a 17 9 d rt 700 (72)t P 2L 2W 19 2L 2(3) L 13 A LW 50 12W W 50 9a a a a 17 9a / 9 17 / 9 9a
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1 Free Pre-Algebra Lesson 0 page Lesson 0 Equations with Fractions Here we practice solving equations that involve fractions. The Solution is A Fraction Even equations with all whole numbers can have a fraction solutions. If the solution is an improper fraction, do not change it to a mied number. The convention in algebra is to write an improper fraction unless it is a solution to a application problem. Eample: Solve. a Check the solution. a a a 7 a / 7 / a 7 a 7 a 7 7 The perimeter of a rectangle is inches. The width is inches. What is the length? P L W L () L L L L / / L The length is inches. The area of a rectangle is 0 in. The length is in. What is the width? A LW 0 W W 0 W / 0 / W 0 The width is inches We don t measure inches in siths, so the answer seems a little strange. If you needed to draw the line with a ruler, you d have to approimate. A vehicle traveled 700 miles at a rate of 7 mph. How much time did the trip take? d rt 700 (7)t 7t 700 7t / / 7 t It took 8 hours. This answer is not the way anyone would really convey the amount of time. We need to convert /8 hours to minutes. How many minutes is /8 hours? 8 0 hours 0 mins hour 0 mins mins At this point you have to make a judgment call depending on the need for precision in the situation. For the purposes of this tet, the answer It took about hours minutes. would be sufficient. The word about lets people know you ve rounded the answer. If you change / minute to seconds, you d get 0 seconds, so a very precise answer would be It took hours, minutes, and 0 seconds. 00 Cheryl Wilco
2 Free Pre-Algebra Lesson 0 page Is That a Fraction, or? If a variable is multiplied by a fraction, we can interpret the equation as having two operations a multiplication followed by a division. Alternativelly, we can solve as a one step equation if we remember that dividing by a fraction is the same as multiplying by the reciprocal. Eample: Solve the equation. 7 Method : We interpret the equation as 7. 7 Method : To divide both sides by 7 we multiply by / 7 / uu 7 7 To solve a problem with a fraction of an amount, we use the structure sentence Part is Fraction of Whole Part = Fraction Whole For eample, /8 of 000 people is calculated , so we know that /8 of 000 people is 7 people. If you know the part and the fraction, you can find the whole by solving an equation. Eample: Set up and solve an equation to find the answer. 0 students, which was / of the students who took the test, agreed that it was ridiculously difficult. How many students took the test? Part = Fraction Whole 0 0 W 0 0 W 0 W 00 0 W students took the test. The manufacturer epected that 00 televisions, which is /00 of the televisions shipped, would be defective. How many televisions were shipped? Part = Fraction Whole W 00 W W 00 W 00, ,000 televisions shipped. 00 Cheryl Wilco
3 Free Pre-Algebra Lesson 0 page Equations with Addition or Subtraction Working with common denominators can be a pain, but necessary with addition and subtraction. Eample: Solve the equations After Veyla cut / yard from the length of fabric, there was only / yard left. What was the original length of fabric? Trevor needed only / page more to have pages done. How much did he have done before? 8 The original length was / yard. 0 He had pages before. 00 Cheryl Wilco
4 Free Pre-Algebra Lesson 0 page More Than One Step You can do these bit by bit or find a common denominator for everything right from the start. The advantage of the second method is that once every term in the equation has the same denominator, we can ignore the denominator and just work with the numerators. Eample: Solve the equations. Method : Bit by bit, one step at a time. Scratch work to add Method : Change all fractions in the problem to have a common denominator. Because the denominator of is common to every term of the equation, we can just ignore it from now on, and use only the numerators. / / If you use Method, be especially careful about whole numbers in the equation. Every term must have the common denominator for this method to work. Eample: Solve the equation becomes 0 I Need To Know Why It s OK to Drop the Common Denominator Why is the same as? Multiply both sides of the equation by : / 0 / 0 Use the distributive property to simplify. 00 Cheryl Wilco
5 Free Pre-Algebra Lesson 0 page Lesson 0: Equations with Fractions Worksheet Name Solve the equations.. 7. y 8. n 8. / of the flowers were roses there were roses. How many flowers were there in all?. m 7. After cutting off / foot, the board was / feet long. What was the original length? Cheryl Wilco
6 Free Pre-Algebra Lesson 0 page Lesson 0: Equations with Variables Homework 0A Name. a a b. How many 7/8 oz. servings are in a oz. bo?. Evaluate a a when a. A tennis ball is fired into the air. The height in feet above 8. the ground t seconds after it is fired is given by the equation h t 00t. Find the height after / seconds.. Use the distributive property to simplify Change to a multiplication and simplify a. 00 Cheryl Wilco
7 Free Pre-Algebra Lesson 0 page 7 7. How many yards is 800 feet? ( feet = yard) 8. How many hours is weeks? ( week = 7 days, day = hours). Solve the equation 8 y. 0. Solve the equation t 7.. Solve the equation 0 0. Use the distance-rate-time formula to solve: A submarine 0. dived 00 feet at the rate of / feet per second. How long did the dive take? 00 Cheryl Wilco
8 Free Pre-Algebra Lesson 0 page 8 Lesson 0: Equations with Variables Homework 0A Answers. a a b a b a b. How many 7/8 oz. servings are in a oz. bo? There are 7 servings in a oz. bo. 7 a. Evaluate a when a A tennis ball is fired into the air. The height in feet above the ground t seconds after it is fired is given by the equation h t 00t. Find the height after / seconds. t h The ball was 0 feet above ground.. Use the distributive property to simplify a. Change to a multiplication and simplify a a a 8a. 00 Cheryl Wilco
9 Free Pre-Algebra Lesson 0 page 7. How many yards is 800 feet? ( feet = yard) 800 feet yard feet yards 8. How many hours is weeks? ( week = 7 days, day = hours) weeks hours 7 days week hours day 800 feet yards. Solve the equation 8 y. 8 y 8 y 8 y 8 0. Solve the equation t t 7. 7 t y 7 7. Solve the equation Since all terms have denominator 0, the denominator can be dropped. / /. Use the distance-rate-time formula to solve: A submarine dived 00 feet at the rate of / feet per second. How long did the dive take? d rt 00 feet 00 t t 00 t t feet t seconds second The dive took seconds. 00 Cheryl Wilco
10 Free Pre-Algebra Lesson 0 page 0 Lesson 0: Equations with Variables Homework 0B Name. b 7 b. How many / 8 inch segments are in a line inches long?. Evaluate when.. A tennis ball is fired into the air. The height in feet above the ground t seconds after it is fired is given by the equation h t 00t. Find the height after 8 / seconds.. Use the distributive property to simplify.. Change to a multiplication and simplify. 00 Cheryl Wilco
11 Free Pre-Algebra Lesson 0 page 7. How many tons is 800 pounds? (000 pounds = ton) 8. How many fluid ounces is / quarts? (8 ounces = cup, cups = quart). Solve the equation a Solve the equationd 0.. Solve the equation 8 8. Use the distance-rate-time formula to solve: A submarine 8. dived 00 feet at the rate of / feet per second. How long did the dive take? 00 Cheryl Wilco
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