Write 4L: 5.6L as a fraction in simplest form with whole numbers in the numerator and denominator.
The correct answer and explanation is:
To express the ratio 4L: 5.6L as a fraction in simplest form, the first step is to convert both the numerator and the denominator into whole numbers. The given ratio is 4L to 5.6L, so to eliminate the decimal in the denominator, we multiply both the numerator and the denominator by 10.
Starting with the ratio: 45.6\frac{4}{5.6}
Now, multiply both parts by 10: 4×105.6×10=4056\frac{4 \times 10}{5.6 \times 10} = \frac{40}{56}
At this stage, the fraction is 4056\frac{40}{56}, but this can be simplified further. To simplify the fraction, we find the greatest common divisor (GCD) of 40 and 56. The GCD of 40 and 56 is 8. Now, divide both the numerator and the denominator by 8: 40÷856÷8=57\frac{40 \div 8}{56 \div 8} = \frac{5}{7}
Thus, the ratio 4L: 5.6L simplifies to the fraction 57\frac{5}{7} in its simplest form.
Explanation:
To simplify a ratio like 4L: 5.6L, the key steps involve eliminating decimals and simplifying the resulting fraction. First, convert the decimal into a whole number by multiplying both the numerator and denominator by 10. After that, you simplify the fraction by finding the GCD of the numerator and denominator and dividing both by that GCD. In this case, the fraction simplifies to 57\frac{5}{7}, which is the simplest form of the ratio. This fraction now represents the original ratio in its most reduced form.