Use the additive inverse to find -24 4/5 - 6 7/10
A. 31 1/2
B. -31 1/2
C. -31 1/10
D. -18 1/10
To find the sum of -24 4/5 and -6 7/10 using the additive inverse, we need to change the sign of -6 7/10 and then add the two numbers together.
The additive inverse of -6 7/10 is 6 7/10. Therefore, we have:
-24 4/5 + (6 7/10)
Now, let's convert the mixed numbers to improper fractions:
-24 4/5 = -124/5
6 7/10 = 67/10
Now, adding the two fractions together:
-124/5 + 67/10
To add these fractions, we need to find a common denominator, which in this case is 10:
-124/5 = -248/10
Now, we can add the fractions:
-248/10 + 67/10 = -181/10
Since -181/10 is a proper fraction, we can convert it back to a mixed number:
-181/10 = -18 1/10
Therefore, the sum of -24 4/5 and -6 7/10 using the additive inverse is -18 1/10.
So, the correct answer is option D) -18 1/10.
Determine the distance between 6.5 and -7.2 on a number line.
A. -13.7
B. 0.7
C. 13.7
D. -0.7
To find the distance between two numbers on a number line, we subtract the smaller number from the larger number and take the absolute value of the result. In this case, the larger number is 6.5 and the smaller number is -7.2.
Therefore, the distance between 6.5 and -7.2 is:
|6.5 - (-7.2)| = |6.5 + 7.2|
Adding 6.5 and 7.2, we get:
6.5 + 7.2 = 13.7
Taking the absolute value of 13.7, we have:
|13.7| = 13.7
So, the distance between 6.5 and -7.2 on the number line is 13.7.
Therefore, the correct answer is option C) 13.7.
Subtract -6 - (-8)
A. 2
B. -2
C. -14
D. 14
To subtract -6 from -(-8), we can simplify the expression by removing the double negation.
-(-8) can be rewritten as +8. So the expression becomes -6 + 8.
Now we can add these two numbers:
-6 + 8 = 2
Therefore, the correct answer is option A) 2.
Subtract 17 - (-8)
A. 35
B. -1
C. 1
D. -35
To subtract -(-8) from 17, we can simplify the expression by removing the double negation.
-(-8) can be rewritten as +8. So the expression becomes 17 + 8.
Now we can add these two numbers:
17 + 8 = 25
Therefore, the correct answer is not one of the given options. The correct answer is 25.
Subtract 17 - (-18)
A. 35
B. -1
C. 1
D. -35
To subtract -(-18) from 17, we can simplify the expression by removing the double negation.
-(-18) can be rewritten as +18. So the expression becomes 17 + 18.
Now we can add these two numbers:
17 + 18 = 35
Therefore, the correct answer is option A) 35.
To find the answer using the additive inverse, you will need to change the signs of both numbers and then add them together.
First, let's convert the mixed numbers to improper fractions:
-24 4/5 = -24 + 4/5
= -24 * 5/5 + 4/5
= -120/5 + 4/5
= (-120 + 4)/5
= -116/5
-6 7/10 = -6 + 7/10
= -6 * 10/10 + 7/10
= -60/10 + 7/10
= (-60 + 7)/10
= -53/10
Now, change the signs of both fractions:
-116/5 becomes 116/5 with a negative sign (-116/5)
-53/10 remains the same (-53/10)
Next, add the two fractions together:
(-116/5) + (-53/10)
To add fractions with different denominators, you need to find a common denominator, which in this case is 10.
Multiply the first fraction by 2/2 and the second fraction by 1/1 (which is equivalent to multiplying by 2/2):
(-116/5) * (2/2) + (-53/10) * (1/1)
= (-232/10) + (-53/10)
= (-232 - 53)/10
= -285/10
Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 5:
-285/10 becomes (-285 ÷ 5) / (10 ÷ 5)
= -57/2
Finally, convert the improper fraction back to a mixed number:
-57/2 = -28 1/2
Therefore, the answer to the equation -24 4/5 - 6 7/10 using the additive inverse is -28 1/2.
The correct option is B. -31 1/2.