How to Find the Absolute Value of a Number
Remember that absolute value is a number's distance from zero., Make the number in the absolute value sign positive., Use simple, vertical bars to show absolute value., Drop any negative signs on the number inside the absolute value marks., Drop the...
Step-by-Step Guide
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Step 1: Remember that absolute value is a number's distance from zero.
An absolute value is the distance from the number to zero along a number line.
Simply put, |−4|{\displaystyle |-4|} is just asking you how far away
-4 is from zero.
Since distance is always a positive number (you can't travel "negative" steps, just steps in a different direction), the result of absolute value is always positive. , At it's most simple, absolute value makes any number positive.
It is useful for measuring distance, or finding values in finances where you work with negative numbers like debt or loans., The notation for absolute value is easy.
Single bars (or a "pipe" on a keyboard, found near the enter key) around a number or expression, like |n|,|3+5|,|−72|{\displaystyle |n|,|3+5|,|-72|}, indicates absolute value. |2|{\displaystyle |2|} is read as "the absolute value of
2."
For instance, |-5| would become |5|. , The number remaining is your answer, so |-5| becomes |5| and then
5.
This is all you need to do|−5|=5{\displaystyle |-5|=5} , If you've got a simple expression, like |−10|{\displaystyle |-10|}, you can just make the whole thing positive.
But expressions like |(−4∗5)+3−2|{\displaystyle |(-4*5)+3-2|} need to be simplified before you can take the absolute value.
The normal order of operations still applies:
Problem:|(−4∗5)+3−2|{\displaystyle |(-4*5)+3-2|} Simplify inside parenthesis: |(−20)+3−2|{\displaystyle |(-20)+3-2|} Add and Subtract:|−26|{\displaystyle |-26|} Make everything inside the absolute value positive: |26|{\displaystyle |26|} Final Answer: 26, When determining longer equations, you want to do all the possible work before finding the absolute value.
You should not simplify absolute values until everything else has been added, subtracted, and divided successfully.
For example:
Problem:1+2+|4−7|5∗|−3∗2|{\displaystyle {\frac {1+2+|4-7|}{5*|-3*2|}}} Perform the order of operations inside and outside the absolute value:3+|−3|5∗|−6|{\displaystyle {\frac {3+|-3|}{5*|-6|}}} Take the absolute values:3+(3)5∗(6){\displaystyle {\frac {3+(3)}{5*(6)}}} Order of operations:630{\displaystyle {\frac {6}{30}}} Simplify to final answer: 15{\displaystyle {\frac {1}{5}}}, Absolute value is pretty easy, but that doesn't mean a few practice problems won't help you keep the knowledge: |12|{\displaystyle |12|} = 12{\displaystyle 12} |−24|{\displaystyle |-24|} = 24{\displaystyle 24} |3+2−11+5−6|{\displaystyle |3+2-11+5-6|} = 7{\displaystyle 7} -
Step 2: Make the number in the absolute value sign positive.
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Step 3: Use simple
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Step 4: vertical bars to show absolute value.
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Step 5: Drop any negative signs on the number inside the absolute value marks.
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Step 6: Drop the absolute value marks.
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Step 7: Simplify the expression inside the absolute value sign.
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Step 8: Always use the order of operations before finding absolute value.
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Step 9: Keep working on some practice problems to get it down.
Detailed Guide
An absolute value is the distance from the number to zero along a number line.
Simply put, |−4|{\displaystyle |-4|} is just asking you how far away
-4 is from zero.
Since distance is always a positive number (you can't travel "negative" steps, just steps in a different direction), the result of absolute value is always positive. , At it's most simple, absolute value makes any number positive.
It is useful for measuring distance, or finding values in finances where you work with negative numbers like debt or loans., The notation for absolute value is easy.
Single bars (or a "pipe" on a keyboard, found near the enter key) around a number or expression, like |n|,|3+5|,|−72|{\displaystyle |n|,|3+5|,|-72|}, indicates absolute value. |2|{\displaystyle |2|} is read as "the absolute value of
2."
For instance, |-5| would become |5|. , The number remaining is your answer, so |-5| becomes |5| and then
5.
This is all you need to do|−5|=5{\displaystyle |-5|=5} , If you've got a simple expression, like |−10|{\displaystyle |-10|}, you can just make the whole thing positive.
But expressions like |(−4∗5)+3−2|{\displaystyle |(-4*5)+3-2|} need to be simplified before you can take the absolute value.
The normal order of operations still applies:
Problem:|(−4∗5)+3−2|{\displaystyle |(-4*5)+3-2|} Simplify inside parenthesis: |(−20)+3−2|{\displaystyle |(-20)+3-2|} Add and Subtract:|−26|{\displaystyle |-26|} Make everything inside the absolute value positive: |26|{\displaystyle |26|} Final Answer: 26, When determining longer equations, you want to do all the possible work before finding the absolute value.
You should not simplify absolute values until everything else has been added, subtracted, and divided successfully.
For example:
Problem:1+2+|4−7|5∗|−3∗2|{\displaystyle {\frac {1+2+|4-7|}{5*|-3*2|}}} Perform the order of operations inside and outside the absolute value:3+|−3|5∗|−6|{\displaystyle {\frac {3+|-3|}{5*|-6|}}} Take the absolute values:3+(3)5∗(6){\displaystyle {\frac {3+(3)}{5*(6)}}} Order of operations:630{\displaystyle {\frac {6}{30}}} Simplify to final answer: 15{\displaystyle {\frac {1}{5}}}, Absolute value is pretty easy, but that doesn't mean a few practice problems won't help you keep the knowledge: |12|{\displaystyle |12|} = 12{\displaystyle 12} |−24|{\displaystyle |-24|} = 24{\displaystyle 24} |3+2−11+5−6|{\displaystyle |3+2-11+5-6|} = 7{\displaystyle 7}
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Nicholas Campbell
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