1. Tuesday’s Test Hints

2. Integers A set of Integers is shown by I. A set of Integers is shown by I. I = (…-4, -3, -2, -1, 0, 1, 2, 3, 4 …) I = (…-4, -3, -2, -1, 0, 1, 2, 3, 4 …) Note that zero is an integer. Note that zero is an integer. It is neither positive or negative. It is neither positive or negative.

3. Multi. And Divi. Integers Follow the rules when multiplying 2 integers. Follow the rules when multiplying 2 integers. 1. The product of 2 integers with the same sign is positive. 1. (+) (+) = (+) 2. (-) (-) = (+) 2. The product of 2 integers with different signs is negative. 1. (-) (+) = (-) 2. (+) (-) = (-)

4. Addition and Subtraction of Integers Standard Notation Standard Notation It is not common practice to write expressions in the following format: It is not common practice to write expressions in the following format: (-2) - (+5) (-2) - (+5) Instead this expression in standard notation is: Instead this expression in standard notation is: –2 - 5 –2 - 5

5. Cont. Remember, if you have a negative outside the brackets, when you drop the brackets change the signs of every term in the brackets. Remember, if you have a negative outside the brackets, when you drop the brackets change the signs of every term in the brackets. Eg. -( -4 + 5 – 5t) = 4 – 5 + 5t Eg. -( -4 + 5 – 5t) = 4 – 5 + 5t

6. Cont. If you have a poistive, or nothing, outside the bracket, than re-write!!! If you have a poistive, or nothing, outside the bracket, than re-write!!! Eg. (5 + 7 – 3f) = 5 + 7 – 3f Eg. (5 + 7 – 3f) = 5 + 7 – 3f Eg. +(6x + 4 – 8) = 6x + 4 - 8 Eg. +(6x + 4 – 8) = 6x + 4 - 8

7. Rational Numbers The set of rational numbers, shown by Q, is the set of all positive and negative numbers that can be written in fractional form. The set of rational numbers, shown by Q, is the set of all positive and negative numbers that can be written in fractional form. Rational numbers are fractions that can be positive or negative. Rational numbers are fractions that can be positive or negative. All rules for fractions apply to rational numbers. All rules for fractions apply to rational numbers. The line between the numerator and the denominator represents the operation of division. The line between the numerator and the denominator represents the operation of division. Therefore a/b = a  b Therefore a/b = a  b

8. + and – of Rational Numbers To add and subtract rational numbers: To add and subtract rational numbers: 1. Convert mixed rational numbers to improper rational numbers. 2. Write all numbers with a common denominator. 3. Combine numerators. Remember to use standard notation. 4. Write the final answer in lowest terms.

9. X of Rational Numbers To multiply rational numbers: To multiply rational numbers: 1. Convert mixed rational numbers to improper rational numbers. 2. Eliminate common factors from the numerator an denominator. 3. Multiply the numerators and then the denominators. 4. Use the rules of integers to determine the sign of the answer. 5. Check that the answer is in lowest terms

10. Rules for Division 1. Convert all mixed rational numbers to improper rational numbers. 2. Multiply by the reciprocal. Flip the fraction after the division sign. 3. Follow the rules for multiplying rational numbers.

11. How to Convert from Decimal to Fraction? Write the decimal over 10, 100, 1000 Write the decimal over 10, 100, 1000 The convert to the lowest form. The convert to the lowest form. Ex…. Ex….