Unit 8 Practice Problems Lesson 1

Unit 8 Practice Problems Lesson 1 Problem 1 Find the area of each square. Each grid square represents 1 square unit. 17 square units. 0 square units 3. 13 square units 4. 37 square units Problem Find the length of a side of a square if its area is: 81 square inches 4. cm 5 3. 0.49 square units 4. square units m

9 inches. cm 5 3. 0.7 units 4. m units Problem 3 Find the area of a square if its side length is: 3 inches. 7 units 3. 100 cm 4. 40 inches 5. x units 9 square inches. 49 square units 3. 10,000 cm 4. 1,600 square inches 5. x square units Problem 4 (from Unit 7, Lesson 14) Evaluate (3.1 10 4 ) ( 10 6 ). Choose the correct answer: A. B. C. D. 5.1 10 10 5.1 10 4 6. 10 10 6. 10 4 C Problem 5 (from Unit 7, Lesson 15) Noah reads the problem, Evaluate each expression, giving the answer in scientific notation. The first problem part is: 5.4 10 5 +.3 10 4. Noah says, I can rewrite 5.4 10 5 as 54 10 4. Now I can add the numbers: 54 10 4 +.3 10 4 = 57.3 10 4. Do you agree with Noah s solution to the problem? Explain your reasoning. Answers vary. Sample response: I don t agree with Noah s solution. His calculations are correct, but his final answer is not in scientific notation. To finish the problem, he should convert his answer to the form 5.73 10 5. Problem 6 (from Unit 7, Lesson 6) 8

Select all the expressions that are equivalent to 3 8. A. B. C. D. (3 ) 4 8 3 3 3 3 3 3 3 3 3 (3 4 ) E. 3 6 3 - F. 3 6 10 A, C, D, E Lesson Problem 1 A square has an area of 81 square feet. Select all the expressions that equal the side length of this square, in feet. 81 A. B. 81 C. 9 D. 9 E. 3 B, C Problem Write the exact value of the side length, in units, of a square whose area in square units is: 36. 37 100 3. 9 4. 5 5. 0.0001 6. 0.11 6. 37 3. 4. 10 3 5 5. 0.01 6. 0.11 Problem 3 Square A is smaller than Square B. Square B is smaller than Square C.

The three squares side lengths are 6, 4., and 11. What is the side length of Square A? Square B? Square C? Explain how you know. Square A: 11 units, Square B: 4. units, Square C: 6. I know this because 11 is between 3 and 4 and 6 is between 5 and 6, so 11 < 4. < 6 and the side length of A is less than the side length of B is less than the side length of C. Problem 4 (from Unit 8, Lesson 1) Find the area of a square if its side length is: 1 cm 5 3. units 7 3. 11 inches 8 4. 0.1 meters 5. 3.5 cm 1 cm 5 9. square units 49 11 3. square inches 64 4. 0.01 square meters 5. 5 cm Problem 5 (from Unit 7, Lesson 15) Here is a table showing the areas of the seven largest countries. country area (in km ) How many more people live in Russia than in Canada?. The Asian countries on this list are Russia, China, and India. The American countries are Canada, the United States, and Brazil. Which has the greater total area: the three Asian countries, or the three American countries? Russia Canada China United States Brazil Australia India 71 10 7 9.98 10 6 9.60 10 6 9.53 10 6 8.5 10 6 6.79 10 6 3.9 10 6 7.1 10 6 more people. The Asian countries (.999 10 7 vs..808 10 7 ) Problem 6

(from Unit 7, Lesson 5) Select all the expressions that are equivalent to 10-6. 1 A. 1000000-1 B. 1000000 1 C. 10 6 D. 10 8 10-1 6 E. ( 10 ) 1 F. 10 10 10 10 10 10 A, C, E, F Lesson 3 Problem 1 Decide whether each number in this list is rational or irrational. -13, 0.134, 37, -77, - 100, -1 3-13 Rational:, 0.134, -77, - 100; Irrational: 37, - 1 3 Problem Which value is an exact solution of the equation m = 14? A. 7 B. 14 C. 3.74 D. 3.74 B Problem 3 (from Unit 8, Lesson ) A square has vertices (0, 0), (5, ), (3, 7), and (-, 5). Which of these statements is true? A. The square s side length is 5. B. The square s side length is between 5 and 6. C. The square s side length is between 6 and 7. D. The square s side length is 7. B Problem 4 (from Unit 7, Lesson 8) Rewrite each expression in an equivalent form that uses a single exponent.. (10 ) -3 (3-3 ) -5-5

3. 3-5 4-5 4. 5 3-5 10-6 (or equivalent). 3-6 (or equivalent) 3. 1-5 (or equivalent) 5 4. ( ) (or equivalent) 3 Problem 5 (from Unit 5, Lesson 5) The graph represents the area of arctic sea ice in square kilometers as a function of the day of the year in 016. Give an approximate interval of days when the area of arctic sea ice was decreasing.. On which days was the area of arctic sea ice 1 million square kilometers? Answers vary. Correct responses should be close to day 75 to day 50.. Days 135, 350, and 360 Problem 6 (from Unit 4, Lesson 14) The high school is hosting an event for seniors but will also allow some juniors to attend. The principal approved the event for 00 students and decided the number of juniors should be 5% of the number of seniors. How many juniors will be allowed to attend? If you get stuck, try writing two equations that each represent the number of juniors and seniors at the event. 40 juniors. Sample reasoning: Solve the system s + j = 00, j = 0.5s (or equivalent), where s represents the number of seniors and j represents the number of juniors. Lesson 4 Problem 1 Find the exact length of each line segment.

. Estimate the length of each line segment to the nearest tenth of a unit. Explain your reasoning. AB = 17, GH = 3. AB is greater than 4 but less than 5 because 4 = 16. GH is smaller than 6 but greater than 5 because 6 = 36. Problem Plot each number on the x -axis: 16, 35, 66. Consider using the grid to help. 16 at 4, 35 a little less than 6, 66 a little more than 8 Problem 3 Use the fact that 7 is a solution to the equation x = 7 to find a decimal approximation of 7 whose square is between 6.9 and 7. Answers vary. Sample responses:.63,.64,.65,.66 Problem 4 (from Unit 7, Lesson 14)

Graphite is made up of layers of graphene. Each layer of graphene is about 00 picometers, or 00 10-1 meters, thick. How many layers of graphene are there in a 6-mm-thick piece of graphite? Express your answer in scientific notation. About 8 10 6. The thickness of the graphite is 6 10-3 meters. The number of 6 10 layers of graphene is given by -3 = 0.008 10 9. This number, in scientific 00 10-1 notation, is 8 10 6, or about 8 million. Problem 5 (from Unit 6, Lesson 6) Here is a scatter plot that shows the number of assists and points for a group of hockey players. The model, represented by y = 5x +, is graphed with the scatter plot. What does the slope mean in this situation?. Based on the model, how many points will a player have if he has 30 assists? For every assist, a player s points have gone up by 5.. Approximately 46. points Problem 6 (from Unit 3, Lesson 5) The points (1, 3) and (14, 45) lie on a line. What is the slope of the line? (or 11) Lesson 5 Problem 1 Explain how you know that 37 is a little more than 6.. Explain how you know that 95 is a little less than 10. 3. Explain how you know that 30 is between 5 and 6. 36 is exactly 6, and 37 is a little more than that.. 100 is exactly 10, and 95 is a little less than that. 3. 5 = 5, 36 = 6, and 30 is in between.

Problem Plot each number on the number line: 6, 83, 40, 64, 7.5 Problem 3 Mark and label the positions of two square root values between 7 and 8 on the number line. Answers vary. Sample response: 55 and 60. Since the values are between 7 = 49 and 8 = 64, any square root of a number between 49 and 64 is a solution. Problem 4 (from Unit 8, Lesson 3) Select all the irrational numbers in the list. 14, - 99-13,, 14, 64 9,, -, - 3 45 99 100 1 Problem 5 (from Unit 8, Lesson ) Each grid square represents 1 square unit. What is the exact side length of each square? 13 units Problem 6 (from Unit 7, Lesson 10) For each pair of numbers, which of the two numbers is larger? Estimate how many times larger. 0.37 6 700 4

0.37 10 6 700 10 4 4.87 10 4 15 10 5 and. and 3. 500, 000 and.3 10 8 700 10 4, about 0 times larger. 15 10 5, about 30 times larger 3..3 10 8, about 500 times larger Problem 7 (from Unit 6, Lesson 4) The scatter plot shows the heights (in inches) and three-point percentages for different basketball players last season. Circle any data points that appear to be outliers.. Compare any outliers to the values predicted by the model. The point at (85, 14) is an outlier.. This point represents a player who had a significantly worse (by about 15% of the attempts) three-point percentage than the model predicts for his height. Lesson 6 Problem 1 Here is a diagram of an acute triangle and three squares. Priya says the area of the large unmarked square is 6 square units because 9 + 17 = 6. Do you agree? Explain your reasoning. No, I disagree. Priya's pattern only works for right triangles, and this is an acute triangle. Problem m, p, and z represent the lengths of the three sides of this right triangle.

Select all the equations that represent the relationship between m, p, and z. A. B. C. D. E. F. m + p = z m = p + z m = z + p p + m = z z + p = m p + z = m B, C, E, F Problem 3 The lengths of the three sides are given for several right triangles. For each, write an equation that expresses the relationship between the lengths of the three sides. 10, 6, 8. 5, 3, 8 3. 5, 5, 30 4. 1, 37, 6 5. 3,, 7 6 + 8 = 10. 5 + 3 = 8 3. 5 + 5 = 30 4. 1 + 6 = 37 5. + 7 = 3 Problem 4 (from Grade 8, Unit 4, Lesson 1) Order the following expressions from least to greatest. 5 10 50,000 1,000.5 1,000 0.05 1.5 1,000 0.05 1 5 10 50,000 1,000

Problem 5 (from Unit 8, Lesson 3) Which is the best explanation for why - 10 is irrational? A. - 10 is irrational because it is not rational. B. - 10 is irrational because it is less than zero. C. - 10 is irrational because it is not a whole number. D. -10 is irrational because if I put - 10 into a calculator, I get -3.167766, which does not make a repeating pattern. A Problem 6 (from Unit 7, Lesson 15) 1 A teacher tells her students she is just over 1 and Write her age in seconds using scientific notation. billion seconds old.. What is a more reasonable unit of measurement for this situation? 3. How old is she when you use a more reasonable unit of measurement? 5 10 9. Years 3. She is about 48 years old. There are 31,536,000 seconds in a year. 5 10 9 31,536,000 is about 47.6. Lesson 7 Problem 1 Find the lengths of the unlabeled sides.. One segment is nunits long and the other is p units long. Find the value of nand p. (Each small grid square is 1 square unit.) a. 40, approximately 6.3 b. 100, exactly 10. a. 10 because 1 + 3 = 10 + = 5

b. 5 (or 5) because 3 + 4 = 5 Problem Use the areas of the two identical squares to explain why 5 + 1 = 13 without doing any calculations. Answers vary. Sample explanation: The areas of the two large squares are the same since they are both 17 by 17 units. The area of the two rectangles on the left square are the same as the area of the 4 triangles in the right square (each pair of triangles makes a rectangle). So the area of the two smaller squares on the left must be the same as the area of the smaller square on the right. This means 5 + 1 = 13. Problem 3 (from Unit 8, Lesson 5) Each number is between which two consecutive integers? 10. 54 3. 18 4. 99 5. 41 3 and 4. 7 and 8 3. 4 and 5 4. 9 and 10 5. 6 and 7 Problem 4 (from Unit 8, Lesson 3) Give an example of a rational number, and explain how you know it is rational.. Give three examples of irrational numbers. Answers vary. Sample response: is a rational number because rational 3 numbers are fractions and their opposites and is a fraction. 3. Answers vary. Sample response:, -1, 5

Problem 5 (from Unit 7, Lesson 4) Write each expression as a single power of 10. 10 5 10 0. 10 9 10 0 10 5. 10 9 Problem 6 (from Unit 4, Lesson 15) Andre is ordering ribbon to make decorations for a school event. For his design, he needs exactly 50.5 meters of blue and green ribbon. There has to be 50% more blue ribbon than green ribbon, plus an extra 6.5 meters of blue ribbon for accents. How much of each color of ribbon does Andre need to order? Andre needs to order 17.5 meters of green ribbon and 3.5 meters of blue ribbon. Strategies vary. Sample strategy: Let b represent the length of blue ribbon and g represent the length of green ribbon. Then b = 5g + 6.5 and b + g = 50.5. Substituting 5g + 6.5 in for b in the second equation gives (5g + 6.5) + g = 50.5. Solving for g gives g = 17.5. Since the two kinds of ribbon must combine to make 50.5 meters, then b = 50.5 17.5, so b = 3.5 meters. Lesson 8 Problem 1 Find the exact value of each variable that represents a side length in a right triangle. h = 6 (because 100 64 = 36 and 36 = 6) k =.5 (because 4.5 36 = 6.5 and 6.5 =.5) m = 1 because 5 4 = 1 n= 90 because 100 10 = 90 p = 17 because 85 68 = 17 Problem (from Unit 8, Lesson 7)

A right triangle has side lengths of a, b, and c units. The longest side has a length of c units. Complete each equation to show three relations among a, b, and c.. 3. c = a + b or c = b + a. 3. c = a = b = a = c b b = c a Problem 3 (from Unit 8, Lesson 7) What is the exact length of each line segment? Explain or show your reasoning. (Each grid square represents 1 square unit.). 3. 4 units. The segment is along the gridlines, so count the squares.. 0 because 4 + = 0 3. 41 because 4 + 5 = 41 Problem 4 (from Unit 7, Lesson 15) In 015, there were roughly 1 10 6 high school football players and 10 3 professional football players in the United States. About how many times more high school football players are there? Explain how you know. There are approximately 500 times more high school football players. 1 10 6 = 0.5 10 3 = 5 10 10 3 Problem 5 (from Unit 7, Lesson 6) Evaluate: 1 3 ( ) -3

1-3. ( ) 1 8. 8 Problem 6 (from Unit 6, Lesson 6) Here is a scatter plot of weight vs. age for different Dobermans. The model, represented by y =.45x +, is graphed with the scatter plot. Here, x represents age in weeks, and y represents weight in pounds. What does the slope mean in this situation?. Based on this model, how heavy would you expect a newborn Doberman to be? The slope means that a doberman can be expected to gain.45 pounds per week.. pounds (the y-intercept of the function). Lesson 9 Problem 1 Which of these triangles are definitely right triangles? Explain how you know. (Note that not all triangles are drawn to scale.) B, D, and E are right triangles. A and C are not. A: 9 + 1 1 = 14 is false + =

B: 50 + 50 = 10 is true C: 16 + 30 = 35 is false D: 10 + 10.5 = 14.5 is true E: 3 + 13 = 4 is true Problem A right triangle has a hypotenuse of 15 cm. What are possible lengths for the two legs of the triangle? Explain your reasoning. Answers vary. Sample responses: 00 and 5; 15 and 10. If the legs of the triangle are a and b, then we can set up the equation a + b = 15. This means a and b must sum to 5. If a = 5, then b = 00. If a = 100, then b = 15. Problem 3 (from Unit 8, Lesson 8) In each part, a and b represent the length of a leg of a right triangle, and c represents the length of its hypotenuse. Find the missing length, given the other two lengths.. a = 1, b = 5, c =? a =?, b = 1, c = 9 c = 13. If a = 1 and b = 5 then 1 + 5 = c.. a = 0. If b = 1 and c = 9 then a + 1 = 9. Problem 4 (from Unit 8, Lesson 6) For which triangle does the Pythagorean Theorem express the relationship between the lengths of its three sides? B

Problem 5 (from Unit 4, Lesson 5) Andre makes a trip to Mexico. He exchanges some dollars for pesos at a rate of 0 pesos per dollar. While in Mexico, he spends 9000 pesos. When he returns, 1 he exchanges his pesos for dollars (still at 0 pesos per dollar). He gets back 10 the amount he started with. Find how many dollars Andre exchanged for pesos and explain your reasoning. If you get stuck, try writing an equation representing Andre s trip using a variable for the number of dollars he exchanged. 0x 9000 x 500 dollars. Sample reasoning: =, where x represents the number 0 10 of dollars he exchanged. Rewrite the equation as 0x 9000 = x, and then solve to find x = 500. Lesson 10 Problem 1 A man is trying to zombie-proof his house. He wants to cut a length of wood that will brace a door against a wall. The wall is 4 feet away from the door, and he wants the brace to rest feet up the door. About how long should he cut the brace? Around 4.5 feet. Solving + 4 = b, we get b = 0, which is approximately 4.5. Problem At a restaurant, a trash can's opening is rectangular and measures 7 inches by 9 inches. The restaurant serves food on trays that measure 1 inches by 16 inches. Jada says it is impossible for the tray to accidentally fall through the trash can opening because the shortest side of the tray is longer than either edge of the opening. Do you agree or disagree with Jada s explanation? Explain your reasoning. I disagree. Explanations vary. Sample explanation: It is impossible for the tray to fall through the opening, but not for the reason Jada gives. The longest dimension of the trash can opening is the diagonal. The diagonal is 130 inches long, because 7 + 9 = 130. The diagonal is between 11 and 1 inches long, because 11 < 130 < 1. The tray cannot fall through the opening because the diagonal is a little shorter than the shortest dimension of the tray. Problem 3 (from Unit 8, Lesson 9) Select all the sets that are the three side lengths of right triangles.

A. 8, 7, 15 B. 4, 10, 84 C. 8, 11, 19 D. 1,, 3 B, C Problem 4 (from Unit 7, Lesson 10) For each pair of numbers, which of the two numbers is larger? How many times larger? 1 10 9 4 10 9 and 5 10 1 3 10 1. and 0 10 4 6 10 5 3. and 1 10 9, 3 times larger. 3 10 1, times larger 3. 6 10 5, 3 times larger Problem 5 (from Unit 3, Lesson 10) A line contains the point (3, 5). If the line has negative slope, which of these points could also be on the line? A. B. C. D. C (, 0) (4, 7) (5, 4) (6, 5) Problem 6 (from Unit 3, Lesson 4) Noah and Han are preparing for a jump rope contest. Noah can jump 40 times in 0.5 minutes. Han can jump y times in x minutes, where y = 78x. If they both jump for minutes, who jumps more times? How many more? Noah jumps 160 times and Han jumps 156 times, so Han jumps 4 more times. Lesson 11 Problem 1 The right triangles are drawn in the coordinate plane, and the coordinates of their vertices are labeled. For each right triangle, label each leg with its length.

Problem Find the distance between each pair of points. If you get stuck, try plotting the points on graph paper. M = (0, -11) and P = (0, ). A = (0, 0) and B = (-3, -4) 3. C = (8, 0) and D = (0, -6) 13. 5 3. 10 Problem 3 (from Unit, Lesson 10) Which line has a slope of 0.65, and which line has a slope of 6? Explain why the slopes of these lines are

0.65 and 6. Slope of 0.65: Slope of 6: Construct triangles perpendicular to the axes whose hypotenuses lie on their line to find the slopes. The slopes of the lines are then the quotient of the length of the vertical edge by the length of the horizontal edge. Problem 4 (from Unit 3, Lesson 7) Write an equation for the graph.

y = x + 5 Lesson 1 Problem 1 What is the volume of a cube with a side length of a. 4 centimeters? b. 3 11 feet? c. s units?. What is the side length of a cube with a volume of a. 1,000 cubic centimeters? b. 3 cubic inches? c. v cubic units? a. 64 cubic centimeters b. 11 cubic feet c. s 3 cubic units. a. 10 cm b. 3 3 inches c. v units 3 Problem Write an equivalent expression that doesn t use a cube root symbol. 3 1. 16 3

3. 3 8000 1 4. 3 64 7 5. 3 15 6. 3 0.07 7. 0.00015 3 1. 6 3. 0 4. 5. 1 4 3 5 6. 0.3 7. 0.05 Problem 3 (from Unit 8, Lesson 11) Find the distance between each pair of points. If you get stuck, try plotting the points on graph paper. X = (5, 0) and Y = (-4, 0). K = (-1, -9) and L = (0, 0) 9. 18 Problem 4 (from Unit 8, Lesson 9) Here is a 15-by-8 rectangle divided into triangles. Is the shaded triangle a right triangle? Explain or show your reasoning. No, it is not. Use the Pythagorean Theorem to find the length of the interior sides of the triangle: the lengths are 145 and 10. The longest side is 15, the length of the rectangle. Now check whether this triangle s side lengths make a + b = c. Because 145 + 100 = 45, not 5, the converse of the Pythagorean Theorem states this triangle is not a right triangle. Problem 5 (from Unit 8, Lesson 10) Here is an equilateral triangle. The length of each side is units. A height is drawn. In an equilateral triangle, the height divides the opposite side into two pieces of equal length. Find the exact height.

. Find the area of the equilateral triangle. 3. (Challenge) Using x for the length of each side in an equilateral triangle, express its area in terms of x. 3 units. 3 units x 3. The area is 3 units 4 Lesson 13 Problem 1 Find the positive solution to each equation. If the solution is irrational, write the solution using square root or cube root notation. t 3 = 16. 3. 4. a m 3 c 3 = 15 = 8 = 343 5. f 3 = 181 t = 6. a = 15 3. 4. 5. m = c = 7 f = 3 181 Problem For each cube root, find the two whole numbers that it lies between.. 3. 4. 3 3 3 3 11 80 10 50 and 3

. 4 and 5 3. 4 and 5 4. 6 and 7 Problem 3 Arrange the following values from least to greatest: 3 530, 48, π, 11, 7 19 3, 3 7, π, 48, 3 530, 19, 11 Problem 4 (from Unit 8, Lesson 8) Find the value of each variable, to the nearest tenth.. 3. x 7.1. f 5.4 3. d 15.1 Problem 5 (from Unit 8, Lesson 10) A standard city block in Manhattan is a rectangle measuring 80 m by 70 m. A resident wants to get from one corner of a block to the opposite corner of a block that contains a park. She wonders about the difference between cutting across the diagonal through the park compared to going around the park, along the streets. How much shorter would her walk be going through the park? Round your answer to the nearest meter.

The walk through the park is about 68 m shorter than the walk around the park. Along the streets: 80 + 70 = 350. Along the diagonal: solve 80 + and get approximately 8. 350 8 = 68. 70 = x Lesson 14 Problem 1 Andre and Jada are discussing how to write as a decimal. Andre says he can use long division to divide 17 by 0 to get the decimal. Jada says she can write an equivalent fraction with a denominator of 100 by 5 multiplying by, then writing the number of hundredths as a decimal. 5 Do both of these strategies work? 17 0. Which strategy do you prefer? Explain your reasoning. 17 3. Write as a decimal. Explain or show your reasoning. 0 Yes, both strategies are effective.. Answers vary. Sample responses: I prefer Jada's method because I can calculate it mentally. I prefer Andre's method because it always works, even if the denominator is not a factor of 100. 17 3. 0.85. Explanations vary. Sample explanation: =, so equals 0 5 85 17 5 100 0 0.85. Problem Write each fraction as a decimal. 9 100. 3. 4. 99 100 9 16 3 10 0.3. 0.99 3. 0.75 4..3 Problem 3 Write each decimal as a fraction. 0.81. 0.076 3. 0.04

4. 10.01 9 10 76. (or equivalent) 10000 1 3. (or equivalent) 5 1001 4. (or equivalent) 100 Problem 4 (from Unit 8, Lesson 13) Find the positive solution to each equation. If the solution is irrational, write the solution using square root or cube root notation.. 3. 4. 5. 6. x = 90 p 3 = 90 z = 1 y 3 = 1 w = 36 h 3 = 64 x = 90. p = 3 90 3. 4. 5. 6. z = 1 y = 1 w = 6 h = 4 Problem 5 (from Unit 8, Lesson 10) Here is a right square pyramid. What is the measurement of the slant height l of the triangular face of the pyramid? If you get stuck, use a cross section of the pyramid.. What is the surface area of the pyramid? 17 units ( 15 + 8 = 89 and 89 = 17). 800 square units (The pyramid is made from a square and four triangles. The square s area, in square units, is 16 = 56. Each triangle s area, in 1 square units, is 16 17 = 136. The surface area, in square units, is 56 + 4 136 = 800.)

Lesson 15 Problem 1 Elena and Han are discussing how to write the repeating decimal x = 0.137 as a fraction. Han says that 0.137 13764 equals. I calculated 1000x = 137.777 99900 because the decimal begins repeating after 3 digits. Then I subtracted to get 999x = 137.64. Then I multiplied by 100 to get rid of the decimal: 13764 99900x = 13764. And finally I divided to get x =. Elena says that 0.137 99900 14 equals. I calculated 10x = 377 because one digit repeats. Then I 900 subtracted to get 9x = 4. Then I did what Han did to get 900x = 14 and 14 x =. 900 Do you agree with either of them? Explain your reasoning. Both strategies are valid. Han and Elena both get fractions that are equal to 0.137. These are equivalent fractions, but Elena's fraction has fewer common factors in the numerator and denominator. The equivalent fraction with the lowest 31 possible denominator is. 5 Problem How are the numbers 0.444 and 0.4 the same? How are they different? Answers vary. Sample response: They are the same in that they are both rational numbers between 0.4 and 0.5, and the first three digits in their decimal expansions are the same. They are different in that 0.4 is greater than 0.444 because it has a greater digit in the ten-thousandths place. 0.444 is a terminating decimal, while 0.4 is an infinitely repeating decimal. Problem 3 Write each fraction as a decimal. a. 3 b. 16 37. Write each decimal as a fraction. a. b. 0.75 0.3 a. 0.6 b. 3.405. 75 a. (or equivalent) 99 1 b. (or equivalent) 3 Problem 4 Write each fraction as a decimal.. 5 9 5 4 48

3. 4. 5. 6. 48 99 5 99 7 100 53 90 0.5. 3. 4. 5. 6. 5 0.48 0.05 0.07 0.58 Problem 5 Write each decimal as a fraction. 0.7. 0. 3. 0.13 4. 0.14 5. 0.03 6. 0.638 7. 0.54 8. 0.15 7 (or equivalent) 9. (or equivalent) 9 3. (or equivalent) 15 14 4. (or equivalent) 99 3 5. (or equivalent) 99 63 6. (or equivalent) 990 47 7. (or equivalent) 900 14 8. (or equivalent) 90 Problem 6. = 4.84 and.3 = 5.9. This gives some information about 5. Without directly calculating the square root, plot 5 on all three number lines using successive approximation.