## Engage NY Eureka Math 6th Grade Module 3 Lesson 8 Answer Key

### Eureka Math Grade 6 Module 3 Lesson 8 Example Answer Key

Example 1.
Ordering Rational Numbers from Least to Greatest
Sam has $10.00 in the bank. He owes his friend Hank$2.25. He owes his sister $1.75. Consider the three rational numbers related to this story of Sam’s money. Write and order them from least to greatest. Answer: – 2.25, – 1.75, 10.00 Example 2. Ordering Rational Numbers from Greatest to Least Jason is entering college and has opened a checking account, which he will use for college expenses. His parents gave him$200. 00 to deposit into the account. Jason wrote a check for $85.00 to pay for his calculus book and a check for$25.34 to pay for miscellaneous school supplies. Write the three rational numbers related to the balance in Jason’s checking account in order from greatest to least.
200.00, – 25.34, – 85.00

### Eureka Math Grade 6 Module 3 Lesson 8 Exercise Answer Key

Exercises 2 – 4
For each problem, list the rational numbers that relate to each situation. Then, order them from least to greatest, and explain how you made your determination.

Exercise 2.
During their most recent visit to the optometrist (eye doctor), Kadijsha and her sister, Beth, had their vision tested. Kadijsha’s vision in her left eye was – 1.50, and her vision in her right eye was the opposite number. Beth’s vision was -1. 00 in her left eye and +0. 25 in her right eye.
– 1. 50, – 1.00, 0.25, 1.50
The opposite of – 1.50 is 1.50, and 1.5015 farthest right on the number line, so if is the greatest. – 1.50 is the same distance from zero but on the other side, so it is the least number. – 1.00 is to the right of – 1.50, so it is greater than – 1.50, and 0.25 is to the right of – 1.00, so it is greater than – 1.00. Finally, 1.50 is the greatest.

Exercise 3.
There are three pieces of mail in Ms. Thomas’s mailbox: a bill from the phone company for $38. 12, a bill from the electric company for$67. 55, and a tax refund check for $25.89. (A bill is money that you owe, and a tax refund check is money that you receive.) Answer: – 67.55, – 38. 12, 25.89 The change in Ms. Thomas’s money is represented by – 38.12 due to the phone bill, and – 67.55 represents the change in her money due to the electric bill. Since – 67.55 is farthest to the left on the number line, it is the least. Since – 38.12 is to the right of – 67.55, It comes next. The check she has to deposit for$25.89 can be represented by 25.89, which Is to the right of – 38.12, and so it is the greatest number.

Exercise 4.
Monica, Jack, and Destiny measured their arm lengths for an experiment in science class. They compared their arm lengths to a standard length of 22 inches. The listing below shows, in inches, how each student’s arm length compares to 22 inches.
Monica: – $$\frac{1}{8}$$
Jack: 1$$\frac{3}{4}$$
Destiny: – $$\frac{1}{2}$$
I ordered the numbers on a number line, and –$$\frac{1}{2}$$ was farthest to the left. To the right of that was –$$\frac{1}{8}$$. Lastly, 1$$\frac{3}{4}$$ is to the right of –$$\frac{1}{8}$$ so 1$$\frac{3}{4}$$ is the greatest.

Exercise 5 – 6
For each problem, list the rational numbers that relate to each situation in order from greatest to least. Explain how you arrived at the order.

Exercise 5.
The following are the current monthly bills that Mr. McGraw must pay:
$122. 00 Cable and Internet$73.45 Gas and Electric
\$45.00 Cell Phone
– 45.00, – 73.45, – 122.00
Because Mr. McGraw owes the money, I represented the amount of each bill as a negative number. Ordering them from greatest to least means I have to move from right to left on a number line. Since – 45.00 is farthest right, it is the greatest. To the left of that is – 73.45, and to the left of that is – 122.00, which means – 122.00 is the least.

Exercise 6.
$$-\frac{1}{3}$$, 0, $$-\frac{1}{5}$$, $$\frac{1}{8}$$
$$\frac{1}{8}$$, 0, $$-\frac{1}{5}$$, $$-\frac{1}{3}$$
I graphed them on the number line. Since I needed to order them from greatest to least, I moved from right to left to record the order. Farthest to the right is $$\frac{1}{8}$$ so that is the greatest value. To the left of that number is 0. To the left of 0 is –$$\frac{1}{5}$$, and the farthest left is –$$\frac{1}{3}$$ so that is the least.

### Eureka Math Grade 6 Module 3 Lesson 8 Problem Set Answer Key

Question 1.
a. In the table below, list each set of rational numbers from greatest to least. Then, in the appropriate column, state which number was farthest right and which number was farthest left on the number line.

b. For each row, describe the relationship between the number in Column 3 and its order in Column 2. Why is this?
The number in Column 3 is the first number listed in Column 2. Since it is farthest right on the number line, it will be the greatest; therefore, it comes first when ordering the numbers from greatest to least.

c. For each row, describe the relationship between the number in Column 4 and Its order in Column 2. Why is this?
The number in Column 4 is the last number listed in Column 2. Since it is farthest left on the number line, it will be the smallest; therefore, it comes last when ordering the numbers from greatest to least.

Question 2.
If two rational numbers, a and b, are ordered such that a is less than b, then what must be true about the order for their opposites: – a and – b?
The order will be reversed for the opposites, which means – a is greater than – b.

Question 3.
Read each statement, and then write a statement relating the opposites of each of the given numbers:
a. 7 is greater than 6.
– 7 is less than – 6.

b. 39.2 is greater than 30.
– 39.2 is less than – 30.

c. –$$\frac{1}{5}$$ is less than $$\frac{1}{3}$$.
$$\frac{1}{5}$$ is greater than –$$\frac{1}{3}$$

Question 4.
Order the following from least to greatest: – 8, – 19, 0, $$\frac{1}{2}$$, $$\frac{1}{4}$$.
– 19, – 8, 0, $$\frac{1}{4}$$, $$\frac{1}{2}$$

Question 5.
Order the following from greatest to least: – 12, 12, – 19, 1$$\frac{1}{2}$$, 5.
12, 5, 1$$\frac{1}{2}$$, – 12, – 19
– 3, 0, –$$\frac{1}{2}$$, 1, – 3$$\frac{1}{3}$$, 6, 5, – 1, $$\frac{21}{5}$$, 4
– 3, 0, –$$\frac{1}{2}$$, 1, – 3$$-\frac{1}{2}$$, 0, 1, 4, $$\frac{21}{5}$$, 5, 6
I drew a number line and started at zero. I located the positive numbers to the right and their opposites (the negative numbers) to the left of zero. The positive integers listed in order from left to right are 1, 4, 5, 6. And since $$\frac{21}{5}$$ is equal to 4$$\frac{1}{5}$$, I know that it is $$\frac{1}{5}$$ more than 4 but less than 5. Therefore, I arrived at 0, 1, 4, $$\frac{21}{5}$$, 5, 6. Next, I ordered the negative numbers. Since – 1 and – 3 are the opposites of 1 and 3, they are 1 unit and 3 units from zero but to the left of zero. And – 3$$\frac{1}{3}$$ is even farther left, since it is 3$$\frac{1}{3}$$ units to the left of zero. The smallest number is farthest to the left, so l arrived at the following order: – 3$$\frac{1}{3}$$ , – 3, – 1, –$$\frac{1}{2}$$ , 0, 1, 4, $$\frac{21}{5}$$, 5, 6.