Question

How do you write \[44:50\] as a fraction, a decimal, and a percent?

Answer 1

Hint:
 Let \[x:y\] be a ratio. This ratio can be converted into a fraction of form \[\dfrac{p}{q}\] where p and q are co primes by writing \[\dfrac{x}{y}\] and eliminating common terms. This ratio can be converted into a decimal by making the denominator of its fraction form into multiples of 10. This ratio can be converted into percent form by multiplying its decimal form with 100.

Complete step by step answer:
According to the question, the given ratio is \[44:50\]. That is here x=44 and y=50.
Now,
1) Conversion of a ratio into fraction: -
\[44:50\]is the given ratio. Let ‘a’ be a fraction form of \[44:50\]. Hence, we can write
a = \[\dfrac{44}{50}\].
Now, by factorization we write 44 as \[2\times 2\times 11\] and 50 as \[2\times 5\times 5\]. Here, we can see that 44 and 50 have 2 in common. So, on eliminating the common term we have
a = \[\dfrac{22}{25}\]. Hence, \[\dfrac{22}{25}\] is the fraction form of \[44:50\] ratio.
2) Conversion of a ratio into decimal: -
Here, we have the fraction form of \[44:50\] as \[\dfrac{22}{25}\]. Its denominator is 25.
We know that 25 multiplied by 4 gives 100 (which is multiple of 10). So, we multiply both numerator and denominator by 4, then we get \[\dfrac{22\times 4}{25\times 4}=\]\[\dfrac{88}{100}\] which is simply 0.88.
3) Conversion of ratio into a percent: -
In the previous conversion, we got that the decimal form of \[44:50\] ratio is 0.88.
So, on multiplying 0.88 with 100,\[0.88\times 100\] we get \[88\%\].

\[\therefore \]\[\dfrac{22}{25}\], 0.88 and \[88\%\] are the fraction form, decimal form and percentage form of the ratio \[44:50\] respectively.

Note:
 We can do the conversion of a ratio into a decimal by simply dividing the numerator of its fraction form with the denominator. We can also do the conversion of a ratio into a percent by multiplying its fraction form by 100 and then simple division.
While calculating decimal form we must round the decimal part.