Perform the indicated operation and, if possible, simplify. Please show all of your work. Write your final answer exactly as a fraction in lowest terms.
14/45 / 26/27
14/45 / 26/27
(14/45) * (27/26) = 378/1215 = 126/405 = 42/135
14/45 /(26/27)=14*27/(45*26)=378/1170=x
x/(18/18)=21/65
3/4 times 11/9 times 90 times 21/90
To divide fractions, you can use the following steps:
Step 1: Keep the first fraction as it is.
Step 2: Flip the second fraction (find its reciprocal) by swapping the numerator and denominator.
Step 3: Multiply the two fractions.
Let's apply these steps to the given problem:
Step 1: Keep the first fraction as it is: 14/45.
Step 2: Flip the second fraction: 26/27 becomes 27/26.
Step 3: Multiply the two fractions: (14/45) * (27/26).
To multiply the fractions, you just need to multiply the numerators together and the denominators together:
Numerator: 14 * 27 = 378.
Denominator: 45 * 26 = 1170.
So, the result of the multiplication is 378/1170.
Now, we need to simplify the fraction to its lowest terms. To do this, we can divide both the numerator and denominator by their greatest common divisor (GCD).
The GCD of 378 and 1170 is 54. By dividing both the numerator and denominator by 54, we can simplify the fraction:
378 ÷ 54 = 7
1170 ÷ 54 = 65
Therefore, the simplified fraction is 7/65.
Final Answer: 14/45 ÷ 26/27 = 7/65.