The Set of Real Numbers Operations with Signed Numbers Addition 1)The sum of two positive numbers is positive. 2)The sum of two negative numbers is negative.

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Presentation transcript:

The Set of Real Numbers

Operations with Signed Numbers Addition 1)The sum of two positive numbers is positive. 2)The sum of two negative numbers is negative.

Operations with Signed Numbers Addition 3)When adding a positive and a negative: Ignore the signs. Subtract the number with the smaller absolute value from the number with the larger absolute value. The answer has the same sign as the number with the larger absolute value.

Operations with Signed Numbers Subtraction Subtraction is the same as adding the opposite - NO DOUBLE SIGNS!! 4 - (-3) = 4 + 3

Operations with Signed Numbers Multiplication and Division 1)The product/quotient of two positives is positive. 2)The product/quotient of two negatives is positive. 3)The product/quotient of a positive and a negative is negative.

Simplifying Radical Expressions 1)Check if the radicand is a perfect square. If so, just simplify. Example or

Simplifying Radical Expressions 2)If the radicand is not a perfect square, determine the largest perfect square that divides into the radicand. Example Simplify the square root of the perfect square. That number becomes the coefficient of the radical. Example

Simplifying Radical Expressions Sometimes, it’s difficult to find the largest perfect square. To help you, you could divide the radicand by 2. Check the perfect squares less than or equal to the quotient. Starting with the larger numbers is a good way of attacking it. Example 180 is a big number!! Where to start? 180  2 = 90 Start with squares less than 90.

Simplifying Radical Expressions 81 doesn’t divide into 180, nor 64, nor 49. But, Example

Simplifying Radical Expressions 3)If the radical has a coefficient, simplify the radical and multiply the coefficients. Example The Most Important Thing: Memorize the Perfect Squares!!

Operations with Fractions Addition and Subtraction Rules The first step when adding and subtracting fractions is to find a common denominator.

Adding and Subtracting Fractions Here, my least common denominator will be 4. Change the second fraction by multiplying numerator and denominator each by 2. Watch signs when adding numerators. Make sure your final answer is in simplest form.

Multiplying Fractions Cross simplify if possible. Multiply across.

Dividing Fractions Take the reciprocal of the second fraction and the problem becomes a multiplication problem. Then, follow the rules for multiplication.