Write the ratio 2.5 to 3.15 as a fraction in simplest form
the ratio 2.5 to 3.15
= 250 : 315
= 50 : 63
so as a fraction ----- 50/63
To write the ratio 2.5 to 3.15 as a fraction in simplest form, we need to convert both numbers to fractions.
To convert 2.5 to a fraction, we need to remember that the decimal point separates the whole number part from the fractional part. Since 2 is the whole number part of 2.5, we can write it as 2/1. The decimal part is 0.5, which can be expressed as 5/10 or simplified to 1/2. Combining the whole number and fractional parts, 2.5 can be written as 2 + 1/2 or 2 1/2 or 2.5/1.
Similarly, to convert 3.15 to a fraction, the whole number part is 3 and the decimal part is 0.15. The decimal 0.15 can be written as 15/100 or simplified to 3/20. Combining the whole number and fractional parts, 3.15 can be written as 3 + 3/20 or 3 3/20 or 3.15/1.
Now, we can write the ratio 2.5 to 3.15 as the fraction (2.5/1) / (3.15/1).
To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 3.15/1 is 1/3.15. Therefore, we can rewrite the ratio as (2.5/1) * (1/3.15).
To multiply fractions, we simply multiply the numerators (top numbers) together and the denominators (bottom numbers) together. So, multiplying, we get (2.5 * 1) / (1 * 3.15).
The numerator simplifies to 2.5, and the denominator simplifies to 3.15.
To express the fraction in simplest form, we need to divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, both the numerator and the denominator are decimals, so it is not immediately clear what their GCD is.
To find the GCD of the numerator and denominator, we need to convert both decimals to fractions in a way that their denominators have no decimals. We can do this by multiplying both the numerator and denominator by a power of 10.
Multiplying the numerator and denominator of 2.5 by 100, we get 250/100.
Multiplying the numerator and denominator of 3.15 by 100, we get 315/100.
Now, we can find the GCD of 250 and 315. The prime factors of 250 are 2 * 5 * 5 * 5, and the prime factors of 315 are 3 * 3 * 5 * 7.
The highest common prime factor of 250 and 315 is 5, so we divide both the numerator and denominator by 5.
Dividing 250 by 5, we get 50, and dividing 315 by 5, we get 63.
Therefore, the simplified fraction of the ratio 2.5 to 3.15 is 50/63.