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In this lesson, we will learn how to find the opposite of a number and how to use this to solve word problems.

Q1:

What is the additive inverse of 0?

Q2:

A chemistry teacher told his students that at ion is an atom that has an unequal number of electrons and protons, and that all ions have a charge. A negative charge means that the ion has more electrons than protons. A positive charge means that it has less electrons than protons.

Which ion in the table has a charge that is not the opposite of the charge of one of the other ions?

Q3:

In Yakutsk, the temperature in February is − 4 0 ∘ F . A weather forecast predicts that a warming trend will increase the temperature to 0 ∘ F . If the temperature increases with an average of 1 0 ∘ per week, how many weeks will it take to reach 0 ∘ F ?

Q4:

Yara saw on the weather report that Alaska’s temperature was 17 degrees below zero. Represent the temperature with an integer.

The temperature in Cape Town can be represented by the opposite of this integer. What is the temperature, in Fahrenheit, in Cape Town?

Q5:

The table shows the scores that ten teams received in a competition. Name two teams whose scores are additive inverses of each other.

Q6:

The opposite of − 4 4 is , and their sum is zero.

Q7:

In an atom, protons have a charge of + 1 , electrons have a charge of − 1 , and the charge of an atom is the sum of the charges of its protons and electrons.

A sodium atom has 11 protons and 11 electrons. Does it have a zero charge?

Q8:

Fady flies a helicopter from a point 10 feet below sea level to a point 10 feet above sea level.

Which integer represents his starting elevation?

Which integer represents his finishing elevation?

What can you say about these integers?

Q9:

Yasmine, Sherif, Nader, Sarah, and Sally play a question-and-answer game. A player steps forward for each correct answer and steps backward for each incorrect answer. During the first round, Sarah takes four steps backward, Yasmine takes five steps forward, Sherif takes five steps backward, Sally takes four steps backward, and Nader does not move. Which two players moved in opposite directions but are the same distance from the starting point?

Q10:

The table shows four friends’ golf scores.

What integer is the opposite of Amir’s score?

Q11:

How can a point 75 m above sea level be represented as an integer?

Q12:

How can a point 125 m below sea level be represented as an integer?

Q13:

In a game, the white counters count as + 1 and the blue counters count as − 1 . Pick the move that would result in a total score of zero.

Q14:

Amira plays the same game for 15 minutes every day. On Sunday her score was − 4 8 . On Monday she gained 15 points, on Tuesday she gained 25, and on Wednesday 10. If her score at the end of Thursday was 0, write an integer to represent the points she gained or lost that day.

Q15:

Amira’s account had a balance of . She then made a deposit of $50.25. Is the balance in her account now 0?

Q16:

The table shows the average recorded temperature over four days.

If we plotted these temperatures on a number line, which two days would be the same distance from zero?

Q17:

Determine the two integers where the first is the opposite of + 7 , the second is greater than the first, and the difference between both is 26.

Q18:

The normal low temperature during January for a town in Alaska is . Nada represented this temperature with a number on a number line. If you plotted the opposite of that number on the number line, between which two integers would it lie?

Q19:

One of addition’s properties is that the sum of a number and its opposite is always equal to zero. Which of the following situations does not demonstrate this property of addition?

Q20:

Two hot air balloons were flying at the same height. Then, Balloon A ascended 15 feet, while balloon B descended 15 feet. If we represent these changes by integers, will they sum to zero?

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