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If $\frac{4}{5}$ of a can of paint covers $1$ ceiling how many cans needed for $6$ ceilings?

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Identify quotients of rational numbers: word problems

Full solution

Q. If

\frac{4}{5}

of a can of paint covers

1

ceiling how many cans needed for

6

ceilings?

Calculate Can Coverage: If $\frac{4}{5}$ of a can covers $1$ ceiling, then $1$ can covers $\frac{1}{(\frac{4}{5})}$ ceilings, which is the same as $\frac{5}{4}$ ceilings.
Determine Number of Cans: To find out how many cans are needed for $6$ ceilings, divide the total number of ceilings by the number of ceilings covered by one can: $6 \div \left(\frac{5}{4}\right)$ .
Calculate Total Ceilings: Calculate $6 \div \left(\frac{5}{4}\right)$ by multiplying $6$ by the reciprocal of $\frac{5}{4}$ , which is $\frac{4}{5}$ .
Round Up to Nearest Whole: So, $6 \times \left(\frac{4}{5}\right) = \frac{24}{5} = 4.8$ .
Round Up to Nearest Whole: So, $6 \times \left(\frac{4}{5}\right) = \frac{24}{5} = 4.8$ .Since we can't have $0.8$ of a can, we'll need to round up to the nearest whole number, which means we need $5$ cans of paint.

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