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What should be subtracted from
68(1)/(15) to get
56(1)/(9) ?

What should be subtracted from $68\frac{1}{15}$ to get $56\frac{1}{9}$ ?

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Operations with rational exponents

Full solution

Q. What should be subtracted from

68\frac{1}{15}

to get

56\frac{1}{9}

?

Convert to Improper Fractions: Convert mixed numbers to improper fractions for easier calculation. $\newline$ $68\left(\frac{1}{15}\right) = \left(68 \times 15 + 1\right)/15 = \frac{1021}{15}$ , $\newline$ $56\left(\frac{1}{9}\right) = \left(56 \times 9 + 1\right)/9 = \frac{505}{9}$ ,
Subtract Fractions: Subtract the second fraction from the first to find the difference. $\newline$ Subtraction: $(1021/15) - (505/9)$ , $\newline$ To subtract, find a common denominator, which is $45$ here. $\newline$ Convert: $1021/15 = (1021 \times 3)/(15 \times 3) = 3063/45$ , $\newline$ $505/9 = (505 \times 5)/(9 \times 5) = 2525/45$ , $\newline$ Now subtract: $3063/45 - 2525/45 = 538/45$ ,
Convert to Mixed Number: Convert the result back to a mixed number to answer the question. $\frac{538}{45} = 11$ remainder $43$ , so it's $11\left(\frac{43}{45}\right)$ ,

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