Chapter 2 Integers And Rational Numbers
Mid Topic
Page 83 Exercise 1 Answer
The set of integers consists of zero, the natural numbers, and their additive inverses.
A rational number is any number which can be expressed as the quotient of two integers. The quotient or the fraction consists of a numerator p and a denominator q. The denominator can never be equal to zero, however it can be equal to one, which than means every integer is a rational number.
\(\frac{p}{q}\), where q ≠ 0
Result
Every integer is a rational number.
Page 83 Exercise 2 Answer
The statement “absolute value can never be negative” is true. The absolute value of a number is its distance from zero on a number line. Since distance is always positive so is the absolute value, with one exception. Absolute value is equal to zero if and only if ∣0∣ = 0. Notice it is still never negative, only positive or equal to zero.
Result
True.
Read And Learn More: enVisionmath 2.0 Grade 6 Volume 1 Solutions
Page 83 Exercise 3 Answer
The statement “every counting number is an integer” is true. The set of integers consists of zero, natural number (or counting numbers) and their opposite numbers. This means that the set of counting numbers is a subset of the set of integers, every counting number is also an integer.
Result
True.
Page 83 Exercise 4 Answer
The statement “a decimal is never a rational number” is false. A decimal is a rational number if it can be written as a fraction.
Result
False.
Page 83 Exercise 5 Answer
The statement “the opposite of a number is sometimes negative” is true. The opposite of a positive number is negative, however the opposite of a negative number is a positive number. The opposite of zero is zero.
Result
True.
Page 83 Exercise 6 Answer
If the absolute value of a number is 52 then that number is either 52 or −52.
52 = ∣52∣ = ∣−52∣
Result
52 or −52
Page 83 Exercise 7 Answer
Let’s say that one unit on a number line is 1 foot and the zero marks sea level. Plot all four treasure chests on the number line. The point which is farthest from zero is the treasure chest that is farthest from sea level. To do this find the absolute value of each number and compare them.
\(|0.75|=0.75 \quad\left|\frac{-5}{4}\right|=\frac{5}{4}=1.25 \quad|-0.5|=0.5 \quad|1|=1\)1.25 > 1 > 0.75 > 0.5
Thus, the treasure chest marked B is farthest from sea level.
Result
Plot all four treasure chests on the number line. The point which is farthest from zero is the treasure chest that is farthest from sea level. Thus, the treasure chest marked B is farthest from sea level.
Page 83 Exercise 8 Answer
M. Milo owes −$85.50, B. Barker −$42.75, and S. Stampas −$43.25. The customer who owes the least amount of money is the one whose account balance has the least absolute value.
∣−85.50∣ = 85.50
∣−42.75∣ = 42.75
∣−43.25∣ = 43.25
The least absolute value is 42.75, so the customer who owes the least amount of money is B. Barker.
Result
B. Barker owes the least amout of money.
Page 84 Exercise 1a Answer
During their first week of a dog walking business Warren and Natasha spent $10 on business cards and $6 on doggie treats, thus the integers that represent the amounts they spent are −$10 and −$6. A 15-minute walk costs $5 and a 30-minute walk costs $10, so Warren earned $5 and Natasha earned $10.
Result
All that apply are: $5, $10, −$10, and −$6.
Page 84 Exercise 1b Answer
When comparing fractions, if you are not sure which is greater, write them as decimals and then compare. For example,
–\(\frac{2}{3}\) = -(2 ÷ 3)
Thus, –\(\frac{2}{3}\) is equal to -0.6666, or approximately -0.67. The fractions written as decimals is then:
–\(\frac{3}{2}\) = -1.5, –\(\frac{2}{3}\) ≈ -0.67, -0.5 and –\(\frac{5}{4}\) = -1.25.
Plot these decimals on the number line. The numbers ordered from most pounds eaten to fewest pounds eaten are: –\(\frac{3}{2}\), –\(\frac{5}{4}\), –\(\frac{2}{3}\), -0.5
Result
–\(\frac{3}{2}\), –\(\frac{5}{4}\), –\(\frac{2}{3}\), -0.5
Page 84 Exercise 1c Answer
The absolute values of the number of pounds of doggie treats eaten each week are:
week one: |-\(\frac{3}{2}\)| = \(\frac{3}{2}\),
week two: |-\(\frac{2}{3}\)| = \(\frac{2}{3}\),
week three: |-\(\frac{5}{4}\)| = \(\frac{5}{4}\),
week four: |-0.5| = 0.5.
The greatest number of pounds eaten was in weeks 1 and 4.
Result
The greatest number of pounds eaten was in weeks 1 and 4.