Fraction Changes: Numerator and Denominator
This problem involves calculating the effect of percentage increases on the numerator and denominator of a fraction and determining the ratio of the new fraction to the original.
Identify Original Fraction Components
Let the original fraction be represented as:
$ \frac{n}{d} $
Where $n$ is the numerator and $d$ is the denominator.
Calculate New Numerator and Denominator
The numerator is increased by 50%:
New Numerator = $ n + (50\% \times n) = n + 0.50n = 1.50n $
The denominator is increased by 80%:
New Denominator = $ d + (80\% \times d) = d + 0.80d = 1.80d $
Form the New Fraction
The new fraction is:
$ \frac{1.50n}{1.80d} $
Determine the Ratio of New to Original Fraction
To find what fraction of the original the new fraction is, we calculate the ratio:
$ \text{Ratio} = \frac{\text{New Fraction}}{\text{Original Fraction}} = \frac{\frac{1.50n}{1.80d}}{\frac{n}{d}} $
Simplify the expression:
$ \text{Ratio} = \frac{1.50n}{1.80d} \times \frac{d}{n} $
Cancel out $n$ and $d$:
$ \text{Ratio} = \frac{1.50}{1.80} $
Simplify the Resulting Fraction
Convert the decimals to a common fraction and simplify:
$ \frac{1.50}{1.80} = \frac{1.5}{1.8} = \frac{15}{18} $
Divide both the numerator and the denominator by their greatest common divisor, which is 3:
$ \frac{15 \div 3}{18 \div 3} = \frac{5}{6} $
The new fraction is 5/6 of the original fraction.
Similar Questions
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Important Questions from Percentage
Radha saves 25% of her income. If her expenditure increases by 20% and her income increases by 29%, then her savings increase by;
The income of A is 45% more than the income of B and the income of C is 60% less than the sum of the incomes of A and B. The income of D is 20% more than that of C. If the difference between the incomes of B and D is Rs. 13200, then the income (in Rs.) of C is:
The price of cooking oil increased by 25%. Find by how much percentage a family must reduce its consumption in order to maintain the same budget.
The population of a city increased by 30% in the first year and decreased by 15% in the next year. If the present population is 11,050 then population 2 years ago was:
The income of A is 30% less than the income of B and the income of B is 137.5% more than that of C. If the income of A is Rs. 28500 less than that of B, then the income (in Rs.) of C is:
