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Includes example problems and word problems that apply absolute value to distance comparisons, turning negative balances into positive amounts, temperature comparisons, and combining distances from 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[E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \nIntegers and Absolute Value  \n\n| Name:   | D | ate:   | S | core:   / 18 |\n| --- | --- | --- | --- | --- |\n\nQuick Review and Helpful Hints  \nThe absolute value | n | is the distance of n from 0 on the number line, so it is never negative:|􀀀7| = 7 and |7| = 7 . Watch a minus sign outside the bars – evaluate the absolute value 􀀂rst, then apply the sign: 􀀀|􀀀5| = 􀀀(5) = 􀀀5 . On the number line, numbers farther right are greater.  \n▷ Example: Evaluate 􀀀|􀀀9| . Work: Work inside the bars 􀀂rst: |􀀀9| = 9 because 􀀀9 is 9 units from zero. Then apply the minus sign outside.⋆ Answer: 􀀀9  \n9 units  \n−9 −6 −3 0  \n|−9| = 9 (distance from 0) .  \n♦ Word Problems  \n15. Diver A is at 􀀀340 feet and Diver B is at 􀀀180 feet. Using absolute value, who is closer to the surface, and by how much?  \n16. An account balance is 􀀀$62 . Write the amount owed as a positive number.  \n17. On a cold morning, one town is 􀀀5◦ and another is 3◦ . Which town is colder?  \n18. Points P = 􀀀7 and R = 5 lie on a number line. Find |P | + |R|, the total distance of the two points from zero.  \n[E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \n1  \nScan Me  \nPractice 􀀏 Progress 􀀏 Succeed | HSPT Math  \nAnswer Keys  \n [E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \n1. 8 7. 23 13. 7  \n2. 15 8. 􀀀20 14. 4  \n3. 􀀀7 9. 0 15. B, by 160 ft  \n4. 34 10. 21 16. $62  \n5. 􀀀12 11. 24 17. 􀀀5◦  \n6. 0 12. 9 18. 12  \nStep-by-Step Explanations  \n1. Start by naming the process: Read what the problem is asking, choose the matching rule, write the setup, and then simplify one step at a time. The setup/work is Absolute value is the distance from zero, and 􀀀8 is 8 units away, so |􀀀8| = 8 . So the 􀀂nal answer is 8.  \n2. A good way to think about this is: Read what the problem is asking, choose the matching rule, write the setup, and then simplify one step at a time. The setup/work is 15 is already 15 units from zero, so |15| = 15 . So the 􀀂nal answer is 15.  \n3. Step by step: Read what the problem is asking, choose the matching rule, write the setup, and then simplify one step at a time. The setup/work is Work inside the bars 􀀂rst: |􀀀7| = 7 . Then the minus sign outside makes it 􀀀7 . So the 􀀂nal answer is 􀀀7 .  \n4. Take it one move at a time: Read what the problem is asking, choose the matching rule, write the setup, and then simplify one step at a time. The setup/work is The distance of 􀀀34 from zero is 34. So the 􀀂nal answer is 34.  \n5. Start by naming the process: Read what the problem is asking, choose the matching rule, write the setup, and then simplify one step at a time. The setup/work is Inside 􀀂rst: |12| = 12 . The outside minus gives 􀀀12 . So the 􀀂nal answer is 􀀀12 .  \n6. A good way to think about this is: Read what the problem is asking, choose the matching rule, write the setup, and then simplify one step at a","cbCaip2vnJXRg67i","https://ap.wps.com/l/cbCaip2vnJXRg67i","pdf",271445,"English","# Quick Review and Helpful Hints\n## Absolute value definition and evaluation rules\n## Example: evaluating absolute value\n## Word problems","[{\"question\":\"What does absolute value mean on the number line?\",\"answer\":\"Absolute value is the distance from 0 on the number line, so it is never negative.\"},{\"question\":\"How do you evaluate an absolute value expression with a minus sign outside the bars?\",\"answer\":\"Evaluate what is inside the bars first, then apply the sign outside the absolute value.\"},{\"question\":\"How can absolute value be used in word problems like distances or balances?\",\"answer\":\"It converts signed quantities into their nonnegative distances from zero, helping determine which value is closer, by how much, or the amount owed as a positive number.\"}]","Integers and Absolute Value - Quick Review and Helpful Hints | PDF"]