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Transcript
Name _________________________________
Date: ____________
Everyday Math Unit 7: Study Guide
Comparing Numbers
You can use a number line to help when comparing numbers. For any pair of numbers on
the number line, the number to the left is less than the number to the right.
Examples:
-13 is less than -6 because -13 is to the left of -5
We use the < (less than) symbol to write -10 < -5
+3 is greater than -8 because +3 is to the right of -8
We use the > (greater than) symbol to write +3 > -8
Try to solve these comparing numbers problems. Write >, <, or =.
-7 _____ 6
-5 + (-5) _____ -10
14 _____ -2 – (-12)
105 _____ -50
-1 _____ - 2
4
7 – (-8) _____ 25/5
1
Write Numbers in Various Forms
Powers of 10:
Numbers like 10, 100, and 1,000 are called powers of 10. They can be written as
products of 10 or in exponential form. See the example for 1 million in the chart below.
Complete the blanks in the chart.
Standard Notation
1,000,000
1,000
10,000
100,000
10,000,000
Repeated Factors
Exponential Notation
10 * 10 * 10 * 10 * 10 * 10
106
Other Forms:
A number in scientific notation is written as a number (at least 1 and less than 10)
multiplied by a power of 10.
Number-and-word notation is used to show large numbers with 1 numeral and 1 word.
See the example for 5 million in the chart below.
Complete the blanks in the chart.
Standard Notation
Scientific Notation
5,000,000
3,000
5 * 10
6
Number-and-Word Notation
5 million
7 * 109
200 million
1.5 * 10
4
2
Using Order of Operations and Parentheses
Rules for Order of Operations:
1.
2.
3.
4.
Do operations inside parentheses.
Calculate all expressions with exponents.
Multiply and divide in order, from left to right.
Add and subtract in order, from left to right.
Remember: PEMDAS!
Circle the number sentences that are true.
25 + (-6) < -32
42 < 24
15 * 15 * 15 < 153
-5 – (-58) = 53
25 > 52 – (-2)
2 +
3
2 <1
3
Insert parentheses when necessary to make the number sentences true.
6 + 3 * 8 = 30
25 + 12 / 3 = 29
-3 + 5 * 2 – (-6) = 13
Write a numerical expression (using parentheses) to fit the story.
Cindy ordered 5 boxes of snowflake
ornaments. Each box holds 8 ornaments.
When the packages arrived, Cindy
discovered 3 broken ornaments.
Bobby bought 2 containers of tennis balls
for his dog Tiger. Each container holds 3
balls. Later he went back to the store and
bought 3 more containers.
_________________
_________________
3
Solve Problems Involving Negative Numbers
(taken from Everyday Math Student Reference Book pg. 92)
Try these:
10 + (-3) = ____
(-12) + (-7) = ____
(-5) – 3 = ____
(-13) - 5 = ____
(-2) - (-4) = ____
4 + (-6) = ____
4
Solve Problems Involving Negative Numbers: Use your
Use both
+ and – counters
+ and – counters to draw a picture that shows an account with a balance
of -$4.
Use both
+ and – counters to draw a picture that shows a balance of $3, using exactly
7 counters.
Remember, if you have the same number of positive and negative counters, your account
balance = $0.
What is the balance in the container? ______
What will be the new balance if you remove 4 counters from the original balance? ______
10
+
5-
+
+
+
+
+
+
+
-
What will be the new balance if you remove 9 +
counters from the original balance? ______
+
-
+
+
-
-
What will be the new balance if you add 7 counters to the original balance? ______
What will be the new balance if you add 3 +
counters to the original balance? ______
5
Line Graphs
Use the graph to answer the questions.
How many bicycles were sold in March? ________________
Which month(s) had the highest number of bikes sold? ________________
What was the decrease in bikes sold between July and October? ________________
How many bicycles were sold in all? ________________
6
Use the following data to create a line graph.
Days of the Week
Number of Pencils
Sharpened This Week
M
Tu
W
Th
F
40
33
30
15
15
__________________________________________
____________________________________
7