1.5 adding and subtracting real numbers i can find the sums and differences of real numbers
TRANSCRIPT
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