How to Find Absolute Value: 15 Steps (with Pictures)

2023 Author: Jason Gerald | [email protected]. Last modified: 2023-08-02 00:13

Calculating the absolute value of a number is easy. You must know the theory underlying absolute equations before solving problems. Whole absolute number is a measure of how far a certain number is from zero. If you think of a number line with a zero in the middle, the absolute value describes how far a certain number is from the zero point.

Step

Method 1 of 2: Calculating Absolute Value

Step 1. Remember that absolute value is the distance of a number from zero

Absolute value is the distance of a certain number from zero on the number line. Simply put, |−4|{displaystyle |-4|}

hanya bertanya tentang seberapa jauh -4 dari nol. Karena jarak selalu bersifat positif (kamu tidak bisa mengambil langkah “negatif”, hanya langkah ke arah yang berbeda), hasil nilai absolut pun akan selalu positif.

Step 2. Make the absolute value number positive

In simple terms, absolute values turn any number positive. Absolute values are useful for measuring distances or finding the value of money when you're dealing with negative numbers, such as when calculating debt or loans.

Step 3. Use two vertical lines to indicate absolute values

Absolute value notation is very simple. Vertical lines (or “pipes” on the keyboard near the “Enter”) key on either side of a number or expression, such as |n|, |3+5|, |−72|{displaystyle |n|, |3+ 5|, |-72|}

menggambarkan nilai absolut.

• |2|{displaystyle |2|}

read as"



Step 4. Remove the negative sign in absolute value notation

Example, |-5| becomes |5|.



Step 5. Discard absolute value notation

The remaining number is the answer you are looking for, so |-5| to |5| then 5. You just need to do this.

• |−5|=5{displaystyle |-5|=5}



Step 6. Simplify mathematical sentences in absolute value notation

If you're dealing with a simple math sentence, like |−10|{displaystyle |-10|}

kamu hanya perlu membuatnya menjadi positif. Namun, kalimat seperti |(−4∗5)+3−2|{displaystyle |(-4*5)+3-2|}

harus disederhanakan sebelum kamu mendapatkan nilai absolut. Urutan operasi matematika biasa masih berlaku:

• Soal:

  |(−4∗5)+3−2|{displaystyle |(-4*5)+3-2|}

• Sederhanakan yang berada dalam tanda kurung:

  |(−20)+3−2|{displaystyle |(-20)+3-2|}

• Tambah dan kurangi:

  |−19|{displaystyle |-19|}

• Buat seluruh bilangan yang berada dalam notasi absolut menjadi positif:

  |19|{displaystyle |19|}

• Jawaban akhir: 19



Step 7. Always use a sequence of mathematical operations before finding absolute values

When calculating longer equations, solve them first before determining absolute values. Don't simplify absolute values before you solve other operations, such as add, subtract, and divide. Example:

• About:

  1+2+|4−7|5∗|−3∗2|{displaystyle {frac {1+2+|4-7|}{5*|-3*2|}}}

• Selesaikan seluruh operasi matematika di dalam dan luar nilai absolut:

  3+|−3|5∗|−6|{displaystyle {frac {3+|-3|}{5*|-6|}}}

• Gunakan nilai absolut:

  3+(3)5∗(6){displaystyle {frac {3+(3)}{5*(6)}}}

• Urutkan sesuai operasi matematika:

  630{displaystyle {frac {6}{30}}}

• Sederhanakan jawaban akhir: 15{displaystyle {frac {1}{5}}}



Step 8. Keep practicing so you can do it

Finding absolute values is relatively easy, but you still need to practice so you don't forget:

• |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}

Method 2 of 2: Solving the Absolute Value of Imaginary Numbers (Equation of



Step 1. Look at complex equations with imaginary numbers, such as "i" or 1{displaystyle {sqrt {-1}}}

dan pecahkan secara terpisah.

Nilai absolut dari bilangan imajiner dan bilangan rasional tidak dapat ditemukan dengan cara yang sama. Kamu bisa menemukan nilai absolut dari persamaan kompleks dengan cara memasukkannya ke rumus jarak. Contoh |3−4i|{displaystyle |3-4i|}

• Soal:

  |3−4i|{displaystyle |3-4i|}

• Catatan: Jika kamu melihat −1{displaystyle {sqrt {-1}}}

you can replace it with" |i|="1{displaystyle"



Step 2. Find the coefficients in a complex equation

Think of 3-4i as the equation of a line. The absolute value is the distance from zero. So, you have to find the distance from zero to the point (3, -4) on the line. The coefficients are two numbers that are not "i." The number with an i next to it is usually the second number, but this isn't important when you're solving equations. To practice, find the following coefficients:

• |1+6i|{displaystyle |1+6i|}

  = (1, 6)

• |2−i|{displaystyle |2-i|}

= (2, -1)

• |6i−8|{displaystyle |6i-8|}

= (-8, 6)



Step 3. Remove the absolute value notation from the equation

You only need the coefficients in this step. Remember, you have to find the distance from the equation to zero. Using the distance formula in the next step is the same as using absolute values.



Step 4. Calculate the cube of the coefficient

To find the distance, you'll use the distance formula, which is x2+y2{displaystyle {sqrt {x^{2}+y^{2}}}}

. Jadi, langkah pertamamu adalah menghitung pangkat dua koefisien yang ada dalam persamaan kompleks. Melanjutkan contoh |3−4i|{displaystyle |3-4i|}

:

• Koefisien:

  (3, -4)

• Masukkan ke dalam rumus jarak:

  32+(−4)2{displaystyle {sqrt {3^{2}+(-4)^{2}}}}

• Hitung pangkat dua koefisien:

  ' 9+16{displaystyle {sqrt {9+16}}}

• Catatan: Baca kembali rumus jarak kalau kamu bingung. Menghitung pangkat dua koefisien akan membuat keduanya positif. Kamu sekarang telah mendapatkan nilai absolut.



Step 5. Add up the numbers raised to the power of two below the square root

This sign means that the number below it will take the square root. Add up the numbers and ignore the root sign for now.

• Coefficient:

  (3, -4)

• Plug it into the distance formula:

  32+(−4)2{displaystyle {sqrt {3^{2}+(-4)^{2}}}}

• Hitung pangkat dua:

  9+16{displaystyle {sqrt {9+16}}}

• Jumlahkan angka yang telah dipangkat dua:

  25{displaystyle {sqrt {25}}}



Step 6. Find the square root to get the final answer

Simplify the equation to get the final answer. This is the "point" distance from the zero imaginary graph. If the square root is not found, leave the number from the last step under the square root -- this is an acceptable final answer.

• Coefficient:

  (3, -4)

• Plug it into the distance formula:

  32+(−4)2{displaystyle {sqrt {3^{2}+(-4)^{2}}}}

• Hitung pangkat dua koefisien:

  9+16{displaystyle {sqrt {9+16}}}

• Jumlahkan koefisien yang telah dipangkat dua:

  25{displaystyle {sqrt {25}}}

• Hitung akar kuadrat untuk mendapatkan jawaban akhir:

  5

• |3−4i|=5{displaystyle |3-4i|=5}



Step 7. Try practicing

Use the mouse to click and highlight the location immediately after the equals sign to see the white answer.

• |1+6i|{displaystyle |1+6i|}

  = √37

• |2−i|{displaystyle |2-i|}

= √5

• |6i−8|{displaystyle |6i-8|}

= 10

tips

• kalau terdapat variabel di dalam notasi nilai absolut, kamu tidak dapat membuang notasi menggunakan metode ini karena jika variabel tersebut negatif, perhitungan nilai absolut akan membuatnya menjadi positif.
• jika terdapat ekspresi matematika di dalam notasi nilai absolut, sederhanakan ekspresi tersebut sebelum menentukan nilai absolut.
• jika terdapat angka positif di dalam notasi nilai absolut, jawabannya selalu angka itu sendiri.
• kamu membutuhkan metode yang berbeda untuk memecahkan persamaan nilai absolut yang memiliki x dan y walaupun metode-metode tersebut tetap menggunakan teori nilai absolut.
• nilai absolut tidak akan pernah sama dengan angka negatif. jadi, jika kamu melihat persamaan, seperti | 2 - 4x| = -7, kamu bisa menentukan bahwa persamaan ini salah tanpa harus memecahkannya terlebih dahulu.