Use the additive inverse to find -12 2/3-(-8 5/6). Wrote the answer as a mixed number.
To find the sum of −12 2/3 and −8 5/6 using the additive inverse, we can rewrite the subtraction as an addition problem by changing the sign of the second fraction:
−12 2/3 + 8 5/6
Next, we need to convert both mixed numbers to improper fractions:
−12 2/3 can be written as -38/3
8 5/6 can be written as 53/6
Now we can add the two fractions:
-38/3 + 53/6
To add the fractions, we need to find a common denominator. The least common multiple of 3 and 6 is 6, so we need to convert both fractions to have a denominator of 6.
-38/3 can be converted to -76/6 (multiply both numerator and denominator by 2).
Now we can add the fractions:
-76/6 + 53/6
= (-76 + 53)/6
= -23/6
To simplify the fraction, we can divide the numerator and denominator by their greatest common divisor, which is 1 in this case.
-23/6 cannot be simplified further.
Therefore, the answer is -23/6, which can be written as a mixed number as -3 5/6.
To find the sum of -12 2/3 and -(-8 5/6), we first need to convert both mixed numbers to improper fractions.
-12 2/3 can be written as -38/3
-(-8 5/6) can be written as 8 5/6 since subtracting a negative number is the same as adding a positive number.
Now we can subtract the two fractions:
-38/3 - 8 5/6
To subtract the fractions, we need to find a common denominator. The least common multiple of 3 and 6 is 6, so we need to convert both fractions to have a denominator of 6.
-38/3 can be converted to -76/6 (multiply both numerator and denominator by 2).
8 5/6 can be converted to 53/6 by multiplying 8 by 6, which equals 48, and adding 5.
Now we can subtract the fractions:
-76/6 - 53/6
= (-76 - 53)/6
= -129/6
To simplify the fraction, we can divide the numerator and denominator by their greatest common divisor, which is 3.
-129/6 = -43/2
Therefore, the answer is -43/2, which can be written as a mixed number as -21 1/2.
Use the additive inverse to find −12 2/3−(−8 5/6)
. Write the answer as a mixed number.
Use the image to answer the question.
A number line ranges from negative 1 to 2 in increments of 1. A solid line with three dots is drawn along the number line, ranging from negative 1 to 2. The first dot is at Negative 1 and is labeled Jason’s friend’s house. dot two is at 0 and labeled Jason’s house. Dot 4 is at 2 and labeled Jason’s school.
Jason rides his bike home from school 2 miles. On his way back home from school, he passes his house to go to his friend's house, which is a mile farther. What is the total distance Jason traveled from school?
(1 point)
The total distance Jason traveled from school can be calculated by adding the distance from school to his house and the distance from his house to his friend's house.
Given that Jason rides his bike 2 miles from school to his house, and then passes his house to his friend's house, which is a mile farther, the total distance Jason traveled from school would be:
2 miles (distance from school to his house) + 1 mile (distance from his house to his friend's house) = 3 miles.
To find the difference between -12 2/3 and -8 5/6 using the additive inverse, we need to change the sign of the second number, -8 5/6, and then add it to the first number, -12 2/3.
The additive inverse of -8 5/6 is 8 5/6.
Now, let's add -12 2/3 and 8 5/6:
-12 2/3 + 8 5/6
To add fractions, we need to find a common denominator:
The common denominator of 3 and 6 is 6.
Now, let's convert the fractions:
-12 2/3 = -12 * 6/6 + 2/3 * 2/2
= -72/6 + 4/6
= -68/6
8 5/6 = 8 * 6/6 + 5/6
= 48/6 + 5/6
= 53/6
Now, let's add:
-68/6 + 53/6
To add the fractions, we add their numerators and keep the denominator the same:
(-68 + 53)/6 = -15/6
Now, let's convert the improper fraction, -15/6, into a mixed number:
-15/6 = -2 3/6
We can simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 3:
-15/6 = -2 * 3/3 * 2
= -2 * 1/1 * 2
= -2 * 2
= -4
Therefore, the difference between -12 2/3 and -8 5/6, using the additive inverse, is -4. So, the final answer, written as a mixed number, is -4.
To find the sum of -12 2/3 and -(-8 5/6) using the additive inverse, we need to understand what the additive inverse of a number is.
The additive inverse of a number is the number that, when added to the original number, gives a sum of zero.
For example, the additive inverse of 3 is -3, because 3 + (-3) = 0. Similarly, the additive inverse of -5 is 5, because -5 + 5 = 0.
In this problem, we have -12 2/3 - (-8 5/6).
To simplify this expression using the additive inverse, we need to change the subtraction of a negative number into an addition of the additive inverse.
So, we rewrite the expression as: -12 2/3 + 8 5/6.
Now, we can find the sum of these two mixed numbers by converting them into improper fractions.
-12 2/3 as an improper fraction is -38/3.
8 5/6 as an improper fraction is 53/6.
Now, we can add -38/3 and 53/6 by finding a common denominator. In this case, the common denominator is 6.
Multiplying -38/3 by 2/2 gives us -76/6, and multiplying 53/6 by 1/1 gives us 53/6.
Now, we can add -76/6 and 53/6 to get -23/6.
Finally, we can convert this improper fraction back into a mixed number.
Dividing -23 by 6 gives us a quotient of -3 with a remainder of -5.
So, the answer is -3 5/6.