Final answer:
By following the order of operations and converting mixed numbers to fractions, we can find the value of 'a' to be 35/112.
Step-by-step explanation:
To solve the given expression 2 1/7 : (1.5a) = 5/14 : 0.8, we need to follow the order of operations and simplify each side of the equation.
Step 1: Simplify the left side of the equation.
The mixed number 2 1/7 can be converted to an improper fraction as (2 * 7 + 1)/7 = 15/7.
The expression becomes 15/7 : (1.5a).
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
15/7 : (1.5a) = 15/7 * 1/(1.5a) = 15/7 * 1/(3/2a) = 15/7 * 2a/3 = (15 * 2a)/(7 * 3) = 30a/21 = 10a/7.
Step 2: Simplify the right side of the equation.
5/14 : 0.8 = 5/14 * 1/0.8 = 5/14 * 1.25 = (5 * 1.25)/14 = 6.25/14 = 25/56.
So, the equation becomes 10a/7 = 25/56.
To solve for 'a', we multiply both sides of the equation by 7.
7 * (10a/7) = 7 * (25/56).
10a = 25/56 * 7 = 25 * 7/56 = 175/56.
Finally, we divide both sides of the equation by 10 to isolate 'a'.
a = (175/56) / 10 = 175/560 = 35/112.