Algebraic and Numerical Expressions

Numeric and Algebraic Expressions Review

​Numeric Expressions vs. Algebraic Expressions

• ​Numeric expressions are made up of two or more numbers and at least one operation

• ​Algebraic expressions are made up of at least one variable, at least one operation, and at least one other variable or number.

  • ​variables are letters that represent unknown values

Multiple Choice

Is the following expression numeric or algebraic?

$$6+8(3-4)$$  

• Numeric

• Algebraic

Multiple Choice

Is the following expression numeric or algebraic?

$$8y\div65$$  

• Numeric

• Algebraic

Multiple Choice

Is the following expression numeric or algebraic?

$$97+x\left(66-23\right)$$  

• Numeric

• Algebraic

Multiple Choice

Is the following expression numeric or algebraic?

$$4^2\div8-\left(2-1\right)$$  

• Numeric

• Algebraic

Multiple Select

Which of the following expressions are algebraic? Choose ALL that apply.

• $$154-y$$  

• $$66\div2\left(6-4\right)$$  

• $$889p$$  

• $$76ab-cd$$  

• $$123-45+67\cdot89$$  

​Writing Expressions

• ​Find the keyword(s) that help you know which operation to use

• ​Write the problem in the order given in the problem unless it's one of the special keywords.

  • ​more than

  • ​less than

  • ​subtracted from

  • ​taken from

Multiple Choice

Which expression represents the phrase "12 increased by 45?"

• $$12\cdot45$$  

• $$12+45$$  

• $$45+12$$  

• $$45\cdot12$$  

Multiple Choice

Which expressions represents the phrase "72 less than y?"

• $$y\ -\ 72$$  

• $$72\div y$$  

• $$y+72$$  

• $$72-y$$  

Multiple Choice

Which expression represents the phrase "the total of 62 and 7 times b?"

• $$62+7+b$$  

• $$62\cdot7+b$$  

• $$7+b\cdot62$$  

• $$62+7b$$  

Multiple Choice

It costs $5 per hour to rent a bike. How much will it cost to rent a bike for h hours?

• $$5+h$$  

• $$5-h$$  

• $$5h$$  

• $$5\div h$$  

Multiple Choice

A concession stand charges $2 per pack of cookies and $4 for each hot chocolate. If I buy c cookies and h hot chocolates, which expression represents my total cost?

• $$2c\ +4$$  

• $$2c+4h$$  

• $$2\ +\ 4h$$  

• $$2h+4c$$  

• ​P - solve all problems in parentheses

• ​E - solve all exponents

• ​MD - solve multiplication and division from left to right

• ​AS - solve addition and subtraction from left to righ

​Order of Operations

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Evaluate the expression: $$6-\left(5-3\right)+10$$  

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Evaluate the expression: $$8-4+2\cdot6$$  

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Evaluate the expression: $$78-15\cdot2+3$$  

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Evaluate the expression: $$20-3\left(4+1\right)$$  

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Evaluate the expression: $$24-16\div4\cdot2+3$$  

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Evaluate the expression: $$5\left(10-16\div2\right)+\left(30-27\right)$$  

​Solving Algebraic Expressions

• ​Substitute the numbers in for their variables

• ​Solve the expression using order of operations

  • ​Parentheses

  • ​Exponents

  • ​Multiply & Divide left to right

  • ​Add & Subtract left to right

Fill in the Blank

Evaluate x - 9 for x = 13.

Fill in the Blank

Evaluate 17m for m = 3.

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Evaluate 6(h+9) for h = 2.

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Evaluate x(8-3) for x = 12.

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Evaluate 4b + 2c for b = 2 and c = 3.

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Evaluate 4(y + 2x) for x = 5 and y = 7.