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Absolute value describes the distance of a number line from 0 without considering which direction from the number lies. A whole number which is positive or negative is known as integers. They can be displayed on the number line while representing the number in the number line. The number in the right side of number line is always greater.
- 3> - 4, 0> - 10, -13< 1 etc
The distance of a number from a zero point is known as absolute values. For example:
| -3 | = 3; | 4 | = 4, - | 3 | = -3 etc
In calculations on the absolute value of an integer can be considered as a positive integer. For example:
2 x |-6| = 2 x 6 =12
5 x |7| = 5 + 7 =12
Rules of signs
In case of dividing or multiplying two integers of a same sign then there is always positive and in case of two differents sign then the reasult sign is negative.
So, to multiply or divide two integers we multiply or divide their absolute value and then select a sign using the rule of signs.
Examples:
(i) -12×3
Multiply the absolute values:12×3=36, then signs are the opposite: -36
Thus, -12×3= -36
(ii) (-8)×(-6)
Multiply the absolute values: 8×6= 48
The signs are the same:48
Thus,(-8)×-6)=48
(iii)10×4
Multiply the absolute values: 10×4= 40
The signs are the same:40
Thus,10×4=40
(iv) \(\frac{45}{-5}\)
Divide the absolute values:\(\frac{45}{-5}\)= 9
The signs are opposite: -9
Thus,\(\frac{45}{-5}\)= -9
(v)\(\frac{-18}{-6}\)
Divide the absolute values:\(\frac{18}{6}\)= 3
The signs are the same: 3
Thus, \(\frac{-18}{-6}\)= 3
(vi) \(\frac{-56}{7}\)
Divide the absolute values: \(\frac{-56}{7}\)= 8
The signs are the opposite: -8
Thus, \(\frac{-56}{7}\)= -8
(vii) \(\frac{32}{8}\)
Divide the absolute values: \(\frac{32}{8}\)= 4
The signs are the same: 4
Thus,\(\frac{32}{8}\)
= 4
(-2)(-4)(-3)= 8(-3)= -24
(-3)(-2)(-4)(-5)= 6×20= 120
While multiplying odd numbers of negative integers we multiply their values and select a negative sign(-) and while multiplying even numbers of negative integers we multiply their values and select a positive sign(+).
Following are the examples;
(i) (-2)(-5)(-2)
Multiply the absolute values: 2×5×2= 20
but(-2)(-5)(-2) = 20
(ii) (-6)(-2)(-1)(-2)
Multiply the absolute values: 6× 2× 1× 2 = 24
but, (-6)(-2)(-1)(-2)= -24
Solution:
3 and 9
Solution:
-10× 4
= - 40
Solution:
( -5)× (-6)
= 30
Solution:
\(\frac{(- 3) (- 5) 2(-8)}{6 (-10)}\)
= \(\frac{- 240}{-60}\)
= 4
Solution:
( -10) + (-2)
= -10 -2
= -12
Solution:
a)(-10) + (-2) = -10 -2 = -12
b) -23 + 8= -15
Solution:
Multiplying the Absolute values:
3 \(\times\) 7 \(\times\) 2 = 42
Thus, (-3) (-7) (-2)
= 21 \(\times\) -2
= -42 ( Since the signs are negative)
Solution:
Multiply the absolute values: 8 \(\times\) 6 = 48
The signs are the same: 48
Thus, (-8) \(\times\) (-6)
= 48
Solution:
Divide the absolute values.
\(\frac{18}{6}\)
The signs are the same.
Thus, \(\frac{-18}{-6}\)
=3
Solution:
(-4) (-2) (-1) (-3)
Multiply the absolute values: 4? 2? 1?3 = 24
Thus, (-4) (-2) (-1) (-3) = 24
Solution:
Divide the absolute values: \(\frac{35}{5}\) = 7
The signs are opposite: -9
Thus, \(\frac{35}{-5}\)
= -7
Solution:
Multiply the absolute values: 25× 4 = 100
The signs are the same: 100
Thus, 25× 4 = 100
Solution:
5 \(\times\) 4 = 20 and
4 + 9 = 13
Solution:
Multiply the absolute values: 24× 8 = 192
The signs are the same. 192
Thus, ( -24)× (-8) = 192
Solution:
Multiply the absolute values:
3× 2× 4×5 = 120
The signs are the same: 120
Thus, (-3)×(-2)× (-4) ×(-5)
= 120
Multiply:
(-4)( imes)(-8)
Multiply:
-24( imes)5
Divide:
(frac{-44}{-11})
Multiply:
(-2)(-3)(-1)(-5)
Multiply:
(-1)(-6)(-8)(-2)
Add or Subtract:
-10-24
Add or subtract:
(-10) + (-2)
Find the absolute value of the following.
| -5|, |20|
Multiply:
(-8) (-10) (-2) (-1)
Multiply and Divide.
(frac{ (-3)(-5)2(-8)}{6(-10)})
Multiply and Divide.
(frac{ 15(-4)(-3)7}{6(-21)})
Multiply:
(-3)(-7)(-2)
Multiply:
(-3)(-2)(-4)(-5)
Multiply:
(-2)(-4)(-3)
Add or Subtract:
7 + (-15)
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