Question

11 3/14−(2−1 11/35):9/25+4/21 .​

Answer 1

11 3/14 - (2 - 1 11/35) : 9/25 + 4/21 = 9 20/21

1) 2 - 1 11/35 = 1 35/35 - 1 11/35 = 24/35

2) 24/35 : 9/25 = 24/35 · 25/9 = (8·5)/(7·3) = 40/21 = 1 19/21

3) 11 3/14 - 1 19/21 = 11 9/42 - 1 19/42 = 10 51/42 - 1 19/42 = 9 32/42 = 9 16/21

4) 9 16/21 + 4/21 = 9 20/21

Answer 2

To solve the expression, let's break it down step by step:

1. Convert mixed numbers to improper fractions: 3/14 = (14 * 0 + 3) / 14 = 3/14 1 11/35 = (35 * 1 + 11) / 35 = 46/35

2. Subtract the second fraction from the first: 3/14 - (2 - 46/35)

3. Perform the subtraction inside the parentheses: 2 - 46/35 = (70 * 2 + 35 - 46) / 35 = 49/35

4. Substitute the result back into the expression: 3/14 - 49/35

5. Find a common denominator for the two fractions, which is 70, as it's the least common multiple of 14 and 35.

6. Convert the fractions to have the same denominator: 3/14 = (14 * 0 + 3) / 14 = 3/14 49/35 = (35 * 1 + 14) / 35 = 49/35

7. Now, the expression becomes: (3/14 * 5/5) - (49/35 * 2/2) = 15/70 - 98/70

8. Combine the fractions: 15/70 - 98/70 = (15 - 98) / 70 = -83/70

Next part of the expression:

9. Add the fractions: 9/25 + 4/21

10. Find a common denominator for the two fractions, which is 525, as it's the least common multiple of 25 and 21.

11. Convert the fractions to have the same denominator: 9/25 = (25 * 0 + 9) / 25 = 9/25 4/21 = (21 * 0 + 4) / 21 = 4/21

12. Now, the expression becomes: (9/25 * 21/21) + (4/21 * 25/25) = 189/525 + 100/525

13. Combine the fractions: 189/525 + 100/525 = (189 + 100) / 525 = 289/525

Now, the final expression is the sum of the results from the two parts:

-83/70 + 289/525

To add these fractions, find a common denominator, which is 525 (the same as in the second part):

-83/70 = (70 * -1 + 13) / 70 = -83/70

Now, the expression becomes:

-83/70 + 289/525

To add the fractions, convert them to have the same denominator:

-83/70 * 75/75 = -6225/525 289/525

Now, the expression becomes:

-6225/525 + 289/525

Finally, add the fractions:

(-6225 + 289) / 525 = -5936/525

The simplified result of the expression is:

-5936/525, which can be further reduced to -64/5.