Lesson 1: Arithmetic Review
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1 Lesson 1: Arithmetic Review Topics and Objectives: Order of Operations Fractions o Improper fractions and mixed numbers o Equivalent fractions o Fractions in simplest form o One and zero Operations on Fractions o Addition and subtraction of fractions o Multiplication and division of fractions o Order of operations with fractions Signed numbers o The number line o Absolute value o Mathematical operations with signed numbers o Simplified form for a signed fraction
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3 Order of Operations PEMDAS If we are working with a mathematical expression that contains more than one operation, then we need to understand how to simplify. The acronym PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. P Terms inside parenthesis ( ) or brackets [ ] E MD AS Exponents and roots Multiplication and division (from Left to Right). Addition and subtraction (from Left to Right). Use the order of operations to evaluate each of the following expressions. Use your calculator to check your answers. Example 1: ( )² = ² = = 10 (7 + 1)= Example : =
4 Example : (1 1 6) = Example : 1 1 = You Try Use the order of operations to evaluate each of the following expressions. Use your calculator to check your answers (1 ) =. 8 (1 ) =
5 Fractions Improper Fractions and Mixed Numbers To change a mixed number to an improper fraction: 1. Multiply the denominator of the fraction by the whole number part of the mixed number. Add the numerator of the fraction to this product. Write this sum over the denominator to form an improper fraction Example 1: Express as an improper fraction To change an improper fraction to a mixed number: 1. Divide the numerator by the denominator. If there is a remainder, write it over the denominator Example : Express an improper fraction as a mixed number. 9 Equivalent Fractions Two fractions are equivalent if they reduce to the same fraction. Example : Find two fractions equivalent to 7
6 Fractions in Simplest Form Fractions are in simplest form if they are completely reduced. Leave fraction answers always in simplest form. Example : Write the following fractions in simplest form. 18 ONE and ZERO Example : YOU TRY. Reduce the fraction 6 to lowest terms.. Rewrite the mixed number 1 as an improper fraction.. Rewrite the improper fraction 11 as a mixed number. 6. Find two fractions equivalent to
7 Operations on Fractions Addition and Subtraction of Fractions To add and subtract fractions: 1. Rewrite mixed numbers as improper fractions. Write the fractions as equivalent fractions with the same denominator. Add or subtract the numerators keeping the same denominator. Write the answer in reduced form. Example 1: Perform the indicated operations 1 1 a. b c. 1 6 = d. 8 =
8 Multiplication and Division of Fractions To multiply fractions: 1. Rewrite mixed numbers as improper fractions. Multiply the numerators. Multiply the denominators. Write your answer in simplest form Example : Multiply. Write your answers in simplest form a. b. 1 8 = c. 7 = d To divide fractions: 1. Rewrite mixed numbers as improper fractions. Change the second fraction to its reciprocal. Multiply the fractions. Write your answer in simplest form Example : Divide. Write your answers in simplest form a. 1 b. 8
9 Order of Operations with Fractions Example : Perform the indicated operations. 1 You Try 7. Perform the indicated operations. Each answer must be written as a reduced fraction. Where appropriate, write your answer as both a mixed number and an improper fraction. a. b. c. d. 1 e. 7 f. 6
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11 Signed Numbers The Number Line Absolute Value The ABSOLUTE VALUE of a number is the distance that number is from 0 on the number line. Example 1: Find the absolute value: a. b. c. d. 0 MATHEMATICAL OPERATIONS WITH SIGNED NUMBERS (+,,,, powers, order of operations) Some hints for working with signed numbers: Use ( ) to separate numbers with negative signs When combining and two signs are given together, use the following rules to resolve the signs: ( )( ) = + ( )(+) = (+)( ) = (+)(+) = + Use the number line to add and subtract Example : Perform the indicated operations. a. + ( ) = b. + = c. ( ) = d. + ( ) = Example : Multiply and divide. a. ( )( 6)= b. ( )= c. 8 = d.
12 Example : Evaluate the following exponents: ( ) = = ( ) = = Example : Perform the indicated operations. 8 ( ) ( ) = SIMPLIFIED FORM FOR A SIGNED FRACTION The following fractions are all equivalent (meaning they have the same value): -1 = 1 - = - 1 Notice that only the placement of the negative sign is different. HOWEVER, only the last one, - 1, is considered to be in simplest form. You Try 8. Find the absolute value: 9. Perform the indicated operations. Show your work, and use your calculator to check. a. ( ) = b. 6 1 ( ) =
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