- 5/6 - 7/8
To subtract fractions, you need to have a common denominator. The common denominator for 6 and 8 is 24.
Step 1: Convert both fractions to have a denominator of 24.
- For the first fraction, multiply the numerator and denominator by 4 to get 20/24.
- For the second fraction, multiply the numerator and denominator by 3 to get 21/24.
Step 2: Subtract the numerators.
20/24 - 21/24 = -1/24
So, the result of subtracting 5/6 from 7/8 is -1/24.
To solve the subtraction of fractions 5/6 - 7/8, we need to have a common denominator. The least common multiple of 6 and 8 is 24, so we will convert both fractions to have a denominator of 24.
Thus, the equivalent fraction for 5/6 with a denominator of 24 is (5/6) * (4/4) = 20/24.
Similarly, the equivalent fraction for 7/8 with a denominator of 24 is (7/8) * (3/3) = 21/24.
Now, we can subtract the fractions: 20/24 - 21/24 = (-1/24).
Therefore, 5/6 - 7/8 equals -1/24.
To evaluate the expression - 5/6 - 7/8, you need to subtract the second fraction from the first fraction. Here's how you can do it:
Step 1: Find a common denominator for both fractions.
The denominators are 6 and 8. To find a common denominator, you need to find the least common multiple (LCM) of 6 and 8, which is 24.
Step 2: Convert the fractions to have the same denominator.
To convert the first fraction, multiply both the numerator and denominator by the same number that makes the denominator 24. In this case, you need to multiply by 4, so you get: - (5/6) x (4/4) = -20/24.
To convert the second fraction, multiply both the numerator and denominator by the same number that makes the denominator 24. In this case, you need to multiply by 3, so you get: (7/8) x (3/3) = 21/24.
Step 3: Subtract the fractions.
Now that both fractions have the same denominator, you can subtract them. When subtracting fractions, subtract the numerators and keep the denominator the same. So, -20/24 - 21/24 = (-20 - 21)/24 = -41/24.
Therefore, the value of -5/6 - 7/8 is -41/24.
-7/8k = - 21
To solve the equation -7/8k = -21, you can begin by isolating the variable k.
Step 1: Multiply both sides of the equation by (8/7) to eliminate the fraction on the left side.
(-7/8k) * (8/7) = (-21) * (8/7)
-k = -24
Step 2: Multiply both sides of the equation by -1 to isolate the variable k by itself.
k = 24
Therefore, the solution to the equation -7/8k = -21 is k = 24.
2 3/4 + 5/6
To add mixed numbers with fractions, you need to convert the mixed number to an improper fraction and then find a common denominator. Here's how you can solve 2 3/4 + 5/6:
Step 1: Convert the mixed number 2 3/4 to an improper fraction.
To convert 2 3/4 to an improper fraction, multiply the whole number (2) by the denominator (4) and add the numerator (3). Then, put the result over the denominator.
2 * 4 = 8
8 + 3 = 11
So, 2 3/4 as an improper fraction is 11/4.
Step 2: Find a common denominator for 11/4 and 5/6.
The denominators are 4 and 6. To find a common denominator, you need to find the least common multiple (LCM) of 4 and 6, which is 12.
Step 3: Convert both fractions to have a denominator of 12.
To convert 11/4 to a fraction with a denominator of 12, multiply both the numerator and denominator by 3. You get (11/4) * (3/3) = 33/12.
To convert 5/6 to a fraction with a denominator of 12, multiply both the numerator and denominator by 2. You get (5/6) * (2/2) = 10/12.
Now, you have 33/12 + 10/12.
Step 4: Add the fractions.
To add fractions, add the numerators and keep the denominator the same. So, 33/12 + 10/12 = 43/12.
Step 5: Simplify if necessary.
If possible, simplify the fraction. In this case, 43/12 cannot be simplified any further.
Therefore, the sum of 2 3/4 and 5/6 is 43/12.
5/6 x 2/3
To multiply fractions, you simply multiply the numerators together, and then multiply the denominators together. Here's how you can solve 5/6 x 2/3:
5/6 x 2/3 = (5 x 2) / (6 x 3) = 10/18
However, it is often preferable to simplify the resulting fraction. In this case, both 10 and 18 have a common factor of 2. Dividing both the numerator and denominator by 2, we get:
10/18 = (10 ÷ 2) / (18 ÷ 2) = 5/9
So, 5/6 x 2/3 simplifies to 5/9.