Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 5.6 yd to 4.9 yd
The correct answer and explanation is:
To express the ratio of 5.6 yards to 4.9 yards as a fraction in its simplest form, we first write it as: 5.64.9\frac{5.6}{4.9}
Next, we eliminate the decimals by multiplying both the numerator and the denominator by 10. This step is done to turn the decimals into whole numbers: 5.6×104.9×10=5649\frac{5.6 \times 10}{4.9 \times 10} = \frac{56}{49}
Now we simplify the fraction 5649\frac{56}{49}. To do so, we find the greatest common divisor (GCD) of 56 and 49. The GCD of 56 and 49 is 7 because 7 is the largest number that divides both 56 and 49 without leaving a remainder.
We divide both the numerator and the denominator by 7: 56÷749÷7=87\frac{56 \div 7}{49 \div 7} = \frac{8}{7}
Thus, the ratio of 5.6 yards to 4.9 yards, simplified as a fraction, is: 87\frac{8}{7}
Explanation:
The ratio 5.64.9\frac{5.6}{4.9} starts with decimal numbers. To simplify it, we first remove the decimals by multiplying both the numerator and denominator by 10, which gives us 56 and 49. After that, we simplify the fraction by dividing both numbers by their GCD, which is 7. This results in the simplified ratio of 87\frac{8}{7}.
When working with ratios, converting decimals to whole numbers makes it easier to simplify, and finding the GCD helps reduce the fraction to its simplest form.