7 2/3 - 1 1/2 of 3 1/3 * 3/4
= 23/3 - 3/2 x 10/3 * 3/4
= 10/3 * 3/4 = 10/3x4/3 = 10x4 / 3x3 = 40/9
= 23/3 - 3/2 = 37/6 = 6 1/6 ANSWER :
6 1/6
To solve the expression 7 2/3 - 1 1/2 of 3 1/3 * 3/4, you first need to simplify the mixed numbers by converting them into improper fractions.
Taking 7 2/3 as an example:
7 can be written as 21/3 since 7 divided by 1 is 7.
Adding this to 2/3 gives us a total of 23/3.
Similarly, 1 1/2 can be converted to 3/2.
Next, simplify 3 1/3:
3 can be written as 9/3 since 3 divided by 1 is 3.
Adding this to 1/3 gives us a total of 10/3.
Now, let's substitute these values into the expression: 23/3 - 3/2 of 10/3 * 3/4.
To simplify mixed numbers, we need to multiply the whole number by the denominator and add the numerator. We then place the total over the denominator.
For 23/3 - 3/2:
The common denominator is 6.
Multiplying 23/3 by 2/2 gives us 46/6.
Multiplying 3/2 by 3/3 gives us 9/6.
Subtracting 9/6 from 46/6 gives us 37/6.
Now, let's simplify 10/3 * 3/4:
To multiply fractions, simply multiply the numerators together and the denominators together.
Multiplying 10/3 by 3/4 gives us (10 * 3) / (3 * 4) = 30/12.
Finally, we can substitute the simplified values back into the original expression:
37/6 - 30/12.
To subtract fractions with different denominators, we need to find a common denominator.
In this case, the common denominator is 12. Since both fractions have denominators that are multiples of 12, we don't need to convert anything.
Subtracting 30/12 from 37/6:
Multiplying 37/6 by 2/2 gives us 74/12.
Subtracting 30/12 from 74/12 gives us 44/12.
Simplifying this fraction by dividing both the numerator and denominator by their greatest common divisor (which is 4), we get 11/3.
To express this improper fraction as a mixed number, we divide the numerator (11) by the denominator (3).
The whole number part is the result of this division (3 in this case), and the remainder becomes the numerator of the fractional part (2 in this case).
So, the answer is 3 2/3.
Therefore, the final answer to the original expression 7 2/3 - 1 1/2 of 3 1/3 * 3/4 is 3 2/3 or 6 1/6.