Notes for Decimals, Fractions and Percentages

Decimals, Fractions and Percentages 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%

 A Quarter can be written… As a fraction: 1/4 As a decimal: 0.25 As a percentage: 25%

Here is a table of commonly occurring values shown in Percent, Decimal and Fraction form:

Percent

Decimal

Fraction

1%

0.01

1/100

5%

0.05

1/20

10%

0.1

1/10

12½%

0.125

1/8

20%

0.2

1/5

25%

0.25

1/4

Conversions

**From Percent to Decimal

To convert from percent to decimal: 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:

 From Percent To Decimal move the decimal point 2 places to the left, and remove the “%” sign.

**From Decimal to Percent

To convert from decimal to percent: multiply by 100, and add a “%” sign.

The easiest way to multiply by 100 is to move the decimal point 2 places to the right:

 From Decimal To Percent move the decimal point 2 places to the right, and add the “%” sign.

**From Fraction to Decimal

The easiest way to convert a fraction to a decimal is to divide the top number by the bottom number (divide the numerator by the denominator in mathematical language)

Example: Convert 2/5 to a decimal

Divide 2 by 5: 2 ÷ 5 = 0.4

**From Decimal to Fraction

To convert a decimal to a fraction needs a little more work.

Example: To convert 0.75 to a fraction

Steps

First, write down the decimal “over” the number 1

 0.75/1

Multiply top and bottom by 10 for every number after the decimal point (10 for 1 number, 100 for 2 numbers, etc)

 0.75 × 100 1 × 100

(This makes a correctly formed fraction)

 75/100

Then Simplify the fraction

 3/4

**From Fraction to Percentage

The easiest way to convert a fraction to a percentage is to divide the top number by the bottom number. then multiply the result by 100, and add the “%” sign.

Example: Convert 3/8 to a percentage

First divide 3 by 8: 3 ÷ 8 = 0.375,
Then multiply by 100: 0.375 x 100 = 37.5

**From Percentage to Fraction

To convert a percentage to a fraction, first convert to a decimal (divide by 100), then use the steps for converting decimal to fractions (like above).

Example: To convert 80% to a fraction

Steps

Example

Convert 80% to a decimal (=80/100):

0.8

Write down the decimal “over” the number 1

 0.8/1

Multiply top and bottom by 10 for every number after the decimal point (10 for 1 number, 100 for 2 numbers, etc)

 0.8 × 10 1 × 10

(This makes a correctly formed fraction)

 8/10

Then Simplify the fraction

 4/5

A Basic Overview of the Number Classification System

A Basic Overview of the Number Classification System

Natural Numbers
Natural numbers are what you use when you are counting one to one objects. You may be counting pennies or buttons or cookies. When you start using 1,2,3,4 and so on, you are using the counting numbers or to give them a proper title, you are using the natural numbers.

Whole Numbers
Whole numbers are easy to remember. They’re not fractions, they’re not decimals, they’re simply whole numbers. The only thing that makes them different than natural numbers is that we include the zero when we are referring to whole numbers. However, some mathematicians will also include the zero in natural numbers and I’m not going to argue the point. I’ll accept both if a reasonable argument is presented. Whole numbers are 1, 2, 3, 4, and so on.

Integers
Integers can be whole numbers or they can be whole numbers with a negative signs in front of them. Individuals often refer to integers as the positive and negative numbers. Integers are -4, -3, -2, -1, 0, 1, 2, 3, 4 and so on.

Rational Numbers
Rational numbers have integers AND fractions AND decimals. Now you can see that numbers can belong to more than one classification group. Rational numbers can also have repeating decimals which you will see be written like this: 0.54444444… which simply means it repeats forever, sometimes you will see a line drawn over the decimal place which means it repeats forever, instead of having a …., the final number will have a line drawn above it.

Irrational Numbers
Irrational numbers don’t include integers OR fractions. However, irrational numbers can have a decimal value that continues forever WITHOUT a pattern, unlike the example above. An example of a well known irrational number is pi which as we all know is 3.14 but if we look deeper at it, it is actually 3.14159265358979323846264338327950288419…..and this goes on for somewhere around 5 trillion digits!

Real Numbers
Here is another category where some other of the number classifications will fit. Real numbers include natural numbers, whole numbers, integers, rational numbers and irrational numbers. Real numbers also include fraction and decimal numbers.

Welcome Back!

I will be co-teaching this year with Ms. Broussard, Ms. Leak, and Mrs. Harrison.  I also have an 8th grade study hall and 7th grade cycle class.  I am looking forward to another great year!

Last Week of School

Tuesday and Wednesday we will have a class review for our final exam.   Wednesday we will have an awards ceremony at 8:30am.  Exams will be Thursday and Friday, both early release days.

~~As time allows we will continue with Xtramath and Odyssey.

~~~All students will be working toward their grade level TEKS according to their IEPs.

May 19 – 23

This week will be spent reviewing for the Final Exam.

Monday – Math terms and symbol’s, Money, Temperature, and Measurements

Tuesday – Geometry, Shapes, and Nets

Wednesday – Math Definitions, Measuring Angles, Identifying Angles, Symmetry, Perimeter and Area

Thursday – Mean, Median, Mode and Graphs

Friday – Finish all Reviews that have not been completed.

~~As time allows we will continue with Xtramath and Odyssey.

~~~All students will be working toward their grade level TEKS according to their IEPs.

May 12-16

Monday – Tuesday ~ Decimals: Hundredths and Tenths

Wednesday – Thursday ~ Percents and Fractions

Friday ~ Test using Decimals, Percents and Fractions

~~As time allows we will continue with Xtramath and Odyssey.

~~~All students will be working toward their grade level TEKS according to their IEPs.

May 5 – May 9

Monday -Wednesday ~ Measuring pints, gallons, quarts, and cups.

Thursday Review for TEST

Friday ~ Test

~~As time allows we will continue with Xtramath and Odyssey.

~~~All students will be working toward their grade level TEKS according to their IEPs.

April 28 ~ May 2

Monday and Tuesday ~ Reading time to the hour, half hour, five minutes and other increments and elapsed time.

Wednesday ~ TEST over reading time increments and elapsed time.

Thursday and Friday ~ compare capacity of measurements using pints, quarts, gallons, and liters.

~~As time allows we will continue with Xtramath and Odyssey.

~~~All students will be working toward their grade level TEKS according to their IEPs.

April 21-25

Just a reminder there is no school tomorrow, Good Friday April 18th.  Happy EASTER!

Monday, April 21st ~ We will have one last class review over STAAR information.

Tuesday and Wednesday ~ STAAR TESTING!

Thursday and Friday ~ Each student will work on Xtramath and Odyssey.

~~~All students will be working toward their grade level TEKS according to their IEPs.