Final answer:
To simplify the expression (75.73 - 7 2/720), convert both the decimal and the mixed number to fractions with a common denominator, subtract them, and simplify the result. If a calculator is used, the approximate simplified expression is 68.84.
Step-by-step explanation:
To simplify the expression: (75.73 - 7 2/720), we first need to convert the mixed number to an improper fraction.
The integer part is 7, and the fractional part is 2/720, so the entire mixed number can be written as 7 + 2/720.
To convert 7 to a fraction with the same denominator as 2/720, we multiply it by 720/720, obtaining 5040/720.
Adding the fractional part, we get 5042/720. Now the expression looks like this: 75.73 - 5042/720.
We need to convert 75.73 to a fraction with the same denominator to proceed with the subtraction. Since there are two decimal places, we can write it as 7573/100.
To get both fractions to have the same denominator, we must find a common denominator which would be the least common multiple (LCM) of 100 and 720.
The LCM of 100 and 720 is 7200, so we multiply the numerator and denominator of 7573/100 by 72, which gives us 545256/7200. Therefore, 75.73 can be rewritten as 545256/7200.
We now subtract the two fractions with a common denominator: 545256/7200 - 5042/720 = (545256 - 5042*10)/7200 = 545,256 - 50420/7200 = 494,836/7200.
This expression can be simplified by dividing both numerator and denominator by the greatest common divisor (GCD).
Without a calculator, we may not have the exact GCD, but we can simplify the fraction as needed for the context.
If we're allowed to use a calculator for this last part, we find that the simplified term is close to but not exactly 68.84, since 494,836/7200 ≈ 68.84. Note that this is an approximation as we are rounding to two decimal places.