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$A cookie factory uses 5//6 of a barrel of oatmeal in each batch of cookies. The factory used 5 5/6 barrels of oatmeal yesterday. How many batches of cookies did the factory make? Write your answer as a fraction or as a whole or mixed number. batches$

A cookie factory uses $5 / 6$ of a barrel of oatmeal in each batch of cookies. The factory used $5$ $5$ / $6$ barrels of oatmeal yesterday. How many batches of cookies did the factory make? $\newline$ Write your answer as a fraction or as a whole or mixed number. $\newline$ batches

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Math Problems

Grade 8

Multiply and divide rational numbers: word problems

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Q. A cookie factory uses

5 / 6

of a barrel of oatmeal in each batch of cookies. The factory used

5

5

6

barrels of oatmeal yesterday. How many batches of cookies did the factory make?

\newline

Write your answer as a fraction or as a whole or mixed number.

\newline

batches

Convert to Improper Fraction: Convert the mixed number to an improper fraction. $\newline$ $5 \frac{5}{6}$ is the same as $(5 \times 6 + 5)/6 = (30 + 5)/6 = \frac{35}{6}$ .
Divide Total Amount: Divide the total amount of oatmeal used by the amount used per batch. $\newline$ The factory used $\frac{35}{6}$ barrels of oatmeal and uses $\frac{5}{6}$ of a barrel per batch. To find out how many batches were made, divide $\frac{35}{6}$ by $\frac{5}{6}$ .
Perform Division: Perform the division by multiplying by the reciprocal of the divisor. $\frac{35}{6} \div \frac{5}{6}$ is the same as $\frac{35}{6} \times \frac{6}{5}.$
Multiply Numerators: Multiply the numerators and denominators. $\newline$ $(35 \times 6)/(6 \times 5) = 210/30$ .
Simplify Fraction: Simplify the fraction. $\frac{210}{30}$ simplifies to $7$ , since $210$ divided by $30$ equals $7$ .