1.5 ADDING AND SUBTRACTING REAL NUMBERSI can find the sums and differences of real numbers.

YOU CAN ADD OR SUBTRACT USING A NUMBER LINE

• 3+5

YOU CAN ADD OR SUBTRACT USING A NUMBER LINE

• 3+(-5)

YOU CAN ADD OR SUBTRACT USING A NUMBER LINE

• -3+5

YOU CAN ADD OR SUBTRACT USING A NUMBER LINE

• -3+(-5)

ABSOLUTE VALUE

• The distance between a number and 0 on the number line.

SAME SIGNS ADD (SSA)

• To add two numbers with the same sign, add their absolute value.

• The sum has the same sign as the addends.

• Examples:• 3+4

• -3 + (-4)

DIFFERENT SIGNS SUBTRACT (DSS)

• To add two numbers with different signs , subtract the absolute values.

• The sum has the same sign as the addend with the greater absolute value.

• Examples:• -3 + 4

• 3 + (-4)

FRACTIONS

• Find the least common denominator.

• Ex: ¾ + (- ) • +(- )• DSS• -

INVERSE PROPERTY OF ADDITION

• Two number the same distance from 0 on a number line are called opposites (ex: 3 and -3)

• A number and its opposite are called additive inverses

• The inverse property of addition says:• For every real number a, there is an additive inverse –a such that

a + (-a) = 0

Examples?

SUBTRACTING REAL NUMBERS

• To subtract a real number, add the opposite• a – b = a + (-b)

• 3 – 5

• 3 – (-5)

1.6 MULTIPLYING AND DIVIDING REAL NUMBERSI can find products and quotients of real numbers.

MULTIPLYING REAL NUMBERS

• The product of two real numbers with different signs is negative.• 2(-3)• -2•3

• The product of two real numbers with the same sign is positive.• 2•3• -2(-3)

SQUARE ROOTS

• Recall that a is a square root of b if a2 = b

• Ex: = 3 but it is also -3 since (-3)2 = 9

• The symbol ± in front of the radical indicates both square roots.

DIVIDING REAL NUMBERS

• The quotient of two real numbers with different signs is negative

• The quotient of two real numbers with the same sign is positive

DIVISION INVOLVING ZERO

• The quotient of 0 and any nonzero real number is 0• 0÷8 = 0

• The quotient of any real number and zero is undefined• 8÷0 = undefined• 0÷0 = undefined

INVERSE PROPERTY OF MULTIPLICATION

• For every real nonzero number a, there is a multiplicative inverse such that

a() = 1

RECIPROCAL

• The reciprocal of a nonzero real number of the form is

• The product of a number and its reciprocal is 1• So, the reciprocal is the multiplicative inverse

DIVIDING FRACTIONS

• When dividing fractions, multiply the reciprocal.

• =

ASSIGNMENT

• Worksheet