What is −6 7/12 − 4 1/3?
To subtract mixed numbers, you need to convert them into improper fractions.
-6 7/12 is equal to -79/12.
-4 1/3 is equal to -13/3.
Now, subtracting the fractions:
-79/12 - 13/3 = (-79/12) * (3/3) - (13/3) * (12/12)
= -237/36 - 156/36 = -393/36
The answer is -393/36. However, we can simplify this fraction. The greatest common divisor (GCD) of 393 and 36 is 9. By dividing both the numerator and the denominator by 9, we obtain the simplified fraction.
(-393/9) / (36/9) = -43/4
Therefore, -6 7/12 - 4 1/3 is equal to -43/4.
What is 12 8/15 − 7 + 71/5 + 15? Simplify your answer.
To subtract mixed numbers, follow these steps:
Step 1: Rewrite the mixed numbers as improper fractions.
Step 2: Find a common denominator.
Step 3: Subtract the fractions.
Step 4: Simplify the result, if possible.
Let's solve the given problem:
Step 1:
−6 7/12 can be written as -((6 x 12) + 7)/12 = - 79/12
−4 1/3 can be written as -((4 x 3) + 1)/3 = - 13/3
Step 2: The common denominator for 12 and 3 is 12.
Step 3:
- 79/12 - 13/3
To subtract the fractions, we need both fractions to have a common denominator of 12. We can multiply the first fraction by 1 (in the form of 4/4) and the second fraction by 4 (in the form of 4/4):
- (79/12) - (13/3) * (4/4)
= - (79/12) - (52/12)
= - (79/12) - (52/12)
= - (131/12)
Step 4: The result, - (131/12), cannot be simplified further.
To subtract mixed numbers like −6 7/12 and 4 1/3, follow these steps:
Step 1: Convert the mixed numbers into improper fractions.
- −6 7/12 is equal to (-6 × 12 + 7)/12 = (-72 + 7)/12 = -79/12.
- 4 1/3 is equal to (4 × 3 + 1)/3 = (12 + 1)/3 = 13/3.
Step 2: Find a common denominator.
To subtract fractions, we need to ensure they have the same denominator. The least common multiple (LCM) of 12 and 3 is 12. Therefore, we need to convert both fractions to have a denominator of 12.
- -79/12 remains as -79/12.
- 13/3 can be converted to (13/3) × (4/4) = 52/12.
Step 3: Subtract the fractions.
Now, we can subtract the two fractions:
-79/12 - 52/12 = (-79 - 52)/12 = -131/12.
Step 4: Simplify (if needed).
The result -131/12 is already in its simplest form and cannot be further simplified.
Therefore, the value of −6 7/12 − 4 1/3 is -131/12.