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Jordan has an extension ladder that currently reaches a height of [tex]\(11 \frac{3}{5}\)[/tex] feet. She needs the ladder to extend to a height of [tex]\(15 \frac{1}{5}\)[/tex] feet. How much longer, in feet, does the ladder need to be extended?
To determine how much longer Jordan's extension ladder needs to be, we must first convert the given mixed fractions to improper fractions and then subtract them.
1. Convert the mixed fractions to improper fractions: - The current height of the ladder is [tex]\( 11 \frac{3}{5} \)[/tex]. To convert this mixed fraction to an improper fraction: [tex]\[
11 \frac{3}{5} = 11 + \frac{3}{5} = \frac{11 \times 5 + 3}{5} = \frac{55 + 3}{5} = \frac{58}{5}
\][/tex] So, [tex]\( 11 \frac{3}{5} \)[/tex] in improper fraction form is [tex]\( \frac{58}{5} \)[/tex].
- The needed height is [tex]\( 15 \frac{1}{5} \)[/tex]. To convert this mixed fraction to an improper fraction: [tex]\[
15 \frac{1}{5} = 15 + \frac{1}{5} = \frac{15 \times 5 + 1}{5} = \frac{75 + 1}{5} = \frac{76}{5}
\][/tex] So, [tex]\( 15 \frac{1}{5} \)[/tex] in improper fraction form is [tex]\( \frac{76}{5} \)[/tex].
2. Subtract the current height from the needed height: - We need to find the difference between [tex]\( \frac{76}{5} \)[/tex] and [tex]\( \frac{58}{5} \)[/tex]: [tex]\[
\frac{76}{5} - \frac{58}{5} = \frac{76 - 58}{5} = \frac{18}{5}
\][/tex]
3. Convert the improper fraction back to a mixed or decimal form: - To convert [tex]\( \frac{18}{5} \)[/tex] to a decimal: [tex]\[
\frac{18}{5} = 3.6
\][/tex]
So, Jordan needs to extend the ladder by [tex]\( 3.6 \)[/tex] feet to reach the required height of [tex]\( 15 \frac{1}{5} \)[/tex] feet.
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