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Chidi puts $2\frac{3}{5}\,\text{KG}$ of bird seed in his large feeder. This is $1\frac{3}{10}$ times as much seed as he puts in his smaller feeder. How much bird seed does Chidi put in his smaller feeder?

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Multiply and divide rational numbers: word problems

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Q. Chidi puts

2\frac{3}{5}\,\text{KG}

of bird seed in his large feeder. This is

1\frac{3}{10}

times as much seed as he puts in his smaller feeder. How much bird seed does Chidi put in his smaller feeder?

Convert to Improper Fractions: To find out how much seed Chidi puts in his smaller feeder, we need to divide the amount of seed he puts in his large feeder by the factor that represents how much more seed is in the large feeder compared to the small one. $\newline$ Calculation: $2 \frac{3}{5}$ KG $\div 1 \frac{3}{10}$ $\newline$ First, convert the mixed numbers to improper fractions. $\newline$ $2 \frac{3}{5} = (2 \times 5 + 3)/5 = \frac{13}{5}$ $\newline$ $1 \frac{3}{10} = (1 \times 10 + 3)/10 = \frac{13}{10}$ $\newline$ Now divide $\frac{13}{5}$ by $\frac{13}{10}.$
Multiply by Reciprocal: To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. $\newline$ Calculation: $(\frac{13}{5}) \times (\frac{10}{13})$ $\newline$ The $13$ s cancel out because they are a common factor in the numerator and denominator. $\newline$ Calculation: $(\frac{13}{5}) \times (\frac{10}{13}) = (\frac{1}{5}) \times (\frac{10}{1}) = \frac{10}{5}$
Simplify the Fraction: Simplify the fraction $\frac{10}{5}$ to get the final answer. $\newline$ Calculation: $\frac{10}{5} = 2$ $\newline$ So, Chidi puts $2$ KG of bird seed in his smaller feeder.

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