Estimate the sum or difference 2 9/8 - 2 1/7
A. 2
b. 1
c. 0
I think the answer is 1 so far.
2 9/8 is about 3
2 1/7 is about 2
3 - 2 = 1
To estimate the sum or difference of 2 9/8 - 2 1/7, we need to first convert the mixed numbers to improper fractions.
2 9/8 = (2 * 8 + 9)/8 = 25/8
2 1/7 = (2 * 7 + 1)/7 = 15/7
Now, we can subtract the two fractions:
25/8 - 15/7
Before we can subtract, we need to find a common denominator. The least common multiple of 8 and 7 is 56. Therefore, we can rewrite the fractions with the common denominator:
(25/8)(7/7) - (15/7)(8/8)
= 175/56 - 120/56
Now, we can subtract the fractions:
175/56 - 120/56
= (175 - 120)/56
= 55/56
So, the estimated difference of 2 9/8 - 2 1/7 is 55/56.
Therefore, none of the options A, B, or C (2, 1, 0) are correct.
To estimate the sum or difference of fractions, you can follow these steps:
Step 1: Convert the mixed numbers to improper fractions.
To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. The result becomes the new numerator, and the denominator stays the same.
For example:
2 9/8 = (2 * 8 + 9) / 8 = 25/8
2 1/7 = (2 * 7 + 1) / 7 = 15/7
Step 2: Find a common denominator.
To add or subtract fractions, they need to have the same denominator. Find a common denominator by multiplying the two denominators together.
In this case, the denominators are 8 and 7. The common denominator is 8 * 7 = 56.
Step 3: Adjust the fractions.
Multiply the numerator and denominator of each fraction by the same value such that the denominators become the common denominator found in Step 2.
For 25/8, multiply the numerator and denominator by 7:
(25 * 7) / (8 * 7) = 175/56
For 15/7, multiply the numerator and denominator by 8:
(15 * 8) / (7 * 8) = 120/56
Step 4: Perform the calculation.
Now that the fractions have the same denominator, you can find the sum or difference.
For the difference, subtract the numerators: 175/56 - 120/56 = 55/56
So, the estimated difference for 2 9/8 - 2 1/7 is 55/56.
None of the provided options (A, B, C) match the answer.