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Arithmetic Operations with Numerical Fractions
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Simplifying Fractions 3
Factoring quadratics
Special Products
Writing Fractions as Percents
Using Patterns to Multiply Two Binomials
Adding and Subtracting Fractions
Solving Linear Inequalities
Adding Fractions
Solving Systems of Equations -
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Integer Exponents
Example 6
Dividing Monomials
Multiplication can Increase or Decrease a Number
Graphing Horizontal Lines
Simplification of Expressions Containing only Monomials
Decimal Numbers
Negative Numbers
Factoring
Subtracting Polynomials
Adding and Subtracting Fractions
Powers of i
Multiplying and Dividing Fractions
Simplifying Complex Fractions
Finding the Coordinates of a Point
Fractions and Decimals
Rational Expressions
Solving Equations by Factoring
Slope of a Line
Percent Introduced
Reducing Rational Expressions to Lowest Terms
The Hyperbola
Standard Form for the Equation of a Line
Multiplication by 75
Solving Quadratic Equations Using the Quadratic Formula
Raising a Product to a Power
Solving Equations with Log Terms on Each Side
Monomial Factors
Solving Inequalities with Fractions and Parentheses
Division Property of Square and Cube Roots
Multiplying Two Numbers Close to but less than 100
Solving Absolute Value Inequalities
Equations of Circles
Percents and Decimals
Integral Exponents
Linear Equations - Positive and Negative Slopes
Multiplying Radicals
Factoring Special Quadratic Polynomials
Simplifying Rational Expressions
Adding and Subtracting Unlike Fractions
Graphuing Linear Inequalities
Linear Functions
Solving Quadratic Equations by Using the Quadratic Formula
Adding and Subtracting Polynomials
Adding and Subtracting Functions
Basic Algebraic Operations and Simplification
Simplifying Complex Fractions
Axis of Symmetry and Vertices
Factoring Polynomials with Four Terms
Evaluation of Simple Formulas
Graphing Systems of Equations
Scientific Notation
Lines and Equations
Horizontal and Vertical Lines
Solving Equations by Factoring
Solving Systems of Linear Inequalities
Adding and Subtracting Rational Expressions with Different Denominators
Adding and Subtracting Fractions
Solving Linear Equations
Simple Trinomials as Products of Binomials
Solving Nonlinear Equations by Factoring
Solving System of Equations
Exponential Functions
Computing the Area of Circles
The Standard Form of a Quadratic Equation
The Discriminant
Dividing Monomials Using the Quotient Rule
Squaring a Difference
Changing the Sign of an Exponent
Adding Fractions
Powers of Radical Expressions
Steps for Solving Linear Equations
Quadratic Expressions Complete Squares
Fractions 1
Properties of Negative Exponents
Factoring Perfect Square Trinomials
Algebra
Solving Quadratic Equations Using the Square Root Property
Dividing Rational Expressions
Quadratic Equations with Imaginary Solutions
Factoring Trinomials Using Patterns
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Decimal Numbers

To multiply and divide decimal numbers, you multiply as if they were whole numbers. After that, the only question is: Where do you put the decimal point?! 

Multiplication: Whole Number and Decimal

Example:

4.36 × 4 = ?

Solution:

First we need to find the total weight. Multiply the average weight by the number of birds, as if it were a whole number.

multiplicand
multiplier
product

Now, where does the decimal go?

First method for placing decimal point: Estimate!

4 × 4 = 16, so the answer must be a little bigger than 16, that is 17.44.

Estimation is reliable and safe, and keeps you in charge throughout the problem!

Estimation also helps you check your answer.

Second method for placing decimal point: Count the number of positions after the decimal points, and cut that many off the answer. The number 4.36 has two positions to the right of the decimal, and the number 4 has none. So cut two positions off from 1744 to get: 17.44

 

Rounding Decimals

To round a number to a particular place value, locate the digit to be rounded.

Suppose we are to round these numbers to the nearest tenth:

If the digit to the right is 0, 1, 2, 3 or 4, the digit we are rounding stays the same. Drop all the digits to the right.

If the digit to the right is 5, 6, 7, 8 or 9, the digit we are rounding is raised by one. Drop all the digits to the right.

 

Example:

42.71 rounded to the nearest tenth is 42.7

32.481 rounded to the nearest tenth is 32.5

 

Dividing a Decimal by a Whole Number

Example:

Divide a decimal by whole number:

Divide 20.46 by 66 .

Note! Put the decimal point in quotient directly above decimal point in dividend.

 

Dividing by a Decimal Number

What do you do with the decimal point in division?

In division, a quotient (the result) is not changed when the dividend and divisor are both multiplied by the same number. This is another use for the identity element.

Example:

Divide 7.2 (dividend) by 0.9 (divisor)

If we multiply both the dividend and divisor by 10, the new division allows us to divide by whole numbers.

Note! Change the divisor (bottom) to a whole number. Do this by multiplying both top and bottom by 10 enough times to make the divisor into a whole number.

Check: 8 × 0.9 = 7.2? Yes!

 

Example:

Divide a decimal by another decimal:

Divide 131.88 by 4.2 .

Remember the identity element? Choose an identify element to make the denominator a whole number. For this example let’s use .

Multiply numerator by 10: 131.88 ×10 = 1318.8

Multiply denominator by 10: 4.2 × 10 = 42

Note! Move the decimal to the right enough to make the divisor (bottom) a whole number. Move the dividend’s (top) decimal the same amount.

Note! Place decimal point in quotient directly above new decimal location in dividend.

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