Use the additive inverse to find 8.7/6 − 26.5/4.
To find 8.7/6 - 26.5/4, we need to have a common denominator.
The common denominator for 6 and 4 is 12.
Now we can rewrite the expression with the common denominator:
8.7/6 - 26.5/4 = (8.7 * (2/2))/(6 * (2/2)) - (26.5 * (3/3))/(4 * (3/3))
= (17.4/12) - (79.5/12)
Now we can subtract the fractions:
= (17.4 - 79.5)/12
= -62.1/12
To find the additive inverse, we simply change the sign of the fraction:
= -(62.1/12)
= -62.1/12
Use the additive inverse to find 8.76−26.54.
To find the additive inverse of a number, we simply change the sign of the number.
In this case, to find -26.54, we change the sign of the number:
-26.54
Therefore, the additive inverse of 26.54 is -26.54.
Now we can perform the subtraction:
8.76 - 26.54 = 8.76 + (-26.54)
= -17.78
Use the additive inverse to find −12 2/3 − (−8 5/6). Write the answer as a mixed number
To find the additive inverse of a number, we simply change the sign of the number.
In this case, to find the additive inverse of -12 2/3, we change the sign of the number:
-(-12 2/3) = 12 2/3
Now, we can rewrite the expression as addition using the additive inverse:
-12 2/3 - (-8 5/6) = -12 2/3 + 8 5/6
Now, we need to find a common denominator to add the fractions. The common denominator for 3 and 6 is 6.
Rewriting the fractions with the common denominator:
-12 2/3 + 8 5/6 = -12 (2/3)(2/2) + 8 (5/6)(1/1) = -12 (4/6) + 8 (5/6)
Simplifying the fractions:
-12 (4/6) + 8 (5/6) = -12 (2/3) + 8 (5/6)
Now, we can add the whole numbers and fractions separately:
-12 (2/3) + 8 (5/6) = -12 + 8 (2/3 + 5/6)
= -4 (2/3 + 5/6)
Now, we need to find a common denominator to add the fractions inside the parentheses. The common denominator for 3 and 6 is 6.
(2/3 + 5/6) = (4/6 + 5/6) = (9/6)
Now, we can continue simplifying the expression:
-4 (9/6) = -4 * (9/6)
Simplifying further:
(9/6) can be reduced to (3/2)
-4 * (3/2) = -12/2
= -6
Therefore, -12 2/3 - (-8 5/6) = -6
The answer is -6, which can also be written as a mixed number: -6 = -5 5/6.
What is the absolute value of subtracting these rational numbers on a vertical number line diagram? −22 − 1 1/2
To find the absolute value of the difference between -22 and -1 1/2, we subtract the two numbers and then take the absolute value of the result.
-22 - (-1 1/2) = -22 + 1 1/2
To add these fractions, we first need to find a common denominator. The common denominator for 1/2 and 2/2 is 2.
-22 + 1 1/2 = -22 + (2/2)(1/1) + (1/2)(1/1) = -22 + 2/2 + 1/2
Simplifying the fractions:
-22 + 1 + 1/2 = -21 + 1/2
Now, taking the absolute value:
|-21 + 1/2| = |-20 1/2|
The absolute value of -20 1/2 is 20 1/2.
Therefore, the absolute value of subtracting -22 and -1 1/2 on a vertical number line diagram is 20 1/2.
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?
The total distance Jason traveled from school can be calculated by adding the distance he rode initially (2 miles) to the additional distance he traveled to his friend's house (1 mile).
So, the total distance Jason traveled from school is 2 miles + 1 mile = 3 miles.