Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 9.2 to 2.3
The correct answer and explanation is:
To convert the ratio of 9.2 to 2.3 into a fraction in simplest form, start by expressing both numbers as fractions. The ratio can be written as: 9.22.3\frac{9.2}{2.3}
To eliminate the decimals, multiply both the numerator and denominator by 10. This will shift the decimal point one place to the right for both numbers: 9.2×102.3×10=9223\frac{9.2 \times 10}{2.3 \times 10} = \frac{92}{23}
Now, simplify the fraction by finding the greatest common divisor (GCD) of 92 and 23. Since 23 is a factor of 92 (because 92 ÷ 23 = 4), divide both the numerator and the denominator by 23: 9223=92÷2323÷23=41\frac{92}{23} = \frac{92 ÷ 23}{23 ÷ 23} = \frac{4}{1}
Thus, the simplified fraction is: 41\frac{4}{1}
This means the ratio of 9.2 to 2.3 in simplest form is 4:1 or simply 4.
Explanation: The steps followed are:
- Convert the ratio to a fraction by dividing 9.2 by 2.3.
- Eliminate the decimals by multiplying both terms by 10.
- Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 23.
- The simplified result is 4, meaning the ratio is 4:1.
The process is straightforward, focusing on eliminating decimals and simplifying the resulting fraction.