Use the additive inverse to find −24 4/5 − 6 7/10
To find the sum of −24 4/5 and −6 7/10 using the additive inverse, we can rewrite the second number as its additive inverse and then perform addition.
The additive inverse of −6 7/10 is 6 7/10, where we simply change the sign.
Now we can add −24 4/5 and 6 7/10:
−24 4/5 + 6 7/10
To add these fractions, we need to find a common denominator. The least common multiple of 5 and 10 is 10.
Converting −24 4/5 to an improper fraction, we get:
−24 4/5 = −(24 * 5 + 4)/5 = −(120 + 4)/5 = −124/5
Converting 6 7/10 to an improper fraction, we get:
6 7/10 = (6 * 10 + 7)/10 = (60 + 7)/10 = 67/10
Now we can add the fractions together:
−124/5 + 67/10
To add these fractions, we first need to find a common denominator. The least common multiple of 5 and 10 is 10.
Converting −124/5 to an equivalent fraction with a denominator of 10, we multiply the numerator and denominator by 2:
−124/5 = −(124 * 2)/(5 * 2) = −248/10
Now we can add the fractions together:
−248/10 + 67/10 = (−248 + 67)/10 = −181/10
Therefore, the sum of −24 4/5 and −6 7/10 using the additive inverse is −181/10.
Use the additive inverse to find −24 4/5 − 6 7/10
To find the sum of the given numbers 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). Write the result over the denominator.
−24 4/5 = (−24 × 5 + 4)/5 = (-120 + 4)/5 = -116/5
To convert −6 7/10 to an improper fraction, multiply the whole number (-6) by the denominator (10) and add the numerator (7). Write the result over the denominator.
−6 7/10 = (−6 × 10 + 7)/10 = (-60 + 7)/10 = -53/10
Step 2: Apply the additive inverse.
Add the inverse of -53/10 to -116/5.
The additive inverse of a fraction a/b is -a/b.
So, the inverse of -53/10 is 53/10.
-116/5 + 53/10 = (-116 × 2)/10 + 53/10 = (-232 + 53)/10 = -179/10
Step 3: Simplify the fraction.
The resulting fraction -179/10 cannot be simplified further.
Therefore, the sum of −24 4/5 and −6 7/10 using the additive inverse is -179/10.
To find the solution to the expression −24 4/5 − 6 7/10 using the additive inverse, you can follow these steps:
Step 1: Convert both mixed numbers to improper fractions.
−24 4/5 = −(24 × 5 + 4)/5 = −(120 + 4)/5 = −124/5
−6 7/10 = −(6 × 10 + 7)/10 = −(60 + 7)/10 = −67/10
Step 2: Find the additive inverse of the second fraction, which means changing its sign.
Additive inverse of −67/10 = 67/10
Step 3: Rewrite the subtraction as addition with the additive inverse.
−124/5 + 67/10
Step 4: Obtain a common denominator for both fractions.
The least common multiple of 5 and 10 is 10. You can multiply the numerator and denominator of the first fraction by 2 to get a common denominator of 10.
−124/5 × 2/2 = −248/10
Step 5: Add the fractions together.
−248/10 + 67/10 = (−248 + 67)/10 = -181/10
Therefore, the solution to the expression −24 4/5 − 6 7/10 is -181/10 or -18 1/10.