Use the additive inverse to find −24 4/5 − 6 7/10.
−31110
negative 31 Start Fraction 1 over 10 End Fraction
−18110
negative 18 Start Fraction 1 over 10 End Fraction
−3112
negative 31 Start Fraction 1 over 2 End Fraction
3112
−24 4/5 − 6 7/10 = -24 4/5 + (-6 7/10)
To find the sum of mixed numbers with different denominators, we first need to find a common denominator. In this case, the common denominator is 10.
Converting -24 4/5 into an improper fraction:
-24 4/5 = (-24 * 5 + 4) / 5 = (-120 + 4) / 5 = -116/5
Converting -6 7/10 into an improper fraction:
-6 7/10 = (-6 * 10 + 7) / 10 = (-60 + 7) / 10 = -53/10
Now, we can add the two fractions:
-116/5 + (-53/10)
To find the sum of fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 10.
-116/5 * 2/2 = -232/10
-232/10 + (-53/10) = -285/10
Converting the improper fraction -285/10 back into a mixed number:
-285/10 = -28 remainder 5 = -28 5/10 = -28 1/2
Therefore, −24 4/5 − 6 7/10 = -28 1/2.
To find the sum using the additive inverse method, you need to change the signs of each term and then add them.
−24 4/5 becomes -24 4/5
−6 7/10 becomes -6 7/10
Now let's add these two numbers:
-24 4/5 + (-6 7/10)
Start by adding the whole numbers: -24 + -6 = -30.
Next, add the fractions. The fractions have different denominators, so we need to find a common denominator. In this case, the least common multiple of 5 and 10 is 10. So, convert the fractions to have a denominator of 10:
4/5 becomes 8/10
7/10 remains the same
Now we can add the fractions: 8/10 + 7/10 = 15/10.
So, the sum is -30 + 15/10.
To simplify 15/10, divide the numerator and the denominator by their greatest common divisor, which is 5:
15 ÷ 5 = 3
10 ÷ 5 = 2
Therefore, the simplified fraction is 3/2.
The final answer is -30 + 3/2, or -30 1/2.