Use the additive inverse to find −24 4/5 - 6 7/10.(1 point)
The additive inverse of a number is the number that, when added to the original number, equals zero.
To find the additive inverse of a mixed number, we can convert it into an improper fraction and then change the sign.
First, let's convert the mixed numbers into improper fractions:
-24 4/5 = -(25*5 + 4)/5 = -129/5
-6 7/10 = -(7*10 + 7)/10 = -77/10
Now, let's find the additive inverse of -6 7/10:
Additive inverse of -77/10 = -(77/10) = -77/10
To find -24 4/5 - 6 7/10, we need to add -129/5 and -77/10:
-129/5 + -77/10 = -(129*2 + 5*77)/(5*10) = -263/10
Therefore, -24 4/5 - 6 7/10 = -263/10.
To find the sum of −24 4/5 and −6 7/10 using the additive inverse, follow these steps:
Step 1: Convert the mixed numbers to improper fractions.
To convert −24 4/5 to an improper fraction, multiply the whole number (-24) by the denominator (5) and add the numerator (4). The denominator remains the same.
−24 4/5 = -24 + 4/5 = -120/5 + 4/5 = -124/5.
Similarly, −6 7/10 can be converted to an improper fraction as follows:
−6 7/10 = -6 + 7/10 = -60/10 + 7/10 = -53/10.
Step 2: Find the additive inverse of the second fraction.
To find the additive inverse of -53/10, change the sign of the numerator:
Additive inverse of -53/10 = 53/10 (It has the same value but opposite sign).
Step 3: Add the two fractions using their common denominator.
-124/5 + 53/10 = (-124 * 2) / (5 * 2) + 53/10
= -248/10 + 53/10
= (-248 + 53) / 10
= -195/10
Step 4: Simplify the fraction (if needed).
The fraction -195/10 is already in simplest form, and it cannot be reduced any further.
Therefore, the sum of −24 4/5 and −6 7/10 is -195/10.