Solving Equations With Fractional Coefficients


 Amberly Flowers
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1 Solving Equations With Fractional Coefficients Some equations include a variable with a fractional coefficient. Solve this kind of equation by multiplying both sides of the equation by the reciprocal of the fraction and canceling factors. x = x = 6 x = x = Multiply both sides by the reciprocal of B. Cancel factors and multiply. Solution. The problem x = x is the same as =. To solve this problem, first multiply both sides by which yields x = 96. Then divide both sides by for the solution x =. Today s lesson combines both these steps into one by using the reciprocal. The next two examples show how you can use this algebra skill to find the missing dimension for either a triangle or a trapezoid. Height =? Base = 6 in Height = in Area = in A = bh 5 = (h) 5 = (h) 0 Area = 5 cm Base = cm = 9 = h h The height of the triangle is 9 cm. Multiplying both sides by ( ) cancels. A = (b + b )h = (6 + b ) = (6 + b ) 6 = (6 + b ) 6 = + b 0 Base =? = 0 = b b Use the distributive property to simplify. The length of base is 0 inches.
2 Lesson Solve.. a. x = b. x = 0 c. 6 x = 5. a. x = b. x = 0 c. x = 9 Find the length of the base. Area = in in. The base of the triangle is. We R e m e m b e r. Two exit signs at The Clockworks are illuminated all the time. Each sign contains a 5watt bulb. At.6 cents per kilowatthour, how much does it cost to light both signs for a week? Round to the nearest whole cent. w h,000 = kwh Convert. Round No. 5 to the nearest tenth. 5.,000 fluid ounces gallons 6. 5 yards = feet Combine like terms. 7. a. 5a b + b c 6a b. 5x x x + x c. x x + x + x
3 Lesson Fill in the chart to show what to say to count back change without a cash register. Amount of purchase. $0. 9. $ $ $5 Customer gave $.00 $ Sue applied three layers of finish to a clock case Carl had built. On Monday she worked hour and 55 minutes, on Wednesday she applied the second coat in hours and 0 minutes, and on Friday it took her hours and 5 minutes to put on the final coat. How much time did it take Sue to finish the clock case? Write the products. Use fractions for those with negative exponents.. a. b 0 = b. y = c.  = d. 5  = Solve. Round to the nearest cent.. Original price of $5 with an increase of %. a. Amount of increase: b. New price:. The price went down 90% from $90.0. New price:. Last month The Clockworks sold clocks with the following prices: $5.99, $5.99, $.99, $5.99, $.99, and $ What was the average cost per clock? Use the formulas to find the areas of the parallelogram and the trapezoid. 6 in.5 cm in 7.5 cm 7 in 5. a. b.
4 Lesson 6. Any number except 0 with an exponent of 0 equals. 7. The longest side of a right triangle is called the.. Numbers in an expression that stand alone without variables are called. 9. a. Another name for average is. b. kilometer mile 5 M a s t e r y D r i l l 0. a. = % b. 96 = c. 5 = d. = Complete the table and graph the equation. x. = y 6 x y y Find the distance between points.. From ( 6, ) to (6, ) is units x Carl ordered a triplechime clock movement for a grandfather clock he is building. The clock movement costs $5.99. If the clock movement represents 0% of the value of the finished clock, what will this clock be worth? Use the percent proportion, and round to the nearest whole dollar. Change to scientific notation.. a. 9,000,000 = b = 5
5 Lessons, Find the height of the trapezoid. Base = in Area =.5 in Base = 5 in 5. The height of the trapezoid is. Constructing a Triangle With Two Given Angles and a Given Side (ASA) You can use a compass and a straightedge to construct a triangle with two given angles and the side between them. These are the given angles: P Q This is the side between the two angles: P Q With the straightedge, draw a segment that is longer than PQ. Label one endpoint P and use the compass to mark the length of PQ with an arc. Label the point of intersection Q. P Q 6
6 Lesson With the compass and straightedge, construct angles equal to P and Q. Extend the segments so they intersect. Name the point of intersection R. Note: You learned how to construct congruent angles in Math 0, Lesson. R Use a compass and a straightedge to construct ABC and DEF from the parts given. P Q. A B A B. D E D E We Remember Solve. 7. a. x = b. x = c. x = 7. a. x = 5 b. 7 x = c. x = 7
7 Lesson Write a as dollars and b as cents. 5. a. 9. cents = b. $0.7 = Find the markup and selling price. Round to the nearest cent. 6. The cost was $. marked up 5%. a. The markup is. b. The selling price is. 7. The cost was $0.5 marked up 0%. The selling price is. Find the total cost. Round to the nearest whole cent.. 70 watts for hours at.6 per hour w h,000 = kwh Solve. 9. a. 0 = b. 6 9 = c. ) 0 0. a. 0 ( 5) = b. = c. 6 ( ) = Rewrite using multiples of 0. Then use the distributive property to find the products.. a. 5() b. (7) c. (05) d. (,0) Simplify Earl lives miles from the shop. As part of his exercise program, Earl walks to the shop when the weather is not too cold. Today he covered the miles in hour and 5 minutes. What was his speed? Use fractions and the distance formula to solve.
8 Lesson M a s t e r y D r i l l. The less than or equal to symbol is. 5. The Pythagorean Theorem is true for every triangle. 6. The formula for finding the volume of a pyramid or cone is. 7. A number factor in a term used with a variable is known as a numerical.. a. quart = fluid ounces b. pint = fluid ounces 9. a. The repeating decimal for is. b. The decimal for is. Solve the logic problem. 0. Inside an antique clock, Earl found an old coin dated 5 B.C. How did he know the old coin was worth nothing? Simplify and solve.. a. 96 = (x + ) b. 7x + 5x 5 = + 5 Divide these numbers in scientific notation.. (6. 0 ) ( 0 6 ) =. ( ) ( 07 ) = Reduce to simplest form. x. a. 6x = b. = x 5 x 9
9 Lesson Use the formulas to find the volume of each solid. Use. for pi. in ft ft in 6 in 5. a. b. Convert. Round to the nearest whole cm in lb kg. 50 yd m Find the volume of each. Round b to the nearest hundredth. ft 7 in ft ft in 9. a. b. Solve for the third angle of the triangle described. 0. If two angles measure and, the third angle measures. Use a compass and a straightedge to construct GHI from the parts given.. G H 0 G H
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