Math 7 Study Guide Name: Key
Unit 3: Rational Reasoning
1. Describe absolute value and give an example using the correct symbol.
Absolute value is the distance a number is from zero.
Example: |-4|=4
2. What is a rational number that is not natural, whole, or an integer.
½ or 2.5 (many other answer possibilities – any fraction or decimal)
3. Simplify: |-112| - |-9|
112 – 9 = 103
4. Order the rational numbers below from least to greatest and graph on a number line:
0, -0.23, -, -1.5, 3, -4.2, 1
-4.2, -1.5, -, -0.23, 0, 1, 3
5. Simplify: 5(-3a +3b) – (4a – 6b)
5•-3a +5•3b – 4a + 6b = -15a + 15b – 4a + 6b = -15a – 4a + 15b + 6b =
-19a + 21b
6. Simplify: -2(x – 4) + 5(–6 – x)
Simplifyied:-2•x – -2•4 + 5•–6 – 5•x = -2x - -8 + -30 – 5x = -2x + 8 + -30 – 5x = -2x – 5x + 8 + -30 = -7x - 22
Given that x = 2, evaluate the expression. -7(2) – 22 = -14 – 22 = -36
7. Solve for m: – - (-8) = –4
– - (-8) = –4
– +8 = –4
-8 -8
-6 • – = –12• -6
m = 72
8. Draw a coordinate plane and label the following points: (-2,4),
(0, -4), (-1,-3), (4,-5)
(-2,4) = move left 2 and up 4 and make a point; (0,-4) = move 0 left or right and down 4 and make a point; (-1,-3) = move left 1 and down 3 and make a point; (4,-5) = move right 4 and down 5 and make a point
9. Translate the following into an equation and solve: Jillian started with 28 plants. She gave 8 of her friends each an equal number of plants. She has 4 left. How many plants did she give each friend?
4 + 8x = 28
-4 -4
8x = 24
8 8
x = 3
She gave plants to 3 friends.
10. The temperatures during a 5 day period in winter in New York were -15°F, 16°F, -3°F, 17°, and -23°. What was the mean temperature over the five day period?
(-15 + 16 – 3 + 17 – 23) = x
5
-8 = x
5
x = -1.6˚F
The mean temperature was -1.6˚F
11. Over six days, the points of a particular stock share fluctuated by: , 4, -7, ,-4. Write the points in order of the greatest decrease to the greatest increase?
-7, -4, , , 4
12. -32, 0, 35, -40, -15, and 39 are temperatures that recorded as the high and lows over a three day period. Which temperature has the highest absolute value?
-40 has the highest absolute value
13. A scuba diver is 60 feet below sea level while a seaplane is 90 feet above sea level. How far apart above the scuba diver is the seaplane?
90 - -60 = 90 + 60 = 150; The seaplane is 150 feet above the scuba diver.
14. Samantha bought a hat for $20 and three pairs of jeans. The total cost was $74.00 If each pair of jeans cost the same amount, how much was one pair of jeans?
74 = 20 + 3x
-20 -20
54 = 3x
3 3
18 = x Each pair of jeans cost $18.
15. Miles bought 3 packages of trading cards. His friend Chase gave him 5 baseball cards. Clay now has a total of 50 baseball cards. How many cards were in each package?
50 = 3x + 5
-5 - 5
45 = 3x
3 3
x = 15 Each package contained 15 baseball cards.
16. Write an equation that has the same solution as -2x + 5 = 4?
-2x + 5 = 4
-5 -5
-2x = -1
-2 -2
x = ½
Any equation that has x = ½ has the same solution. For example: 2 = 4x
17. What are the two steps used to solve the following equation:
-10x – 14 = -22
Add 14 to both sides; Divide both side by -10.
18. The temperature was 45 degrees Fahrenheit when Nena awoke. The temperature dropped 5 degrees per hour. How many hours did it take for the temperature to drop to -5 degrees Fahrenheit?
45 – 5x = -5
-45 -45
-5x = -50
-5 -5
x = 10
It took 10 hours for the temperature to drop to -5 degrees Fahrenheit.