Use that additive inverse to find -24 4/5 -6 7/10
To find the additive inverse of a number, we simply change its sign.
So, the additive inverse of -24 4/5 would be 24 4/5.
Therefore, to find the sum of -24 4/5 and -6 7/10, we can change the signs and add the numbers:
(-24 4/5) + (-6 7/10) = - (24 4/5) - (6 7/10)
First, let's add the whole numbers:
24 + 6 = 30.
Next, let's add the fractions:
4/5 + 7/10 = (8/10) + (7/10) = 15/10 = 3/2.
Putting it all together, we have:
- (24 4/5) - (6 7/10) = -(30 3/2) = -30 - 3/2.
Therefore, the sum of -24 4/5 and -6 7/10 is -30 3/2.
To find the sum of -24 4/5 and -6 7/10 using the additive inverse, we can convert both mixed numbers into improper fractions first.
To convert -24 4/5 to an improper fraction:
- Multiply the whole number (-24) by the denominator of the fraction (5): -24 * 5 = -120.
- Add the numerator (4) to the result: -120 + 4 = -116.
- Keep the same denominator: -116/5.
To convert -6 7/10 to an improper fraction:
- Multiply the whole number (-6) by the denominator of the fraction (10): -6 * 10 = -60.
- Add the numerator (7) to the result: -60 + 7 = -53.
- Keep the same denominator: -53/10.
Now that we have -24 4/5 as -116/5 and -6 7/10 as -53/10, we can find their sum using the additive inverse.
Additive inverse of -53/10: 53/10 (By changing the sign)
Now, we can add the two fractions:
-116/5 + 53/10 =
To perform addition, we need to find the common denominator between 5 and 10, which is 10.
Multiply the first fraction's numerator and denominator by 2 (to make the denominator 10):
(-116 * 2)/(5 * 2) = -232/10
Now, we can add the fractions:
-232/10 + 53/10 =
Combine the numerators while keeping the same denominator:
(-232 + 53)/10 = -179/10.
Therefore, the sum of -24 4/5 and -6 7/10 is -179/10.
To find the sum of two numbers with different signs, we can use the concept of additive inverse. The additive inverse of a number is the number that, when added to the original number, equals zero. In other words, it is the opposite of the number.
In this case, we have -24 4/5 and -6 7/10. To simplify the calculation, we can convert both mixed numbers into improper fractions.
-24 4/5 = -(24 + 4/5) = -(120/5 + 4/5) = -(124/5)
-6 7/10 = -(6 + 7/10) = -(60/10 + 7/10) = -(67/10)
Now that we have both numbers as improper fractions, we can apply the concept of additive inverse. In this case, we want to find the sum, so we need to add the additive inverse of one number to the other.
The additive inverse of -(67/10) is (67/10) itself, as adding these two fractions would yield zero.
Now we can perform the addition:
-(124/5) + (67/10)
To add these two fractions, we need a common denominator. In this case, the least common multiple of 5 and 10 is 10. So, we can rewrite the fractions with a common denominator:
-(124/5) + (67/10) = -(124/5) + ((67/10) * (2/2))
Multiplying the numerator and denominator of (67/10) by 2, we get:
-(124/5) + (134/20)
Now that both fractions have the same denominator, we can add the numerators:
-(124/5) + (134/20) = (-124 + 134)/20 = 10/20 = 1/2
Therefore, the sum of -24 4/5 and -6 7/10 is 1/2.
To verify the answer, you can convert 1/2 back into a mixed number by dividing the numerator (1) by the denominator (2):
1 ÷ 2 = 0 with a remainder of 1
So, the mixed number representation of 1/2 is 0 1/2.
Therefore, the sum of -24 4/5 and -6 7/10 is indeed 0 1/2.