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Unit 1: The Number System Review Material The unit 1 test will be on the application of the following skills and concepts: Rational Numbers Rational numbers can be expressed as one integer divided by another. Rational numbers either terminate or repeat. Absolute Value Absolute value is the distance from zero. We need to use the absolute value when finding the distance between two points. This is because distance must be positive, but differences can be positive or negative. Taking the absolute value makes the number positive. Opposites Opposites are numbers that are the same distance from zero. Their sum is always zero. Comparing and Ordering Rational Numbers Positive numbers are larger than negative numbers. Positive numbers that are further from zero are larger. Negative numbers that are further from zero are smaller. Operations with Rational Numbers Addition Adding numbers with the same sign: add the absolute value of the numbers and keep the original sign. Adding numbers with different signs: subtract the smaller absolute value from the larger absolute value. If the positive number has the larger absolute value, the answer is positive. If the negative number has the larger absolute value, the answer is negative. Subtraction Same-change-change Keep the first number the same- change subtraction to addition- change the number to its opposite Solve as an addition problem. Multiplication Multiply the two numbers If the numbers have the same sign, the answer is positive. If the numbers have different signs, the answer is negative. *Note: this applies to two numbers (-2)(-3)(-1) is negative. (-2)(-3) is positive since a negative times a negative is positive. Now we have a positive times (-1) which is negative since a positive times a negative is negative. Divison Divide the two numbers If the numbers have the same sign, the answer is positive. If the numbers have different signs, the answer is negative. Dividing by zero: You cannot divide by zero. Look at the example 13 ÷ 0. We can rewrite this as multiplication: 0 x _____ = 13 But zero times anything is zero so there is no number that when multiplied by zero will equal 13. Expressing fractions as decimals: Use long division to express fractions as decimals The decimals will terminate or repeat. We show repeating decimals by placing a bar above the repeating number(s). Fractions Adding and Subtracting A common denominator is needed to add and subtract fractions. Once you have a common denominator, add or subtract the numerators. Put the answer over the denominator. The denominator remains the same. Multiplying Multiply the numerators and multiply the denominators. Put the product of the numerators over the product of the denominators Dividing Same-change-flip Keep the first fraction the same- change division to multiplication- flip the second fraction Then solve as multiplication Mixed numbers Turn mixed numbers into improper fractions to add, subtract, multiply or divide Multiply the denominator by the whole number. Then add the numerator. Put the answer over the original denominator. Order of Operations Parenthesis - Exponents - Multiplication and Division (left to right) - Addition and Subtraction (left to right) Word Problems Review your classwork and homework for examples