Represent Expressions

Evaluating Expressions

Using GEMA

GEMA

Remember to use GEMA to help you solve expressions.

G

• "G" Stands for Grouping.

• Remember in math when we group things together we us ( )

• Example: (5+2) x 3

• Grouping is the most important. If you see grouping you must do it first in an expression.

Multiple Choice

What operation comes first in this expression? 5 x 2 + (5-1)

• 5 x 2

• 2 + 5

• 5 - 1

E

• "E" stands for Exponents

• Example 10²

• Exponents are the second most important operation. You do them after the grouping but before everything else

• Exponents mean repeated multiplication

• 10² = 10 x 10 = 100

Multiple Choice

What is the correct multiplication sentence for 10³?

• 10 x 3 = 30

• 10 x 10 = 100

• 10 x 10 x 10 = 1,000

M

• "M" stands for Multiplicative, NOT multiplication

• Multiplicative operations are multiplication and division

• You solve these from left to right (like reading a book)

• Multiplicative operations are the 3rd most important. You solve division/multiplication after Grouping and Exponents but before Addition and Subtraction.

Multiple Select

Which of these would you solve using multiplication first? SELECT TWO ***Remember if division and multiplication are in the same problem you solve them from left to right?

• $$\left(5\ +\ 2\right)\times6$$  
  

• $$5\div5\times5$$  
  

• $$5+2\times6$$  

• $$\left(5\ \times\ 2\right)+\left(2\div1\right)$$  

A

• "A" stands for additive, NOT addition

• Additive operations are subtraction and addition

• You solve these left to right as well (if expression only has addition or subtraction)

• Additive operations are the weakest of the operations. They come after everything else.

Multiple Choice

Which of these is solved correctly?

• 5 - 2 + 1 = 2

• 5 - 2 + 1 = 4

The next several slides are going to be practice questions.

Please make sure you solving the questions correctly using scratch paper to show your work. Take your time for each question. Make sure to use GEMA!!!

Multiple Choice

Which expression simplifies to 27?

• $$2\ \times10\ -2\ +5$$

• $$2\ \times10+5+1$$

• $$2\times\left(5\ \times2\right)+7$$

Multiple Choice

Which expression is equal to 18?

• $$8\ +\ \left(12-2\right)$$

• $$\left(8+12\right)-10$$

• $$12\ -\left(4\ +2\right)$$

Multiple Choice

Evaluate:

$$8\ +\ \left(15\div5\right)+\left(3\ \times23\right)$$  

• 70

• 75

• 80

• 85

Multiple Choice

Evaluate:

$$\left(65+53\right)-\left(27-19\right)$$  

• 118

• 110

• 126

• 116

Multiple Choice

Which expression is equal to 59?

• $$50+\left(7+1\right)$$

• $$50+\left(9\times2\right)$$

• $$50+\left(18-9\right)$$

Multiple Choice

$$Expression\ A:\ 10\ \times3+9$$   $$Expression\ B:\ 10\ \times\left(3\ +9\right)$$             Compare the above expressions. 

• The value of A is greater than the value of B

• The value of B is greater than the value of A

• The value of A is equal to the value of B

When writing expressions it is important to look for key words. The following slides we will be reviewing those key words.

Study these words

Multiple Select

Which of the following words mean we will be adding?

• Sum

• Add

• Addition

• Plus

Study these words

Multiple Select

Which of the following words means we are going to be multiplying?

• Product of

• Sum

• Quotient

• Multiply

• Double

Study these words

Multiple Choice

Which of these words means we are going to be subtracting?

• minus

• product

• sum

• multiply

Study these words

Multiple Choice

Which of these words is the answer to a division problem?

• quotient

• product

• sum

• difference

Other important key words

• The word "from" means you need to reverse the order of the numbers

• Example: Subtract 18 from 20 means: 20 - 18. You see how we reversed where 18 and 20 were.

• If the word "and" is in-between two numbers it means you are combining numbers. You are grouping the numbers together. Think about a Peanut butter AND Jelly sandwich. They are grouped together.

• In math we group things together with ( ).

• Example: 5 plus the product of 2 and 5 would be: 5 + (2 x 5)

• The word "by" can also mean grouping.

Let's Practice those skills

Multiple Choice

Which expression shows "multiply 5 by 6 and then add 2.

• $$5\ +\ 6\ +\ 2$$

• $$\left(5\ \times6\right)\ -2$$

• $$\left(5\ \times6\right)+2$$

Multiple Choice

Which expression correctly shows the sum of 30 and 7 minus the product of 6 and 4?

• $$\left(30\ +\ 7\right)-\left(6\ \times4\right)$$

• $$\left(30+7\right)+\left(6\ \times4\right)$$

• $$\left(30+7\right)-\left(6+4\right)$$

Multiple Select

Harry has a number that is 4 times larger than the difference of 15 and 5. Which of the following expressions represent Harry's number? SELECT ALL THAT APPLY.

• 4 x (15 - 5)

• (15 - 5) x 4

• 4 x (5 - 15)

• 4 x 15 - 5