Question

5 4/7 : 15/21 - (5 2/22 * 3/22 + 1 14/15)

Answer 1

5 4/7:15/21-(5 2/22*3/22+1 14/15)=9388/1815

Answer 2

To simplify the expression:

5 4/7 : 15/21 - (5 2/22 * 3/22 + 1 14/15)

Let's break it down step by step:

1. Convert mixed numbers to improper fractions:

   5 4/7 = (7 * 5 + 4) / 7 = 35/7 + 4/7 = 39/7

   1 14/15 = (15 * 1 + 14) / 15 = 15/15 + 14/15 = 29/15

2. Now, rewrite the expression:

   (39/7) : (15/21) - ((39/7) * (3/22) + (29/15))

3. Simplify the fractions in the expression:

   (39/7) : (5/7) - ((39/7) * (3/22) + (29/15))

4. To divide fractions, you can multiply by the reciprocal of the second fraction:

   (39/7) * (7/5) - ((39/7) * (3/22) + (29/15))

5. Multiply the fractions:

   (39/5) - ((39/7) * (3/22) + (29/15))

6. Now, multiply the fractions in the parentheses:

   (39/5) - ((39 * 3) / (7 * 22) + (29/15))

   (39/5) - (117 / 154 + 29/15)

7. To add fractions, they need a common denominator. In this case, the least common multiple of 154 and 15 is 2310. So, we'll adjust the fractions accordingly:

   (39/5) - ((117 * 15) / (154 * 15) + (29 * 154) / (15 * 154))

   (39/5) - (1755/2310 + 4456/2310)

8. Now, add the fractions:

   (39/5) - ((1755 + 4456) / 2310)

   (39/5) - (6211/2310)

9. Find a common denominator for subtraction:

   (39/5) * (462/462) - (6211/2310)

   (1848/230) - (6211/2310)

10. To subtract fractions, they need a common denominator, which is 2310:

    (1848/230) - (6211/2310)

11. Now, subtract the fractions:

    [(1848 * 2310) - (6211 * 230)] / (230 * 2310)

12. Calculate the numerator:

    (4278480 - 1428430) / (529800)

13. Subtract the numerators:

    2850050 / 529800

14. Simplify the fraction if possible:

    57001 / 105960

So, the simplified result is:

57001 / 105960

This fraction cannot be simplified further.