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Write two types of problems you could solve by calculating
4(1)/(5)-2(2)/(3). Use two different meanings of subtraction.

Write two types of problems you could solve by calculating $4 \frac{1}{5}-2 \frac{2}{3}$ . Use two different meanings of subtraction.

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Multiplication with rational exponents

Full solution

Q. Write two types of problems you could solve by calculating

4 \frac{1}{5}-2 \frac{2}{3}

. Use two different meanings of subtraction.

Pizza Left After Lunch: Problem $1$ : You have $4\frac{1}{5}$ of a pizza left from last night, and you eat $2\frac{2}{3}$ slices for lunch. How much pizza do you have left?
Fraction Subtraction: Calculate the fraction of the pizza left after eating lunch. $4\left(\frac{1}{5}\right) - 2\left(\frac{2}{3}\right) = \left(\frac{21}{5}\right) - \left(\frac{8}{3}\right)$
Common Denominator: Find a common denominator to subtract the fractions. $\newline$ Common denominator for $5$ and $3$ is $15$ . $\newline$ $(\frac{21}{5}) \cdot (\frac{3}{3}) - (\frac{8}{3}) \cdot (\frac{5}{5}) = (\frac{63}{15}) - (\frac{40}{15})$
Subtract Fractions: Subtract the fractions. $\newline$ $(\frac{63}{15}) - (\frac{40}{15}) = \frac{23}{15}$
Convert to Mixed Number: Convert the improper fraction to a mixed number. $\frac{23}{15} = 1 \frac{8}{15}$
Ribbon Left After Gifts: Problem $2$ : You have $4\frac{1}{5}$ meters of ribbon, and you use $2\frac{2}{3}$ meters to wrap some gifts. How much ribbon is left?
Length Calculation: Calculate the length of the ribbon left after wrapping the gifts. $\newline$ $4\left(\frac{1}{5}\right) - 2\left(\frac{2}{3}\right) = \left(\frac{21}{5}\right) - \left(\frac{8}{3}\right)$
Common Denominator: Find a common denominator to subtract the fractions. $\newline$ Common denominator for $5$ and $3$ is $15$ . $\newline$ $(\frac{21}{5}) \cdot (\frac{3}{3}) - (\frac{8}{3}) \cdot (\frac{5}{5}) = (\frac{63}{15}) - (\frac{40}{15})$
Subtract Fractions: Subtract the fractions. $\newline$ $(\frac{63}{15}) - (\frac{40}{15}) = \frac{23}{15}$
Convert to Mixed Number: Convert the improper fraction to a mixed number. $\frac{23}{15} = 1 \frac{8}{15}$

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