What fraction must be subtracted from the sum of 2 1/6 and 2 7/12 to give 3 1/4?
To solve this problem, we need to find the fraction that must be subtracted from the sum of 2 1/6 and 2 7/12 to give 3 1/4.
First, we convert all the mixed numbers into improper fractions:
2 1/6 = 12/6 + 1/6 = 13/6
2 7/12 = 24/12 + 7/12 = 31/12
3 1/4 = 12/4 + 1/4 = 13/4
Next, we find the sum of 13/6 and 31/12:
13/6 + 31/12 = (2*13 + 1*31)/(2*6) = 113/12.
Finally, we find the fraction that must be subtracted from 113/12 to give 13/4:
113/12 - x/12 = 13/4
Multiplying both sides of the equation by 12 to get rid of the denominator, we have:
113 - x = 39
Subtracting 113 from both sides, we have:
-x = -74
Dividing both sides by -1, we have:
x = 74.
Therefore, the fraction that must be subtracted from the sum of 2 1/6 and 2 7/12 to give 3 1/4 is 74/12 or 37/6.
To solve this problem, we need to find the fraction that must be subtracted from the sum of 2 1/6 and 2 7/12 to give 3 1/4.
First, let's convert all the mixed numbers to improper fractions:
2 1/6 = (2 × 6 + 1) / 6 = 13/6
2 7/12 = (2 × 12 + 7) / 12 = 31/12
3 1/4 = (3 × 4 + 1) / 4 = 13/4
Now, we can find the sum of 13/6 and 31/12:
13/6 + 31/12 = (13 × 2 + 31) / 12 = 57/12
To find the fraction that must be subtracted to obtain 13/4, we subtract 13/4 from 57/12:
57/12 - 13/4 = (57 × 1 - 13 × 3) / 12 = (57 - 39) / 12 = 18/12 = 3/2
Therefore, the fraction that must be subtracted from the sum of 2 1/6 and 2 7/12 to give 3 1/4 is 3/2.
To find the fraction that must be subtracted from the sum of 2 1/6 and 2 7/12 to give 3 1/4, we need to subtract the sum of 2 1/6 and 2 7/12 from 3 1/4. Here's how:
Step 1: Find a common denominator for all the fractions involved. The least common denominator (LCD) for 6, 12, and 4 is 12.
Step 2: Convert all the fractions to have a denominator of 12.
- 2 1/6 can be converted to an improper fraction as (2 * 6 + 1) / 6 = 13/6. Multiplying the numerator and denominator by 2 gives us 26/12.
- 2 7/12 remains the same.
Step 3: Add 26/12 and 2 7/12 together.
26/12 + 2 7/12 = (26 + 2 * 12 + 7) / 12 = (26 + 24 + 7) / 12 = 57/12
Step 4: Subtract the sum of the converted fractions, which is 57/12, from 3 1/4.
3 1/4 can be converted to an improper fraction as (3 * 4 + 1) / 4 = 13/4. Multiplying the numerator by 3 gives us 39/12.
39/12 - 57/12 = (39 - 57) / 12 = -18/12
Therefore, the fraction that must be subtracted from the sum of 2 1/6 and 2 7/12 to give 3 1/4 is -18/12.