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Answer :
Sure, let's solve this step-by-step!
We start with a fraction [tex]\(\frac{18}{20}\)[/tex].
We need to find a number, let's call it [tex]\( x \)[/tex], such that when [tex]\( x \)[/tex] is subtracted from both the numerator and denominator of [tex]\(\frac{18}{20}\)[/tex], the resulting fraction equals [tex]\(15 \frac{11}{13}\)[/tex].
First, let's convert the mixed number [tex]\(15 \frac{11}{13}\)[/tex] to an improper fraction:
[tex]\[ 15 \frac{11}{13} = 15 + \frac{11}{13} = \frac{15 \times 13 + 11}{13} = \frac{195 + 11}{13} = \frac{206}{13} \][/tex]
The equation we need to solve is:
[tex]\[ \frac{18 - x}{20 - x} = \frac{206}{13} \][/tex]
To solve for [tex]\( x \)[/tex], cross-multiply to clear the fractions:
[tex]\[ 13 \times (18 - x) = 206 \times (20 - x) \][/tex]
Expand and simplify:
[tex]\[ 13 \times 18 - 13x = 206 \times 20 - 206x \][/tex]
[tex]\[ 234 - 13x = 4120 - 206x \][/tex]
Now, combine like terms by isolating [tex]\( x \)[/tex] on one side:
[tex]\[ 206x - 13x = 4120 - 234 \][/tex]
[tex]\[ 193x = 3886 \][/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{3886}{193} \approx 20.1347150259067 \][/tex]
So, the number you are looking for is approximately [tex]\( 20.134715 \)[/tex].
We start with a fraction [tex]\(\frac{18}{20}\)[/tex].
We need to find a number, let's call it [tex]\( x \)[/tex], such that when [tex]\( x \)[/tex] is subtracted from both the numerator and denominator of [tex]\(\frac{18}{20}\)[/tex], the resulting fraction equals [tex]\(15 \frac{11}{13}\)[/tex].
First, let's convert the mixed number [tex]\(15 \frac{11}{13}\)[/tex] to an improper fraction:
[tex]\[ 15 \frac{11}{13} = 15 + \frac{11}{13} = \frac{15 \times 13 + 11}{13} = \frac{195 + 11}{13} = \frac{206}{13} \][/tex]
The equation we need to solve is:
[tex]\[ \frac{18 - x}{20 - x} = \frac{206}{13} \][/tex]
To solve for [tex]\( x \)[/tex], cross-multiply to clear the fractions:
[tex]\[ 13 \times (18 - x) = 206 \times (20 - x) \][/tex]
Expand and simplify:
[tex]\[ 13 \times 18 - 13x = 206 \times 20 - 206x \][/tex]
[tex]\[ 234 - 13x = 4120 - 206x \][/tex]
Now, combine like terms by isolating [tex]\( x \)[/tex] on one side:
[tex]\[ 206x - 13x = 4120 - 234 \][/tex]
[tex]\[ 193x = 3886 \][/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{3886}{193} \approx 20.1347150259067 \][/tex]
So, the number you are looking for is approximately [tex]\( 20.134715 \)[/tex].
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