Summer Assignment Review

Classifying Numbers and Solving Equations by Clearing Fractions or Decimals

Classifying Numbers

4.5

** What kind of number is not real?

PracticeDetermine if the number is real, justify your answer.

1) 2) 3)

Classify each number.

4) 5) 1.2121212121 6)

= -9 Real - Integer= 9i Not Real - Imaginary

= 3i Not Real - Imaginary

** Will there ever be a time when a negative under the radical will produce a Real number? Yes, odd roots. because

Integer Rational Imaginary

PracticeMake an ordered list to classify the number in as many ways possible.

7) 8) 1.2112111211112… 9)

Real, Rational, Integer

Real, Irrational

Real, Rational, Integer,Whole Number,Natural Number

Why should we use organized lists ?

Solving Equations by Clearing Fractions

ExampleThe least common multiple of 2,3, and 6 …

6Multiply every term in the equation by 6

Solve the resulting equation.

6 ∙23𝑥+6 ∙

12𝑥=6 ∙

56+6 ∙2 𝑥

4 𝑥+3𝑥=5+12𝑥7 𝑥=5+12𝑥−5 𝑥=5𝑥=−1

PracticeSolve:

1) 2) 3)

4) 5)

𝑥=−16

4 𝑥=1517

11 𝑥=6

Clearing DecimalsYou can clear decimals by converting them to fractions and multiplying by the LCD (there is no need to reduce the fractions, or re-write the equation with them).

Solve 2.3=2310,1.13=

113100

,0.04=4100

Multiply every term in the equation by the LCD.

100 ∙2.3𝑥−100 ∙1.13=100 ∙0 .04 𝑥

230 𝑥−113=4 𝑥

Hint: The term with the most decimal paces tells you which power of ten to multiply by (or how many decimal places to move).

Solve the resulting equation.

−113=−226 𝑥𝑥=

113226

𝑥=12

PracticeSolve:

1) 2 3)

4)

𝑥=4

𝑥=−1415

𝑥=1

𝑥=2516