Question

How do you find the fractional notation for the ratio of 490 to 413?

Answer 1

Hint: In mathematics, the ratio is a very commonly used term, the ratio of two numbers signifies how many times one number contains or is contained in another. For example, if person A has Rs.8 and person B has Rs.3 then the ratio of their money is eight to 3 and is written as $ 8:3 $ . While converting a ratio into a fraction, we write the term on the left side of the ratio as the numerator and the term on the right side as the denominator. This way, we can write the ratio of 490 to 413 in the fractional notation.

Complete step-by-step answer:
The given ratio is written as $ 490:413 $ , 490 will be the numerator and 413 will be the denominator so it is written in fractional notation as $ \dfrac{{490}}{{413}} $ .
But converting the ratio into a fraction is not enough; we have to simplify the fraction too as follows –
 $ \dfrac{{490}}{{413}} = \dfrac{{7 \times 7 \times 2 \times 5}}{{7 \times 59}} = \dfrac{{70}}{{59}} $
Hence the fractional notation for the ratio of 490 to 413 is $ \dfrac{{70}}{{59}} $ .
So, the correct answer is “ $ \dfrac{{70}}{{59}} $ ”.

Note: For simplifying a fraction, we write both the numerator and the denominator as a product of their prime factors, then we divide both the numerator and the denominator by the common factors and the remaining fraction is called the simplified fraction.