Fraction, Decimal, Percent Review

Including Prime Factorizationand Order of Operations

I can generate equivalent FRACTIONS, DECIMALS, and PERCENTS using real world problems.

I can order a set of rational numbers arising from mathematical and real-world contexts.

I can generate equivalent numerical expressions using order of operations, including whole number exponents and prime factorization.

Fractions, Decimals, and Percents are just different ways of showing the same value:

A Half can be written...

   

As a fraction: 1/2

As a decimal: 0.5

As a percentage: 50%

Fractions, Decimals, Percents:Some of the Sight Fractions

Always make a fraction, decimal, percent chart:

Fraction Decimal (out of 1.00)

Percent (out of 100)

Fraction to Decimal If they give you the fraction, write it in the table.

Otherwise, use the numeric data to write the fraction. (Remember, numerator is what they are asking for and denominator is how many make a whole).

Be careful, sometimes they give you the parts and sometimes they give you the whole.

Examples: 20 boys and 30 girls. Fraction of boys: 20/50

Fraction of girls: 30/50. (Add to get whole) 80 marbles and 20 are red. Fraction of red

marbles: 20/80 Fraction of not red marbles: 60/80 (Subtract to get Not Red Part)

Fraction to Decimal

Fraction Decimal Percent

• Check if you can simplify the fraction. (eg. 9/12 = ¾) Know your sight fractions!

• See if you can multiply the denominator to make 10, 100, or 1000. = = .45

• Remember your multiplication facts 10 x 10 = 100, 25 x 4 = 100, 20 x 5 = 100, 50 x 2 = 100, 8 x 125 = 1000

• Divide the numerator by the denominator.

• If it is a mixed number, just put the whole number in front of the decimal.

Fraction to Decimal Examples:

Fraction Decimal Percent

Try putting these fractions in the table and converting to decimal:

•

•

• 2

Fraction to Decimal Examples:

Fraction Decimal Percent

Try putting these fractions in the table and converting to decimal:

• Sally had 6 blue marbles, 9 green marbles and 5 yellow marbles. Write the fraction and decimal of marbles that are not green.

• There were 50 questions on a test. Mikey got 43 correct. Write the fraction and decimal to represent the questions Mikey got correct. Write the fraction and decimal to represent the questions he got incorrect.

Decimal to Percent

Fraction Decimal Percent

Since Percent means “out of 100” , move the decimal 2 places to the right. Just follow the arrow. Moving the decimal twice is the same thing as multiplying by 100 to put the decimal behind the hundredths place.

Then just add the percent sign behind the new number.

For example: .78 = 78% Don’t worry if there is still a decimal in the number. For example:

.124 = 12.4%

Decimal to Percent

Fraction Decimal Percent

Now you try, put these in the table. Remember, make the arrow to help you.

.37

.08

4.35

.032 .6

Percent to Decimal

Fraction Decimal Percent

divide by 100, and remove the "%" sign.

The easiest way to divide by 100 is to move the decimal point 2 places to the left:

Remember, follow the arrow:

85% = .85 230% = 2.3 1.35% = .0135 Add zeros when

needed.

Percent to Decimal

Fraction Decimal Percent

Now you try it. Put the following percents in the table and change them to decimal. Remember to draw the arrow to help you.

98% 760% 3.23% .58%

Decimal to Fraction

Fraction Decimal Percent

Say it, Write it, Simplify it!

Say the decimal the correct mathematical way.

Write the fraction exactly as you said it.

Simplify it if possible.

Example: .15 is “fifteen hundredths” = ÷5

÷5

320

Decimal to Fraction

Fraction Decimal Percent

Now, you try it! Put these decimals in the table and convert them to fractions in simplest form:

.38 2.44 1.55 .08 .004

Benchmark Question 1:Hint: Change all numbers to the same thing. Either fraction, decimal or percent. First, think which one would be easiest.

Benchmark Question 3:Make sure you make the Fraction, Decimal, Percent Chart

Benchmark Question 12: Make Fraction, Decimal, Percent Chart! What does percent mean?

Benchmark Question 13: Make Fraction, Decimal, Percent Chart

Benchmark Question 41: (Note: Actually adds up to 55)

Prime Factorization

Key Vocabulary -

Prime Number – Exactly 2 factors, one and itself.Ex. 2, 3, 5, 7, 11….The only way to make these products is to multiply one times itself.

Composite Number – More than 2 factors.Ex. 6 because factors are 1 x 6, 2 x 3.

Neither – 0 and 1 are neither.

What about the number 2? Is it prime, composite or neither?

True or False? All even numbers are composite. Why or why not?

Is 39 prime? Why or Why not?

Remember your divisibility rules!

Factor Tree Example:

120

Start with any two factors.

12 10Check if these are prime or composite. 2 6 2

5

Circle any prime numbers and stop. Keep going if composite.

2 3

120 = 2 x 2 x 2 x 3 x 5 Write the prime numbers (circled factors) least to greatest.Multiply to check!

Write using exponents if correct: 120 = x 3 x 5

Prime Factorization:Your turn. Make the factor tree and write the prime factorization of 180. Do all your steps:

Factor Tree, Write the factors least to greatest, Checking Steps, and Exponents.

180

Benchmark Question 21

Order of Operations:

P - Parentheses (), { } , [ ] Any type of grouping symbols are always done first. If there is more than one

operation in parentheses, they all have to be done before you can

move on. In this case pretend like what is in parentheses is a brand new problem.

E - Exponents.

MD - Multiply and/or Divide from Left to Right. Remember, fractions mean to divide. A number next to a

parentheses means to multiply.

AS - Add and/or Subtract from Left to Right.

Always make this checklist and check it off as you go!

Order of Operations Example:

P

E

MD

AS

80 – 5 ( 12 + 8 2 ) + 3 = ÷

80 – 5 ( 12 + 4 ) + 3 =

80 – 5 ( 16 ) + 3 =

80 – 80 + 3 =

0 + 3 = 3

Order of Operations:

P

E

MD

AS

60 + 12 3 x 2 – ÷

P

E

MD

AS

4 ( 8 – 3 + 1) 2

Your Turn:

Benchmark Question 22

Benchmark Question 43