addition and subtraction with rational numbers

Integers

Compare positive and negative numbers

Number Line

Addition

negative

numbers that lower than 0

positive

numbers that higher than 0

Compare zero to negative numbers

numbers that lower than 0

Compare zero to positive numbers

numbers that higher than 0

What process can you use to solve addition problems on a number line?

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different signs

like signs

steps

number line

steps

number line

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the sign of the product or quotient will be positive

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  • plus sign / addition sign.
  • minus sign / subtraction sign.

× times sign / multiplication sign.

÷ OR / division sign.

= equals sign.

< less than.

greater than.

≠ NOT equal to.

subtracting

Algorithem

Number line

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both 0<

both 0>

one 0< one 0>

answer will be bigger than 0

add them

answer will be greater than the first number

the answer will always be less than 0

add the numbers and make the awnser negative

take the absulute value of each number

subtract smaller number from bigger number

the answer has the sign of the bigger number

one number >0, one number <0

both numbers >0

both numbers <0

look at the signs to detect where to start and which way to go

from the starting point always move left

answer less than the first number

answer could be positive or negative

from the start always move right

2 minus signs = addition sign plus.

multiplication

Canels

non-canels

division

Canels

X/8 = 5

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reduce the fraction 1x = 5x8

do the multiplication bye bye "1" X = 40

multiply both sides by 8

8/8 = 5x8

(T)(-Z)

(-t)(-z)

(T)(z)

multiply normally

turn the 2 mines signs into a plus sign

multiply normaly

multiply

since one is negative the end result becomes negative

non-canels

divide both sides by 6

reduce the fraction 1x = 9

bye bye "1" X=9

-Z divided -X

Z divided-X

Z divided X

6 X = 54

6/6 = 54/6

A positive number divided by a negative number equals a negative number

A positive number divided by a positive number equals a positive number

a negative number divided by a negative number equals a positive number.