Solving Equations Containing Decimals
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- Raymond Leon Arnold
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1 60305 Practice A Solving Equations Containing Decimals Solve. Choose the letter for the best answer. 1. t A t 9.7 C t 6.3 B t 8.3 D t p F p H p 12.6 G p 9.4 J p h A h 0.5 C h 9 B h 4.5 D h z 2.1 F z 4.9 H z 14.7 G z 0.3 J z 2.8 Solve. 5. x h k g w m n j p y x m s f d c h a At the movie theater, a gift certificate for 15 tickets costs $ What is the cost of each ticket? 24. Four couples are going to a concert. If each ticket costs $5.90, how much will it cost to buy tickets for all 8 people?
2 Solve. Practice B Solving Equations Containing Decimals 1. t p r e w z p h k x n y p j g y x c e f d w m s Jeff paid a flat fee of $ for a year's worth of vet visits for his 4 cats. He made 14 visits during the year. What was the average cost per visit?
3 Solve. Practice C Solving Equations Containing Decimals 1. t p c e w g a h k r j p y x z a b d s v f n t w Sam lives 3.5 times farther from school than Sara does. Sam lives 13.3 miles from school. How far from school does Sara live? 26. The Bow-Wow Pet Shop made a profit of $74,239 this year. This was $81,668 more than the profit from last year. What was the profit last year?
4 Review for Mastery Solving Equations Containing Decimals You can solve equations with decimals the same way you solve equations with whole numbers. Remember to always perform the same calculation on both sides of the equation to keep the two sides equal. You can use addition to solve a subtraction equation involving decimals. x x x 8.15 You can use subtraction to solve an addition equation involving decimals. n n n 40 Addition undoes subtraction. Subtraction undoes addition. Solve. 1. e x e x e x 3. w b w b w b 5. t p r k
5 LESSON 3-5 Review for Mastery Solving Equations Containing Decimals (continued) You can use division to solve a multiplication equation involving decimals. 3.6y 9 3.6y y 2.5 You can use multiplication to solve a division equation involving decimals. a a a 75.6 Division undoes multiplication. Multiplication undoes division. Solve g f g f 8.04 g n m n m 6.3 n 13. 8y c f 9.1 m 15. s h
6 Challenge The Pairs Event When you solve a system of equations, you solve two different equations at once. The solution to a system of equations is an ordered pair (x, y). Example: 2.5x 50 x y 10.5 First, solve the first equation for x: x 20. Then use the solution from the first equation to solve for y in the second equation. x y 10.5 x y 10.5 y 9.5 The solution to the system of equations is the ordered pair (20, 9.5). Solve each system of equations. 1. x x x y 10 y x 9.6 x y x 4. x x x y 3x 1.7 x 2y y 3.5 x 7. 6x x 0.3 y x 3.4 y x x y x x x 3.64 x x y 1.1 3x y x y 0.35
7 Problem Solving Solving Equations Containing Decimals Write the correct answer. 1. The diameter of the secondary mirror in NASA s Hubble telescope is 0.3 meter. The primary mirror is 8 times as large. What is the diameter of the primary mirror? 2. A cubic centimeter of titanium weighs grams. The same volume of gold weighs 19.3 grams. How much more does a cubic centimeter of gold weigh? 3. Brianna drives 3.35 miles to work every day. This is 1.75 miles less than Darius drives to work every day. How far does Darius drive to work? Choose the letter for the best answer. The table shows the orbital velocity of some of the planets. 5. How much greater is the orbital velocity of Mercury than that of Uranus? A miles per second B miles per second C 7.03 miles per second D 4.23 miles per second 6. How many miles does Mercury travel in an hour? F 1,784.4 miles G 107,064 miles H 10,706.4 miles J 17,844 miles 7. How many miles does Jupiter travel in a minute? A 8.12 miles B 81.2 miles C miles D miles _ 4. The weight of an object on Mars is 0.38 times its weight on Earth. How much would a 125-pound person weigh on Mars? _ Planet Planets' Orbital Velocity Orbital Velocity (mi/s) Mercury Venus Earth 18.5 Mars Jupiter 8.12 Saturn 6.02 Uranus During the time it takes Saturn to travel 32,508 miles, how much time has elapsed on Earth? F 5,400 minutes G 1, minutes H 195,698 seconds J 90 minutes
8 Reading Strategies Compare and Contrast Compare the steps for solving equations with whole numbers to the steps for solving equations with decimals. Solving Equations with Whole Numbers Step 1: This is a subtraction problem. Add to get x by itself. Step 2: Add 145 to both sides of the equation. Example: x 145 1,720 Step 3: Solve x 1,865 x , Solving Equations with Decimals Step 1: This is a subtraction problem. Add to get x by itself. Step 2: Add 1.45 to both sides of the equation. Example: x Step 3: Solve. x Use the chart to answer the following questions. x Compare the steps in solving an equation with whole numbers to the steps for an equation with decimals. What do you notice? 2. What is different about solving an equation with whole numbers and solving an equation with decimals? Compare solving a multiplication equation with whole numbers to one with decimals: 3y 702; 3y Answer each question. 3. What is the first step in solving both equations? 4. What operation will you use first in the two equations? 5. Compare the number you divide by on both sides of the whole number equation to the number you divide by in the decimal equation.
9 Puzzles, Twisters & Teasers Messy Problems! Solve the equations. Then use the variables to answer the riddle. 1.8 g 3.8 g 60t 54 t n n h h 7.9 i 12.7 i e I 0.8 e 4.9 I y y 1.2b 1.44 b a a r r 3.2w 8 w d d s x s x Why are basketball players sloppy eaters?,
10 LESSON 3-5 Practice A 1. B 2. H 3. B 4. G 5. x h k g w m n j p y x m s f d c h a $ $47.20 Practice B 1. t p r e w z p h k x n y p j g y x c e f d w m s $19.25 Practice C 1. t p c e w g a h k r j p y x z a b d s v f n t w miles 25. $7,429 Review for Mastery ; ; ; t p r k ; ; 6; ; 6 ; ; ; ; ; y c s h 2.88 Challenge 1. (12.7, 15.4) 2. (2, 19.2) 3. (3.12, 0.78) 4. (0.85, 4.25) 5. (0.4, 0.2) 6. (1.98, 6.93) 7. ( 1.2, 2.2) 8. ( 2.7, 3.3) 9. ( 4.3, 2.15) 10. ( 10.4, 21.9) 11. (1.4, 4.2) 12. ( 1.28, 1.63) Problem Solving meters grams miles pounds 5. B 6. G 7. D 8. J Reading Strategies 1. The steps are the same. 2. Whole numbers are used in whole number equations and decimals are used in decimal equations. 3. Get y by itself on one side of the equation. 4. division
11 5. Divided by 3 in both types of equations. Puzzles, Twisters & Teasers g. 2 t. 0.9 n h i. 4.8 e l y. 0.9 b. 1.2 a r. 16 w. 2.5 d s x THEY RE ALWAYS DRIBBLING
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