Write the ratio; 0.43 to 0.86 as fraction in lowest terms
The Correct Answer and Explanation is:
To express the ratio 0.43 to 0.86 as a fraction in its lowest terms, follow these steps:
- Write the ratio as a fraction:
The ratio 0.43 to 0.86 can be written as: 0.430.86\frac{0.43}{0.86}0.860.43 - Remove the decimals:
To eliminate the decimals, multiply both the numerator and denominator by 100. This will shift the decimal points two places to the right: 0.43×1000.86×100=4386\frac{0.43 \times 100}{0.86 \times 100} = \frac{43}{86}0.86×1000.43×100=8643 - Simplify the fraction:
Now, simplify the fraction 4386\frac{43}{86}8643. To do this, find the greatest common divisor (GCD) of 43 and 86. Since 43 is a prime number, the only divisors of 43 are 1 and 43. Check if 43 divides 86: 86÷43=286 \div 43 = 286÷43=2 Therefore, 43 divides 86 exactly. - Divide both the numerator and denominator by 43:
Now, divide both the numerator and denominator by 43 to simplify the fraction: 4386=43÷4386÷43=12\frac{43}{86} = \frac{43 \div 43}{86 \div 43} = \frac{1}{2}8643=86÷4343÷43=21
So, the ratio of 0.43 to 0.86 in its lowest terms is 12\frac{1}{2}21.
Explanation:
A ratio expresses a relationship between two quantities. To convert a ratio to a fraction, you can treat it as a fraction where the first quantity is the numerator and the second quantity is the denominator. In this case, 0.43 is the first quantity (numerator) and 0.86 is the second (denominator). By multiplying both the numerator and the denominator by 100, we convert the decimals to whole numbers, making it easier to simplify. Simplifying the fraction involves finding the greatest common divisor of the numerator and denominator and dividing both by that divisor. In this example, the GCD of 43 and 86 is 43, so we divide both terms by 43, yielding the simplified fraction 12\frac{1}{2}21.
