Add, Subtract, Multiply, Divide Rational Numbers

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Basic Operations

By: Kevvin Hankins, EDS, MDIV​

​Standard: MGSE7.NS.3

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Solve real-world and mathematical problems involving the four operations with rational numbers. 

​Learning Targets

​I can:

• Represent real-world problems that add, subtract, multiply, or divide rational numbers with models, drawings, and equations.

• Explain how an equation represents a problem.

• Solve real-world problems by adding, subtracting, multiplying, and dividing rational numbers. ​

Minuend: the number you are subtracting from.

Subtrahend: the number that is to be subtracted from the minuend.

Difference : the answer to the subtraction problem.

​Subtration

Addends:  the numbers being added.

Sum: the answer to the addition problem.

​Addition

​Basic Operations Vocabulary

Basic Operations​

​Dividend: the number you need to divide.

Divisor: the number you will use to divide.

Quotient: the answer to the division problem.

Remainder: a leftover when the dividend could not be divided evenly.

​

​Division

Factors: the numbers being multiplied.

​Product: the answer to the multiplication problem.

​Multiplication

​Basic Operations

Basic Operations​

There are four main operations in math.

​​Addition

​

​​Subtraction

​

​​Multiplication

​

​​Division

​

​What are the four fundamental operations?

Words that tell us to

ADD

Words that tell us to

Multiply

Words that tell us to

Divide

Multiple Select

Which of the following words mean to ADD? (check all that apply)

• Sum

• In all

• Difference

• Twice

Multiple Select

Which of the following words mean to SUBTRACT? (check all that apply)

• Minus

• In all

• Difference

• Quotient

Multiple Select

Which of the following words mean to MULTIPLY? (check all that apply)

• Difference

• In all

• Times

• Product

Multiple Select

Which of the following words mean to DIVIDE? (check all that apply)

• Quotient

• Each

• Split Equally

• Product

Fill in the Blank

The phrase "in-all" tells you that you should ____________.

Fill in the Blank

The word "quotient" tells you that you should ____________.

Fill in the Blank

The word "less" tells you that you should ____________.

Fill in the Blank

The word "product" tells you that you should ____________.

Integer Operations

Today, we are reviewing how to add, subtract, multiply and divide integers.

Adding Integers

• When you are adding two positive integers there is an increase in value

• When you are adding a positive and a negative integer there is a decrease in value

• When you are adding a negative and a positive integer there is an increase in value

• When you are adding two negative integers there is a decrease in value

Examples:

(+2) + (+10) = +12

(+5) + (-2) = +3

(-3) + (+6) = +3

(-5) + (-6) = -11

Multiple Choice

(+4) + (+2)

• -6

• +6

• 2

• -2

Multiple Choice

(+5) + (-2)

• +3

• +7

• -7

• -3

Multiple Choice

(-4) + (+5)

• -9

• -1

• +9

• +1

Multiple Choice

(-4) + (-6)

• -10

• +2

• -2

• +10

Subtracting Integers

• When you are subtracting two positive integers there is a decrease in value

• When you are subtracting a positive and a negative integer there is an increase in value

• When you are subtracting a negative and a positive integer there is a decrease in value

• When you are subtracting two negative integers there is an increase in value

Examples:

(+2) - (+10) = -8

(+5) - (-2) = +7

(-3) - (+6) = -9

(-5) - (-6) = +1

Multiple Choice

(+5) - (+3)

• -2

• +8

• +2

• -8

Multiple Choice

(+7) - (-2)

• +9

• +5

• -5

• -9

Multiple Choice

(-6) - (+4)

• +10

• -2

• +2

• -10

Multiple Choice

(-3) - (-4)

• +1

• +7

• -7

• -1

Rules for Multiplying Integers

• When you multiply two numbers with the SAME sign you will get a positive answer

• When you multiply two numbers with DIFFERENT sings you will get a negative answer

Multiple Choice

(-2)(-2)

• -4

• +4

Multiple Choice

(+4)(+6)

• +24

• -24

Multiple Choice

(-5)(2)

• -10

• +10

Rules for Dividing Integers

• The rules for dividing integers are the same as multiplying integers

This graphic is a great tool for helping you to remember the rules when it comes to multiplying and dividing integers.

Multiple Choice

$$10\ \div\ 2$$   

• 5

• -5

Multiple Choice

$$-24\ \div\ 6$$  

• +4

• -4

Multiple Choice

$$-32\ \div\ 8$$  

• -4

• +4

Multiple Choice

$$-72\ \div\ 8$$  

• -9

• +9

Poll

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