Adding and Subtracting
-15 + 22
7
-8 × 7
-56
-5 + 3 × (-2)
-11
A bank account has a balance of -25. If a deposit of 60 is made, what is the new balance?
35
Is the product of two negative rational numbers positive or negative? Explain how you know.
Positive. Multiplying two negatives is the same as taking the opposite of a negative.
-4.5 - (-1.2)
-3.3
-3.2 ÷ 0.4
-8
(1.5 - 2.5) ÷ 0.5
-2
The temperature was -12 degrees F at midnight. By noon, it had risen 25.5 degrees F. What was the temperature at noon?
13.5
Which is greater: -0.33 or -1/3? Justify your answer.
-0.33. On a number line, -0.33 is to the right of -0.33333... (-1/3).
3/4 + (-5/8)
1/8
-2/3 × (-9/10)
3/5
-1/2 × (4/5 - 1/5)
-3/10
A hiker descends a mountain at a rate of 2 1/2 miles per hour. What is the hiker's change in elevation after 3.5 hours?
-8.75
If a is a negative number and b is a positive number, will a - b always be positive, always be negative, or can it be both? Provide an example.
Always negative. Subtracting a positive is the same as adding a negative; two negatives added together always result in a negative.
-12 1/2 - 5 3/4
-18 1/4
-4 1/2 ÷ 1 1/8
-4
-10 + (-2)3 ÷ 4
A submarine is at -150 feet. It rises 40 1/4 feet, then drops 20.5 feet. What is its final depth?
-130.25
Explain why dividing by 0.5 is the same as multiplying by 2 using the rules of rational numbers.
0.5 is 1/2. Dividing by a fraction is multiplying by its reciprocal (2/1).
-0.75 + 1/5 - (-1.2)
0.65
-0.6 × (-1.5) × (-2)
-1.8
(-3.5 + 1.5) / (-0.5 × 2)
2
A stock price started at 45.5 . Over 5 days, it changed by -1.2, 0.5, -2.1, -0.8, and 1.4. What was the average daily change in the stock price?
-0.44
Does the expression - | a+b | always result in a negative number or zero, regardless of the values of a and b? Explain your reasoning.
Yes. Absolute value is always greater than or equal to 0. The negative sign outside the absolute value makes any positive result negative and keeps zero as zero.