Integers
What does the number 0 represent in the context of temperatures?
0 is the point between positive and negative — neither above nor below freezing; a neutral reference.
Where would –4 be located on a number line? (Count units and what direction from zero)
Four units to the left of 0.
Which is greater: –3 or –5 and why?
–3 is greater (because it is closer to zero).
Solve: ½ + ¼
¾
Convert 0.75 to a fraction.
¾
If the temperature is –5 degrees in the morning and 3 degrees in the afternoon, how much did the temperature change?
It changed by 8 degrees (because from –5 up to 0 is +5, then +3 more = +8).
What does it mean when a number is to the right of 0 on the number line?
It is a positive number; greater than zero.
Compare the rational numbers ½ and 0.75. Which is larger?
0.75 (since 0.75 = ¾ and ¾ > ½).
What is 3.5 – 1.2?
2.3
Convert ¼ to a decimal.
0.25
What is the opposite of –7?
+7
Identify the opposite of 5 on the number line.
–5
Arrange these numbers from least to greatest: –1, 2, 0, –3.
–3, –1, 0, 2
If you have $50 and spend $20, how much do you have left?
$30
What is 60% as a fraction?
60% = 60/100 = 3/5
How would you represent a debt of $20 using integers?
–20 (negative twenty dollars)
If 3 is plotted on the number line, what is the distance from 0?
3 units
Write a statement comparing –4 and 2 using <, >, or =.
–4 < 2
2 × (3 + 4)
2 × 7 = 14
Convert 0.8 to a percent.
80%
Explain how positive and negative numbers can represent quantities in a bank account.
Positive numbers represent deposits or money you have; negatives represent owing money or being overdrawn (debt).
Plot –2, 0, and 3 on the number line and explain their positions.
You place –2 two units left of 0, 0 in the center, and 3 three units to the right. That shows negative, zero, and positive.
Explain why –2 is less than 0 in a real-world context.
If you owe $2 (–2), that is less money than having $0; or on a vertical scale, going down 2 is lower than being at zero.
Apply the distributive property to simplify. 3(4c + 5)
12c+15
How would you express 3/5 as a decimal and a percent?
3/5 = 0.6 = 60%