Use the additive inverse to find −12 2/3−(−8 5/6). Write the answer as a mixed number.
Use the additive inverse to find −1223−(−856). Write the answer as a mixed number
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To find the sum of −12 2/3 and −8 5/6 using the additive inverse, we can rewrite the subtraction as addition by changing the sign of the second number.
The additive inverse of −8 5/6 is 8 5/6.
Now, we can add the two numbers together:
−12 2/3 + (8 5/6)
= −12 2/3 + 8 5/6
To add these mixed numbers, we need to have a common denominator for the fractions. The least common multiple (LCM) of 3 and 6 is 6.
Converting the fractions with the common denominator of 6:
−12 2/3 + 8 5/6
= −12 * 6/6 + 2/3 * 2/2 + 8 * 6/6 + 5/6
= −72/6 + 4/6 + 48/6 + 5/6
Now, we can combine the fractions:
= (−72 + 4 + 48 + 5)/6
= (−63/6)/6
Simplifying the fraction:
= −63/6
= −10 1/2
Therefore, the answer to the expression −12 2/3 − (−8 5/6) is −10 1/2.
To find the difference between −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 term.
First, let's convert the mixed numbers to improper fractions:
−12 2/3 = −(12 * 3 + 2) / 3 = −(38/3)
−8 5/6 = −(8 * 6 + 5) / 6 = −(53/6)
Now, rewrite the subtraction as an addition:
−12 2/3 − (−8 5/6) = −(38/3) + (53/6)
To add fractions, we need to have a common denominator. In this case, the common denominator is 6 (the least common multiple of 3 and 6).
−(38/3) + (53/6) = −((38 * 2)/(3 * 2)) + (53/6)
= −(76/6) + (53/6)
Now, we can add the fractions:
−(76/6) + (53/6) = (53 - 76)/6
= -23/6
Since the fraction is negative, we can write the answer as a mixed number. Let's convert -23/6 to a mixed number:
Divide the numerator (-23) by the denominator (6): -23 ÷ 6 = -3, with a remainder of -5.
Therefore, the answer is -3 5/6.
To find the sum of these two numbers, we need to subtract the second number from the first number.
The additive inverse of a number x is the number that, when added to x, equals zero. So, the additive inverse of −8 5/6 is 8 5/6.
Now, we can rewrite the given expression as −12 2/3 + 8 5/6.
To add these fractions, we need a common denominator.
The least common multiple of 3 and 6 is 6.
Converting both fractions to have a denominator of 6, we get:
−12 2/3 + 8 5/6 = −12 * 2/3 * 2/2 + 8/1 * 5/6 * 1/1
= −24/6 + 40/6
Now, we can add the two fractions:
−24/6 + 40/6 = 16/6
Simplifying the fraction, we get:
16/6 = 8/3
So, the answer is 8/3, which can be written as a mixed number as 2 2/3.