	Algebra Tutorials!

	Thursday 21st of November



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	Scientific Notation
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	Graphing Equations in Three Variables
	What the Standard Form of a Quadratic can tell you about the graph
	Simplifying Radical Expressions Containing One Term
	Adding and Subtracting Fractions
	Multiplying Radical Expressions
	Adding and Subtracting Fractions
	Multiplying and Dividing With Square Roots
	Graphing Linear Inequalities
	Absolute Value Function
	Real Numbers and the Real Line
	Monomial Factors
	Raising an Exponential Expression to a Power
	Rational Exponents
	Multiplying Two Fractions Whose Numerators Are Both 1
	Multiplying Rational Expressions
	Building Up the Denominator
	Adding and Subtracting Decimals
	Solving Quadratic Equations
	Scientific Notation
	Like Radical Terms
	Graphing Parabolas
	Subtracting Reverses
	Solving Linear Equations
	Dividing Rational Expressions
	Complex Numbers
	Solving Linear Inequalities
	Working with Fractions
	Graphing Linear Equations
	Simplifying Expressions That Contain Negative Exponents
	Rationalizing the Denominator
	Decimals
	Estimating Sums and Differences of Mixed Numbers
	Algebraic Fractions
	Simplifying Rational Expressions
	Linear Equations
	Dividing Complex Numbers
	Simplifying Square Roots That Contain Variables
	Simplifying Radicals Involving Variables
	Compound Inequalities
	Factoring Special Quadratic Polynomials
	Simplifying Complex Fractions
	Rules for Exponents
	Finding Logarithms
	Multiplying Polynomials
	Using Coordinates to Find Slope
	Variables and Expressions
	Dividing Radicals
	Using Proportions and Cross
	Solving Equations with Radicals and Exponents
	Natural Logs
	The Addition Method
	Equations

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Adding and Subtracting Decimals

Objective Learn how to add and subtract decimals.

The only idea needed to add or subtract decimals, beyond the standard algorithms for addition and subtraction of whole numbers, is the alignment of the numbers so the decimal points line up one above the other.

The Algorithm

Let's begin by introducing the following algorithm, since it will allow you to solve problems right away.

Addition and Subtraction Algorithm for Decimals

1. Write both decimals, one above the other, with the decimal point of one directly over the decimal point of the other.

2. Add or subtract the numbers as if they were whole numbers, ignoring the decimal point.

3. Place the decimal point in the answer directly below the decimal points in the numbers being added or subtracted.

Example 1

Add 2.12 and 3.59.

Solution

Write the two numbers one above the other, with the decimal points aligned.

2.12

+ 3.59

Add the digits, ignoring the decimal points at this step.

	₁
2.12
+ 3.59
5 71

Insert a decimal point in the answer, directly below the other decimal points.

2.12
+ 3.59
5.71

So, the sum of 2.12 and 3.59 is 5.71. 1

Example 2

Subtract 1.01 from 3.17.

Solution

3.17			Line up the decimal points.
- 1.01			Subtract as with whole numbers.
2.16			Place the decimal point in the answer.

In some addition and subtraction problems, there will be more digits to the right of the decimal point in one number than in the other number. Therefore, it is very important to align the decimal points in problems where this is true. It may be helpful to insert one or more zeros to the right of the last digit of the number with fewer decimal places so that both numbers have the same number of digits to the right of the decimal point. The example below shows this procedure.

Example 3

Add 2.1 and 5.432.

Solution

Be sure to align the decimal points even though the numbers do not have the same number of digits.

2.100			Annex zeros; 2.1 = 2.100.
+ 5.432

Now use the algorithm to find the sum.

2.100
+ 5.432
7.532

So, the sum of 2.1 and 5.432 is 7.532.

Estimation

Just as when adding and subtracting whole numbers, estimation should be used to check the reasonableness of the answer to a decimal sum or difference. For example, consider the sum of 2.9 and 4.3. Since 2.9 is almost 3 and 4.3 is about 4, their sum should be approximately 3 + 4 or 7. Using the algorithm, 2.9 + 4.3 = 7.2. The estimate of 7 indicates that 7.2 is a reasonable result for the sum.