Absolute Value LESSON 8 Plug In Understanding Absolute Value The absolute value of a number You can use a number line to The distance from 25 to 0 is 5 is its distance from 0 on a help you find the absolute value units . That means the absolute number line . of a number . value of 25 is 5 . |25| means “the absolute value of 25 ”. Ϫ5 Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 1 Ϫ5 Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 1 The point is on 25 on the number line . |25| 5 5 I can think of I get it! Since a distance absolute value as a Count the number is always positive, the distance. of units from the absolute value of a number point to 0. is always positive. Words to absolute value number line Know a number’s distance from 0 on a number line a line that shows numbers placed in order |23| means “the absolute value of 23 ”. Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 1 2 3 4 LLC rning, Lea ISCUSS D Can an absolute value be 0? Explain . umph Tri 4 201 © A You can find the absolute value of a positive number . law D O by Find |7| . 1 Plot the number 7 on a 7 hibited Think: I need to find the absolute value of . pro is number line . k boo 2 Count the number of s thi Ϫ1 0 1 2 3 45 67 8 9 10 of units to 0 . t par 3 This distance is the There are units from 0 to 7 . any absolute value . |7| 5 Duplicating Lesson 8 74 CC13_Mth_G6_SE_Final.indd 74 21/05/13 11:37 AM 8 Absolute Value B You can find the absolute value of a negative number . D O Find |210| . 210 1 Draw a point on a number Think: I need to find the absolute value of . line for 210 . 2 Count the number of units Ϫ10 Ϫ9 Ϫ8 Ϫ7 Ϫ6 Ϫ5 Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 1 to 0 . There are units from 210 to 0 . 3 This distance is the absolute value . |210| 5 I get it! Taking the absolute value of a positive number doesn’t change the number. C You can find the absolute value of a number by Taking the absolute value keeping or changing its sign . of a negative number D O makes it positive. Find |12| and |250| . 1 Think about the meaning The absolute value of a number is always positive . of absolute value . Since 12 is already positive, to find |12| remove the absolute value 2 Write the absolute values . symbols and its sign . Since 250 is negative, to find |250| remove the absolute value symbols and change its sign from to . |12| 5 and |250| 5 PRACTICE Draw a point on a number line to show the integer and find its absolute value. LLC 1 |4| 5 2 |22| 5 rning, Lea Ϫ5 Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 1 2 3 4 5 Ϫ5 Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 1 2 3 4 5 umph Tri 4 201 © . Find the absolute value of the integer. law by 3 |28| 5 4 |15| 5 5 |2126| 5 hibited pro is k boo s thi of t par any Duplicating 75 CC13_Mth_G6_SE_Final.indd 75 21/05/13 11:37 AM POWER uP Finding Opposites on a Number Line Negative numbers are to the left of 0 and The numbers 5 and 25 both have an absolute positive numbers are to the right of 0 . value of 5 . They are both 5 units away from 0 . |25| 5 5 25 and 5 are opposites . |5| 5 5 Ϫ5 Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 1 2 3 4 5 Numbers are opposites when they Ϫ5 Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 1 2 3 4 5 have the same absolute value but are on different sides of 0 . Positive and negative I get it! The numbers 5 numbers are on opposite and 25 are both 5 units sides of zero on the number from 0 on the number line, line. but have opposite signs. Words to positive number negative number opposites Know a number greater than zero a number less than zero numbers that have the same absolute value but different 15 215 signs read as “negative fifteen” 15 and 215 are opposites . S CUS DI S Does every whole number, fraction, integer, and decimal except 0 have an opposite? Explain . LLC rning, Lea A You can use a number line to find the opposite of a positive number . D O umph Tri Find the opposite of 7 . 4 201 7 1 The number 7 is units to the of 0 . © Determine which side of . law 0 the given number is on . by Draw a point . Ϫ8 Ϫ7 Ϫ6 Ϫ5 Ϫ4 Ϫ3 Ϫ2 Ϫ10 1 2 3 4 5 6 7 8 2 Count the same number hibited pro To find its opposite, count units to the of 0 . is of units in the opposite k direction from 0 and boo s thi draw a point . of t 3 par Write the answer . The opposite of 7 is . any Duplicating Lesson 8 76 CC13_Mth_G6_SE_Final.indd 76 21/05/13 11:37 AM 8 Absolute Value The opposite of a positive number B You can use a number line to find the opposite of a negative number . is negative, and D O the opposite of a Find the opposite of 24 . negative number 4 1 Determine which side The number 24 is units is positive. of 0 the given number to the of 0 . is on . Draw a point . 2 Count the same number of units in the Ϫ6 Ϫ5 Ϫ4 Ϫ3 Ϫ2 Ϫ10 1 2 3 4 5 6 opposite direction from To find its opposite, count units to the of 0 . 0 and draw a point . The opposite of 24 is . 3 Write the answer . S CUS DI S On the number line below, locate a number (other than 0) and its opposite . What is the opposite of the opposite of your original number? Explain . Ϫ8 Ϫ7 Ϫ6 Ϫ5 Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 1 2 3 4 5 6 7 8 PRACTICE Find the opposite of the number shown on the number line. 1 2 Ϫ5 Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 1 2 3 4 5 Ϫ5 Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 1 2 3 4 5 The opposite of 23 is . The opposite of 2 is . Plot the number on the number line. Then, find its opposite and plot it on the number line. LLC 3 28 The opposite of 28 is . rning, Lea umph Ϫ10 Ϫ9 Ϫ8 Ϫ7 Ϫ6 Ϫ5 Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 1 2 3 4 5 6 7 8 9 10 Tri 4 201 4 6 The opposite of 6 is . © . law by Ϫ10 Ϫ9 Ϫ8 Ϫ7 Ϫ6 Ϫ5 Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 1 2 3 4 5 6 7 8 9 10 hibited pro Use the number line to find the opposite of the opposite of the given number. is k boo 5 s The opposite of the opposite of 12 is . thi of t par Ϫ15 Ϫ14 Ϫ13 Ϫ12 Ϫ11 Ϫ10 Ϫ9 Ϫ8 Ϫ7 Ϫ6 Ϫ5 Ϫ4 Ϫ3 Ϫ2 Ϫ1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 any Duplicating 77 CC13_Mth_G6_SE_Final.indd 77 21/05/13 11:37 AM READY TO gO Absolute Value You can find the absolute values You can use absolute value to You can use the absolute value of all rational numbers, which find and compare distances from of a number to describe its size, include integers . a reference point . or its distance from a reference point . The numbers you work with in The elevation 35 5. feet is the real world are often rational 35 5. feet above sea level . 35 5. feet and 235 5. feet are numbers . both 35 5. feet from sea level, The elevation 235 5. feet is but in opposite directions . 35 5. feet below sea level . The reference point is 0 feet, or sea level . The absolute I get it! I can use the absolute value of a rational value of a real-world quantity number is its to describe it in real terms. distance from 0! Words to rational number Know a number that can be written as a ratio of two integers __1 __7 0 75,. 215, 0, 7​ 2 , 22 5,. ​ 9 S CUS DI S Describe the temperature 24°F, using its absolute value . What is the reference point in this case? LLC lEssOn lInk rning, Lea Plug In POWER uP gO! umph Tri A number line can help you A number line can help you 4 201 find the absolute value of a find opposite numbers. © number. I see! I can use . law absolute value to by Ϫ3 Ϫ2 Ϫ1 0 1 2 3 describe positive Ϫ3 Ϫ2 Ϫ1 0 1 2 3 and negative rational hibited pro 22 and 2 are opposites . is numbers in real-world |22| 5 2 k situations! boo s thi of t par any Duplicating Lesson 8 78 CC13_Mth_G6_SE_Final.indd 78 21/05/13 11:37 AM 8 Absolute Value The absolute value of the negative work togEThER balance describes You can describe a real-world the size of her debt! situation using absolute value . • A balance of 2$35 23. means Jeanne spent more money than she had in her negative 35 dollars and 23 bank account, and her balance is now 2$35 23.