Use the additive inverse to find −12 and 2/3−(−8 and 5/6). Write the answer as a mixed number.
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What is the absolute value of subtracting these rational numbers on a vertical number line diagram? −22−112
(1 point)
What is the absolute value of subtracting these rational numbers on a vertical number line diagram? −22−1 and 1/2
(1 point)
To find the difference between -12 and 2/3 and -8 and 5/6 using additive inverse, we need to change the sign of -8 and 5/6. The additive inverse of any number is a number that, when added to the original number, gives a sum of zero.
The additive inverse of -8 and 5/6 is 8 and 5/6 since (-8 and 5/6) + (8 and 5/6) = 0.
Now, we can find the difference by adding -12 and 2/3 to the additive inverse of -8 and 5/6:
(-12) + (2/3) + (8 and 5/6)
First, we need to convert -12, 2/3, and 8 and 5/6 into a common denominator. The least common multiple of 3 and 6 is 6. Let's convert each number into sixths.
-12 as sixths: (-12) * (6/6) = -72/6
2/3 as sixths: (2/3) * (2/2) = 4/6
8 and 5/6 as sixths: (8 * 6 + 5)/6 = 53/6
Now, let's add them together:
(-72/6) + (4/6) + (53/6)
Combining the numerators:
(-72 + 4 + 53)/6 = (-15)/6
Since -15/6 is an improper fraction, we can simplify it. -15 divided by 6 equals -2 with a remainder of -3.
Therefore, the answer is -2 and -3/6, which can be simplified further as -2 and -1/2.
So, the mixed number answer is -2 and -1/2.
To find the absolute value of -22 - 1 1/2, we need to subtract the values on a vertical number line diagram.
We represent -22 on the number line by moving down 22 units from 0.
Next, we need to represent -1 1/2 on the same number line. To do this, we divide the length between 0 and 1 into two equal parts and move 1 unit and half upwards from 0.
Now, to find the difference, we subtract 1 1/2 from -22. Since subtraction is equivalent to adding the opposite, we can rewrite the expression as -22 + (-1 1/2).
To add -1 1/2 to -22 on the number line diagram, we move 1 unit and a half upwards from -22.
Now, we can see that the absolute value of the expression -22 - 1 1/2 is the distance between 0 and the point represented by the sum on the number line diagram.
Counting the number of units from 0 to the calculated point, we find that the absolute value is 23 1/2.
Therefore, the absolute value of -22 - 1 1/2 is 23 1/2.
To find the absolute value of a number or expression, we simply ignore the sign and consider the numerical value only.
In this case, we want to find the absolute value of -22 - 1/12.
To represent -22 on a vertical number line diagram, we start at 0 and move downwards by 22 units.
To represent 1/12 on the same number line, we divide the length between 0 and 1 into 12 equal parts and move 1 unit upwards.
Now to find the difference, we subtract 1/12 from -22. Since subtraction is equivalent to adding the opposite, we can rewrite the expression as -22 + (-1/12).
To add -1/12 to -22 on the number line diagram, we move 1 unit downwards from -22.
Now, we can see that the absolute value of the expression -22 - 1/12 is the distance between 0 and the point represented by the sum on the number line diagram.
Counting the number of units from 0 to the calculated point, we find that the absolute value is 22 and 1/12 or 22 1/12.
Therefore, the absolute value of -22 - 1/12 is 22 1/12.
To find the additive inverse of a number, we simply change the sign of the number.
The additive inverse of −12 is 12.
Now let's subtract 2/3 − (−8 5/6).
First, we need to convert the mixed number −8 5/6 into an improper fraction.
To do this, we multiply the whole number by the denominator of the fraction and add the numerator. Then we put this sum over the original denominator.
−8 * 6 = −48
−48 + 5 = −43
So −8 5/6 as an improper fraction is −43/6.
Now we have 2/3 − (−43/6).
To subtract fractions, we need to find a common denominator.
The common denominator of 3 and 6 is 6.
So we rewrite 2/3 as 4/6.
Now we have 4/6 − (−43/6).
To subtract these fractions, we simply subtract the numerators and keep the common denominator.
4 - (−43) = 4 + 43 = 47.
So now we have 47/6 as our answer.
To write this as a mixed number, we divide the numerator by the denominator:
47 ÷ 6 = 7 with a remainder of 5.
The mixed number form of 47/6 is 7 5/6.
Therefore, the answer is 7 5/6.