

• 3x

• 3-x

• x-3

• $$\frac{3}{x}$$

Multiple Choice

w increased by 5

• w - 5
• 5w
• w + 5
• w / 5

Multiple Choice

Fourteen subtracted from a number written as an expression is

• 14-x

• x-14

• x/14

• 14+x

There are many ways to write a multiplication and division expression.

Multiple Choice

twenty times a number

• 20 + x

• x - 20

• 20x

• x/20

Multiple Choice

the quotient of seven and a number

• 7/x

• x/7

• x - 7

• 7 - x

Multiple Choice

ten divided by a number

• x + 10

• 10 - x

• 10/x

• x/10

Multiple Choice

the quotient of a number and twelve

• x + 12

• x - 12

• 12/x

• x/12

Multiple Choice

Jamal helped his grandmother plant her vegetable garden. He planted 3 rows of zucchini seeds and 4 rows of yellow squash seeds. Each row had s seeds. Which expression represents how many seeds Jamal planted in all?

• 3s + 4s

• 3s + 4

• 4s + 3

• 34s

Multiple Choice

If m represents the amount of money Zoe had, which expression represents how he spent $28?

• $$m\ -\ 28$$
  

• $$m\ +\ 28$$

• $$28m$$

• $$\frac{m}{28}$$

Multiple Choice

If g represents Edna’s grade, which expression shows that she earned 5 points extra credit?

• $$g\ +\ 5$$

• $$g\ -\ 5$$

• $$5g$$

• $$\frac{g}{5}$$

Multiple Choice

If p represents the points Kia scored in a game, which expression shows how she tripled her point total?

• $$3p$$

• $$3\ -\ p$$

• $$3\ +\ p$$

• $$\frac{p}{3}$$

Multiple Choice

If c represents the cookies the Joe bought, which expression shows how much he split between himself and 3 siblings?

• $$\frac{c}{4}$$

• $$4c$$

• $$c\ +\ 4$$

• $$c\ -\ 4$$

Multiple Choice

Polly, Jack, and Cara went to a craft store to buy special beads to make friendship bracelets. Each friend plans to put s star-shaped beads on their bracelet. Which expression represents how many star-shaped beads the friends should buy?

• $$3s$$

• $$s\ +\ 3$$

• $$s\ -\ 3$$

• $$\frac{s}{3}$$

Multiple Choice

For a big dinner, Hayley needs to extend her dining room table. Without the extra piece, the table is 6 feet long by 3 feet wide. Extending it increases the length e feet. Which expression represents the area of the table with the extension?

• $$3\left(6\ +\ e\right)$$

• 36e

• 3 + 6e

• $$\frac{e}{6}\ +\ 3$$

Multiple Choice

Tiana went to Game Stop to purchase a gaming system. They had a special promotion where for a limited time systems were half the price. She also had a coupon for $25 dollars off the sale price. If g represents the game system, which expression represents the sale price along with the coupon?

• $$\frac{g}{2}\ -\ 25$$

• $$\frac{g}{2}+25$$

• $$2g\ -\ 25$$

• $$\frac{g}{25}-2$$

Multiple Choice

Luke's parents hired a clown for his birthday party. The clown charges $100 plus an additional $20 per hour. If h represents the hours, which expression represents how much Luke's parents spent on the clown?

• $$100\ +\ 20h$$

• $$100h\ +\ 20$$

• $$100\ +\frac{h}{20}$$

• $$100\ +\ h$$

Multiple Choice

The debate team bought 18 matching T-shirts to split among its members. Each member of the team will get t T-shirts. Choose the expression that shows how many people are on the debate team.

• $$\frac{18}{t}$$

• 18t

• 18 + t

• $$18\ -\ t$$