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Vanessa got 7(3)/(10) hours of sleep and her brother got 9(3)/(5) hours of sleep. How much longer did her brother sleep than her? Give your answer in simplest form. [?]([])/([]) hours Enter

Vanessa got 7310 7 \frac{3}{10} hours of sleep and her brother got 935 9 \frac{3}{5} hours of sleep. How much longer did her brother sleep than her?\newlineGive your answer in simplest form.\newline[?][][] [?] \frac{[]}{[]} hours\newlineEnter

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Full solution

Q. Vanessa got 7310 7 \frac{3}{10} hours of sleep and her brother got 935 9 \frac{3}{5} hours of sleep. How much longer did her brother sleep than her?\newlineGive your answer in simplest form.\newline[?][][] [?] \frac{[]}{[]} hours\newlineEnter
  1. Convert to Improper Fraction: Convert Vanessa's sleep time from mixed number to improper fraction.\newlineVanessa's sleep time: 7310=7010+310=7310 7\frac{3}{10} = \frac{70}{10} + \frac{3}{10} = \frac{73}{10} hours.
  2. Convert Brother's Time: Convert her brother's sleep time from mixed number to improper fraction.\newlineHer brother's sleep time: 935=455+35=485 9\frac{3}{5} = \frac{45}{5} + \frac{3}{5} = \frac{48}{5} hours.
  3. Find Sleep Time Difference: Subtract Vanessa's sleep time from her brother's sleep time to find out how much longer her brother slept.\newlineDifference in sleep time: 485−7310 \frac{48}{5} - \frac{73}{10} .\newlineTo subtract these fractions, find a common denominator.
  4. Find Common Denominator: The common denominator for 55 and 1010 is 1010. Convert 485 \frac{48}{5} to a fraction with a denominator of 1010.\newline485=48×25×2=9610 \frac{48}{5} = \frac{48 \times 2}{5 \times 2} = \frac{96}{10} .
  5. Subtract Fractions: Now subtract the two fractions with the common denominator.\newline9610−7310=96−7310=2310 \frac{96}{10} - \frac{73}{10} = \frac{96 - 73}{10} = \frac{23}{10} hours.
  6. Simplify Fraction: Simplify the fraction 2310 \frac{23}{10} if possible.\newlineSince 2323 is a prime number and 1010 is not a multiple of 2323, the fraction is already in simplest form.

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