Question

1. write the opposite of each integer.

a. 5
b. - 13
c. -(-22)
d. -31
e. -50
f. -(-66)

1. choose efficient methods compare the integers and write the integer with the greater value.

a. -5, 1
b. -6, -7
c. -9, 8
d. -12, -(-10)
e. -(-9), 11
f. -(-4), 3

1. apply math models the display at the right shows the daily low temperatures for several consecutive days in a new england city. write the temperatures in order from least to greatest. on which day was it the coldest?

mon tue wed thu
4° -5° -7° 7°

1. analyze and persevere in a bank account, a paid - out expense is called a debit, and a deposit is called a credit. would you use positive or negative integers to represent credits? debits? explain.
2. higher order thinking atoms have negatively charged particles called electrons and positively charged particles called protons. if an atom has more protons than electrons, the atom has a positive electric charge. if it has more electrons than protons, it has a negative electric charge. which integer would represent the electric charge of an atom that has an equal number of electrons and protons?

Explanation:

37.

Step1: Recall opposite - integer rule

The opposite of an integer \(a\) is \(-a\). Also, \(-(-a)=a\).

Step2: Find opposite of each integer

A. The opposite of \(5\) is \(- 5\).
B. The opposite of \(-13\) is \(13\).
C. \(-(-22)=22\), its opposite is \(-22\).
D. The opposite of \(-31\) is \(31\).
E. The opposite of \(-50\) is \(50\).
F. \(-(-66)=66\), its opposite is \(-66\).

38.

Step1: Recall integer - comparison rule

Positive integers are greater than negative integers. Among negative integers, the one with a smaller absolute - value is greater.

Step2: Compare each pair

A. Since \(1\) is positive and \(-5\) is negative, \(1>-5\).
B. \(\vert - 6\vert=6\) and \(\vert - 7\vert = 7\), and \(6 < 7\), so \(-6>-7\).
C. Since \(8\) is positive and \(-9\) is negative, \(8>-9\).
D. \(-(-10)=10\), and \(10>-12\).
E. \(-(-9)=9\), and \(11 > 9\).
F. \(-(-4)=4\), and \(4>3\).

39.

Step1: Recall integer - ordering rule

Negative integers are less than positive integers. Among negative integers, the one with a larger absolute - value is smaller.

Step2: Order the temperatures

The temperatures are \(-7^{\circ},-5^{\circ},4^{\circ},7^{\circ}\).
The coldest day is the day with the lowest temperature. So, it was coldest on Wednesday.

40.

Answer:

37: A. \(-5\); B. \(13\); C. \(-22\); D. \(31\); E. \(50\); F. \(-66\)
38: A. \(1\); B. \(-6\); C. \(8\); D. \(-(-10)\); E. \(11\); F. \(-(-4)\)
39: Temperatures in order: \(-7^{\circ},-5^{\circ},4^{\circ},7^{\circ}\); Coldest day: Wednesday
40: Positive integers for credits, negative integers for debits.
41: \(0\)