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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