“Reduce Fractions to lowest terms” 6 divided by 3.66
The Correct Answer and Explanation is:
Correct Answer:
To reduce the fraction 6 ÷ 3.66 to its lowest terms, first convert it into a fraction:63.66\frac{6}{3.66}3.666
Now multiply both the numerator and denominator by 100 to eliminate the decimal:6×1003.66×100=600366\frac{6 \times 100}{3.66 \times 100} = \frac{600}{366}3.66×1006×100=366600
Now reduce this fraction by dividing both numerator and denominator by their greatest common divisor (GCD). The GCD of 600 and 366 is 6.600÷6366÷6=10061\frac{600 \div 6}{366 \div 6} = \frac{100}{61}366÷6600÷6=61100
So, the reduced fraction is:10061\boxed{\frac{100}{61}}61100
Explanation (Like in the Books):
Reducing fractions to their lowest terms means simplifying a fraction so that the numerator and denominator share no common factor other than 1. This makes the fraction easier to understand and work with, especially when comparing or performing arithmetic operations.
The first step is to recognize that dividing one number by another can be written as a fraction. So, the expression 6 ÷ 3.66 becomes the fraction 6/3.66. Since the denominator contains a decimal, it is best to eliminate the decimal by multiplying both numerator and denominator by a power of 10. In this case, multiplying both by 100 gives 600/366.
The next step is to simplify. To do that, we must find the greatest common divisor (GCD) of the two numbers. The GCD is the largest number that divides both the numerator and the denominator evenly. For 600 and 366, the GCD is 6.
Now divide both parts of the fraction by 6:
- 600 ÷ 6 = 100
- 366 ÷ 6 = 61
This gives the simplified form 100/61, which is already in its lowest terms because 100 and 61 have no common factors other than 1.
Reducing fractions helps in achieving clarity and accuracy in mathematical calculations and ensures consistency when comparing values or computing further.
