To solve the given expression:
5((4)/(7))/1((5)/(21))-(5((2)/(15))*((3)/(22))+1((14)/(15)))
First, simplify the division:
= 5 ((4)/(7)) / 1 ((5)/(21)) - (5 ((2)/(15)) ((3)/(22)) + 1 * ((14)/(15)))
= 5 (4/7) / (5/21) - (5 (2/15) * (3/22) + 14/15)
Next, evaluate each part:
= 20/7 / 5/21 - ((10/15) * (3/22) + 14/15)
= 20/7 / 5/21 - (2/3 * 3/22 + 14/15)
= 20/7 * 21/5 - (2/22 + 14/15)
= 420/35 - (1/11 + 14/15)
= 12 - (1/11 + 14/15)
Now, find a common denominator for the fractions:
= 12 - ((15/15) (1/11) + (11/11) (14/15))
= 12 - (15/165 + 14/165)
= 12 - 29/165
= 12 * 165/165 - 29/165
= 1980/165 - 29/165
Combine the fractions:
= (1980 - 29) / 165
= 1951/165
Therefore, the final answer is 1951/165.
To solve the given expression:
5((4)/(7))/1((5)/(21))-(5((2)/(15))*((3)/(22))+1((14)/(15)))
First, simplify the division:
= 5 ((4)/(7)) / 1 ((5)/(21)) - (5 ((2)/(15)) ((3)/(22)) + 1 * ((14)/(15)))
= 5 (4/7) / (5/21) - (5 (2/15) * (3/22) + 14/15)
Next, evaluate each part:
= 20/7 / 5/21 - ((10/15) * (3/22) + 14/15)
= 20/7 / 5/21 - (2/3 * 3/22 + 14/15)
= 20/7 * 21/5 - (2/22 + 14/15)
= 420/35 - (1/11 + 14/15)
= 12 - (1/11 + 14/15)
Now, find a common denominator for the fractions:
= 12 - ((15/15) (1/11) + (11/11) (14/15))
= 12 - (15/165 + 14/165)
= 12 - 29/165
= 12 * 165/165 - 29/165
= 1980/165 - 29/165
Combine the fractions:
= (1980 - 29) / 165
= 1951/165
Therefore, the final answer is 1951/165.