Janet is $55\frac{3}{4}$ inches tall. Carl Is $1\frac{3}{8}$ inches shorter than Janet and Jane is $1\frac{1}{5}$ inches shorter than Carl. How tall is Jane

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Add and subtract rational numbers: word problems

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Q. Janet is

55\frac{3}{4}

inches tall. Carl Is

1\frac{3}{8}

inches shorter than Janet and Jane is

1\frac{1}{5}

inches shorter than Carl. How tall is Jane

Convert to Improper Fraction: Convert Janet's height to an improper fraction. $\newline$ $55 \frac{3}{4}$ inches = $(55 \times 4 + 3)/4 = (220 + 3)/4 = \frac{223}{4}$ inches.
Subtract Height Difference: Subtract Carl's height difference from Janet's height. Carl is $1\frac{3}{8}$ inches shorter than Janet, so: $\frac{223}{4} - 1\frac{3}{8}$ inches = $\frac{223}{4} - \left(1 \times 8 + 3\right)/8$ = $\frac{223}{4} - \frac{11}{8}$ inches.
Find Common Denominator: Find a common denominator to subtract the fractions. $\newline$ The common denominator for $4$ and $8$ is $8$ . $\newline$ Convert $\frac{223}{4}$ to eighths: $\frac{223}{4} \times \frac{2}{2} = \frac{446}{8}$ . $\newline$ Now subtract: $\frac{446}{8} - \frac{11}{8} = \frac{446 - 11}{8} = \frac{435}{8}$ inches. $\newline$ Carl's height is $\frac{435}{8}$ inches.
Subtract Height Difference: Subtract Jane's height difference from Carl's height. $\newline$ Jane is $1\frac{1}{5}$ inches shorter than Carl, so: $\newline$ $\frac{435}{8} - 1\frac{1}{5}$ inches $= \frac{435}{8} - \left(1 \times 5 + 1\right)/5 = \frac{435}{8} - \frac{6}{5}$ inches.
Convert to Mixed Number: Find a common denominator to subtract the fractions. $\newline$ The common denominator for $8$ and $5$ is $40$ . $\newline$ Convert $\frac{435}{8}$ to fortieths: $\frac{435}{8} \times \frac{5}{5} = \frac{2175}{40}$ . $\newline$ Convert $\frac{6}{5}$ to fortieths: $\frac{6}{5} \times \frac{8}{8} = \frac{48}{40}$ . $\newline$ Now subtract: $\frac{2175}{40} - \frac{48}{40} = \frac{2175 - 48}{40} = \frac{2127}{40}$ inches. $\newline$ Jane's height is $\frac{2127}{40}$ inches.
Convert to Mixed Number: Find a common denominator to subtract the fractions. $\newline$ The common denominator for $8$ and $5$ is $40$ . $\newline$ Convert $\frac{435}{8}$ to fortieths: $\frac{435}{8} \times \frac{5}{5} = \frac{2175}{40}$ . $\newline$ Convert $\frac{6}{5}$ to fortieths: $\frac{6}{5} \times \frac{8}{8} = \frac{48}{40}$ . $\newline$ Now subtract: $\frac{2175}{40} - \frac{48}{40} = \frac{(2175 - 48)}{40} = \frac{2127}{40}$ inches. $\newline$ Jane's height is $\frac{2127}{40}$ inches.Convert Jane's height back to a mixed number. $\newline$ $\frac{2127}{40} = 53 \frac{7}{40}$ inches.