Unit 2: Rational Numbers Test Review

What are we asked to find? More than 375 customers? A store can have only 375 customers at one time. At 11:00 p.m., this store had 316 customers. Over the course of an afternoon, of the customers leave and 67 come into the store. Does the amount of customers exceed 375? Show your work. What are the facts? Maximum customers 375 Started at 316 leave 67 enter What are we asked to find? More than 375 customers? First, we need to know how many left: One-fourth of 316 You can also see this as a division problem 316 ÷4 = 79 So, 79 customers left

What are we asked to find? More than 375 customers? A store can have only 375 customers at one time. At 11:00 p.m., this store had 316 customers. Over the course of an afternoon, of the customers leave and 67 come into the store. Does the amount of customers exceed 375? Show your work. What are the facts? Maximum customers 375 Started at 316 leave 67 enter What are we asked to find? More than 375 customers? Next, subtract 79 from 316 to see how many customers remain in the store. 316 – 79 = 237

What are we asked to find? More than 375 customers? A store can have only 375 customers at one time. At 11:00 p.m., this store had 316 customers. Over the course of an afternoon, of the customers leave and 67 come into the store. Does the amount of customers exceed 375? Show your work. What are the facts? Maximum customers 375 Started at 316 leave 67 enter What are we asked to find? More than 375 customers? Finally, add the 67 customers entering to current amount of 237. 67 + 237 = 304 There are 304 customers in the store. Therefore the amount of customers is NOT greater than 375.

2. Maria is making cheese dip that requires cups of cheddar cheese 2. Maria is making cheese dip that requires cups of cheddar cheese. The only measuring tools she has in her kitchen are equivalent to cup, cup, and cup. A. What would be one way to measure out the cheese for the dip? Explain. The 3 whole cups can be measured using the one-half cup measure since it is the largest tool. 1/2 1/2 1/2 1/2 This makes a total of six halves. The 3/8 can be seen as 2/8 and 1/8. We need to convert these to the measuring tools we have. 1/2 1/2 2/8 is equal to ¼. 1/8 is equal to 2/16

Therefore, we can measure the cheese dip using 6/2 + ¼ + 2/16 2. Maria is making cheese dip that requires cups of cheddar cheese. The only measuring tools she has in her kitchen are equivalent to cup, cup, and cup. A. What would be one way to measure out the cheese for the dip? Explain. 1/2 1/2 Therefore, we can measure the cheese dip using 6/2 + ¼ + 2/16 1/2 1/2 1/2 1/2

2. Maria is making cheese dip that requires cups of cheddar cheese 2. Maria is making cheese dip that requires cups of cheddar cheese. The only measuring tools she has in her kitchen are equivalent to cup, cup, and cup. A. What would be one way to measure out the cheese for the dip? Explain. Can you see another way to measure 3 3/8 cups?

2. Maria is making cheese dip that requires cups of cheddar cheese 2. Maria is making cheese dip that requires cups of cheddar cheese. The only measuring tools she has in her kitchen are equivalent to cup, cup, and cup. B. Maria wishes to cut the recipe in half. How can she measure the cheese for the dip now? Explain. We only need half of 3 3/8 cups, so we can use 3/2. 1/2 We also need half of the 3/8. Turn eighths to sixteenths to get 6/16 1/2 Half of 6/16 is 3/16. 1/2 So, we can cut the recipe in half and use 3/2 + 3/16 , which equals 27/16 or 1 11/16

Score Difference from Monthly Average (F°) 3. The table below shows the difference in golf scores for a week from the monthly average. For example, a difference of +5 means that the score for the day was 5 points higher than the average. A. Find the average of the values in the table. Day Score Difference from Monthly Average (F°) Sunday -5 Monday +2 Tuesday -3 Wednesday -1 Thursday +8 Friday -4 Saturday -15 *Remember, to find the average, add all numbers, then divide by the number of values you have. N P -5 +2 -3 +8 -1 -4 -15 -28 + 10 = -18

Average is approximately -2.57 3. The table below shows the difference in golf scores for a week from the monthly average. For example, a difference of +5 means that the score for the day was 5 points higher than the average. A. Find the average of the values in the table. Day Score Difference from Monthly Average (F°) Sunday -5 Monday +2 Tuesday -3 Wednesday -1 Thursday +8 Friday -4 Saturday -15 Divide (-18) by 7. 2 . 5 7 Divide 18 by 7, but remember the answer is negative since a negative ÷ by a positive is a negative. .0 -14 4 -35 5 Average is approximately -2.57 -49 1

Score Difference from Monthly Average (F°) 3. The table below shows the difference in golf scores for a week from the monthly average. For example, a difference of +5 means that the score for the day was 5 points higher than the average. B. Explain what this value means in terms of the scores for the week. Day Score Difference from Monthly Average (F°) Sunday -5 Monday +2 Tuesday -3 Wednesday -1 Thursday +8 Friday -4 Saturday -15 The average of -2.57 tells us that the average score for the week was approximately 2.57 points lower than the monthly average.

4. For numbers 4A-4F, Select Yes or No to indicate whether each of the following are equivalent to . +_______________ YES +_______________

4. For numbers 4A-4F, Select Yes or No to indicate whether each of the following are equivalent to . 10 YES -_______________ NO

4. For numbers 4A-4F, Select Yes or No to indicate whether each of the following are equivalent to . 14 ÷ 3 YES is the same as… NO

5. A clown fish starts at sea level and dives 30 feet 5. A clown fish starts at sea level and dives 30 feet. He then dives another 15 feet to reach a sea anemone. If it takes the clown fish 3 seconds to reach the sea anemone from sea level, what was the fish’s rate of descent in feet per second? Sea Level The fish’s rate of descent is -15 feet per second. 3 seconds -30 feet -45 ÷ 3= -15 -15 feet Sea Anemone Total: -45 feet

5. From the sea anemone, the clown fish swims up 18 feet, but then dives 6 feet lower to avoid a shark. In relation to sea level, what is the fish’s elevation? Sea Level The fish’s elevation is now -33 feet. -45+18 =-27 -30 feet -27-6 = -33 -15 feet Sea Anemone Total: -45 feet

6. Which of the following fractions is equivalent to (-14) ÷ (-5)? * This can also be written *Remember, a negative number divided by a negative number is a positive result, so A. B. C. This answer is negative, so is incorrect This answer is negative and also the reciprocal (flipped), so is incorrect This answer is negative, so is incorrect

6. Which of the following fractions is equivalent to (-14) ÷ (-5)? * This can also be written *Remember, a negative number divided by a negative number is a positive result, so D. E. F. This answer is correct because it is the mixed number form. This answer is the reciprocal (flipped), so is incorrect This answer is correct since a negative divided by a negative is positive.

7. Solve. Select all correct answers. A. C. B. D. This is just the division problem: Which is the same as… 2 1 Incorrect Correct: Equivalent Incorrect-Answer when multiplying Correct

8. Which of the following fractions is/are equivalent to 8. Which of the following fractions is/are equivalent to ? Select all that apply. A. D. B. E. C. F. *A fraction is negative when the negative symbol is in the numerator, in the denominator, or in front of the fraction. Incorrect: positive value Correct: Equivalent Correct: Same as above Correct: Equivalent Incorrect: Positive and reciprocal Incorrect: Reciprocal

9. Is -0.87 a rational number? Explain your reasoning? *A rational number is a number that can be written as a fraction where the denominator is not zero. In decimal form, the decimal must be either terminating (ending) or repeating. The number above is a rational number because it is a decimal that terminates (ends).

10. Solve the equation below. -32 ÷ 8 = Write a story context for this division problem. Explain what the quotient means in terms of the story context. Example: You owe your mom $32. You will pay her the same amount of money each week for 8 weeks. How much money will you give her each week? -4 You will pay her $4 each week for 8 weeks.

11. Which of the following numbers cannot be divided 11. Which of the following numbers cannot be divided? Select all that apply. A. 3 ÷ 0 D. 0 ÷ 5 B. E. C. 8 ÷ 7 F. 5 ÷ 2 *A number is irrational and can’t be divided when the denominator is 0.

Less than $4.25 Greater than $4.25 12. For 12A – 12F, place each value in the appropriate space in the chart. 12A. 13 quarters and 15 nickels 12B. 12 dimes and 42 nickels 12C. 12 quarters and 35 nickels 12D. 16 pennies and 25 dimes 12E. 20 pennies and 17 quarters 12F. 74 pennies and 49 nickels Less than $4.25 Greater than $4.25 12 A. 13Q and 15N ($3.25 + .75 =$4.00) 12 C. 12Q and 35N ($3.00 + 1.75 =$4.75) 12 B. 12D and 42N ($1.20 + 2.10 =$3.30) 12 E. 20P and 17Q ($.20 + 4.25 =$4.45) 12 D. 16P and 25D ($.16 + 2.50 =$2.66) 12 F. 74P and 49N ($.74 + 2.45 =$3.19)