1/2 * 4/3 + 5/6 / 7 / 8
To simplify the expression:
1/2 * 4/3 + 5/6 ÷ 7 ÷ 8
First, let's deal with the division operation:
5/6 ÷ 7 ÷ 8
To divide fractions, you multiply by the reciprocal of the divisor.
5/6 ÷ 7 ÷ 8 = 5/6 * 1/7 * 1/8
Now, let's simplify the multiplication:
5/6 * 1/7 * 1/8 = (5 * 1 * 1) / (6 * 7 * 8)
= 5 / 336
Now, we can substitute this value back into the original expression:
1/2 * 4/3 + 5/336
To add fractions, we need a common denominator. In this case, the common denominator is 2 * 3 = 6.
1/2 * 4/3 + 5/336 = (1 * 3) / (2 * 3) * 4/3 + 5/336
= 3/6 * 4/3 + 5/336
= 12/18 + 5/336
Now, we can find a common denominator for the two fractions and add them:
12/18 + 5/336 = (12 * 336) / (18 * 336) + 5/336
= 4032/6048 + 5/336
= (4032 + 5 * 18) / 6048
= (4032 + 90) / 6048
= 4122/6048
Since the numerator and denominator have no common factors other than 2, we can simplify further:
4122/6048 = (2 * 2061) / (3 * 2016)
= 2061/1008
So, the simplified form of the expression is 2061/1008.