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Do Now 2/1/10 Take out HW from Friday Text p. 258, #8-40 evens, & 11 Copy HW in your planner. Text p. 262, #2-34 evens Chapter 5 TEST Tuesday Be ready to copy Problem of the Week #1. Homework Text p. 258, #8-40 evens & #11 8) -0.0875 10) 4.02 11) 263 , 5.24, 5.3 , 134 , 5 9 12) -1/3 14) 3 1/3 16) 3/8 18) -9/34 20) 7 27/28 25 25 20 22) -1 1/3 24) 2 5/17 4 26) a 9 4n 7 5 28) 30) -1 5/6 32) 8 1/3 34) -1 1/8 36) 1/2 38) 2/9 40) -17/21 Objective SWBAT review writing fractions as decimals and vice versa, adding and subtracting like and unlike fractions, multiplying fractions, dividing fractions, and solving equations and inequalities with rational numbers. Section 5.1, “Rational Numbers” A RATIONAL NUMBER is a number that can be written as a quotient of two integers (a fraction). Numbers that cannot be written as a fraction are called IRRATIONAL. Writing Decimals as Fractions Decimal numbers can be one of the following: 1) terminating rational 0.375 3 8 2) repeating (follows a pattern) rational 0.454545... 0.45 5 11 3) nonrepeating (goes on forever without a pattern) irrational 2.23606797749... 5 Writing Decimals as Fractions Write the following decimal as fraction. 0.45 How do you say this? “Forty-five hundredths” 45 100 Simplify 335 2 255 9 20 Writing Decimal Numbers As Mixed Numbers Rewrite the decimal number as a sum. Write the decimal as a fraction. 1.375 + Simplify 375 1000 “Three hundred seventy-five thousandths” 1 + 3 8 3 125 8 125 3 8 3 1 8 Writing Decimals as Fractions Write the following decimal as a fraction. 0.09 For repeating decimals use the following strategy: 0.090909… If there are two repeating digits in the decimal, place the digits over 99. 09 99 Simplify, if possible 33 3 3 11 1 11 If there is one repeating digit in the decimal, place the digit over 9. If there are three repeating digits in the decimal, place the digits over 999. Writing Fractions as Decimals 7 Rewrite the fraction as a decimal. 8 A fraction is the quotient of two integers 7 8 This means 7 divided by 8. 7 8 0 87 5 8 7 .0 0 64 6 56 4 40 Finished Section 5.2 “Adding and Subtracting Like Fractions” Adding Fractions with Common Denominators To ADD fractions with common denominators, add their numerators together. Add the numerators a b ab c c c 2 3 7 7 2 3 5 7 7 7 Section 5.2 “Adding and Subtracting Like Fractions” Subtracting Fractions with Common Denominators To SUBTRACT fractions with common denominators, subtract their numerators. Subtract the numerators a b a b c c c 5 1 6 6 4 2 6 3 Section 5.3 “Adding and Subtracting Unlike Fractions” Fractions with Different Denominators To ADD or SUBTRACT fractions with different denominators follow these steps: 1. Rewrite the fractions using a common denominator. 2. Add or subtract the numerators. What is the common denominator? 2 1 5 7 2 2 7 14 5 5 7 35 1 1 5 5 7 7 5 35 14 5 19 35 35 35 “Adding and Subtracting Mixed Numbers” Mixed Numbers with Different Denominators To ADD & SUBTRACT mixed numbers do the following: 1. Write the fractions as improper fractions 2. Write fractions using the LCD. 3. Add or subtract the numerators 4. Simplify if necessary Try It Out 1 3 4 1 4 8 1. Improper fractions 17 11 4 8 2. Write fractions using LCD. 34 11 8 8 3. Simplify 23 8 7 2 8 5w 7 w Simplify the Expression. 12 9 Find the LCD for 12 and 9. LCD = 36 Rewrite equivalent fractions using the LCD. 5w ? 12 36 7w ? 9 36 5w 5w 3 15w 12 12 3 36 7 w 7 w 4 28w 9 94 36 15w 28w 13w 36 36 36 Section 5.4, “Multiplying Fractions” Multiplying Fractions To multiply fractions: 1. Rewrite fractions as improper fractions (when necessary) 2. Multiply the numerators and denominators. 3. Simplify if necessary. a c ac b d bd 3 4 12 5 7 35 Section 5.5, “Dividing Fractions” Dividing Fractions To divide fractions: 1. Rewrite fractions as improper fractions (when necessary) 2. Write the reciprocal of the second fraction. 3. Multiply the numerators and denominators. 4. Simplify if necessary. a c a d ad b d b c bc 3 4 3 7 21 1 1 5 7 5 4 20 20 Section 5.6, “Using Multiplicative Inverses to Solve Equations” Multiplicative Inverse Property To solve an equation that has a fractional coefficient, you can multiply each side of the equation by the fraction’s multiplicative inverse. MULTIPLICATIVE INVERSE = RECIPROCAL 4 x 12 7 Solve for x. 7 4 7 x 12 4 7 4 Multiply each side of the equation by the MULTIPLICATIVE INVERSE of 4/7 7 1x 12 4 Multiply -3 12 7 1x 1 4 1 Divide (cancel) common factors x 21 Section 5.7, “Equations and Inequalities with Rational Numbers” Another way to solve an equation with fractions is to clear fractions by multiplying the WHOLE EQUATION by the LCD of the fractions. The resulting equation is equivalent to the original equation WITHOUT fractions. Solving Equations by Clearing Fractions 11 4 1 x 15 5 3 15 Find LCD of all fractions in the equation, then multiply the whole equation by the LCD. 4 1 11 x 5 3 15 15 11 x 15 15 4 5 11x 12 5 15 11x 7 x Use distributive property and simplify each term of the equation. Two-step equation. Solve for x. 11x 1212 512 11 7 x 11 11 1 3 7 11 Solving Equations by Clearing Decimals 2.3 5.14 0.8m Look for the greatest number of decimal places. Then multiply the WHOLE EQUATION by that power of 10. 100 2.3 5.14 0.8m 100 2.3 100 5.14 100 0.8m 230 514 80m 230(514) 514 514 80m 284 80m 284 80m 80 80 m 3.55 Use distributive property and simplify each term of the equation. Two-step equation. Solve for m. BLUFF! Homework Text p. 262, #2-34 evens Chapter 5 TEST tomorrow!!