Dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of (1)/(6) is (6)/(1). Multiplying the numerators gives 7 × 6 = 42, and multiplying the denominators gives 8 × 1 = 8.

Dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of (1)/(6) is (6)/(1). Multiplying the numerators gives 7 × 6 = 42, and multiplying the denominators gives 8 × 1 = 8.

A bag holds 7/8 kg of rice. If each small container holds 1/6 kg of rice, how many full containers can be filled? how will we know which is numerator and denominator- in fractions a part of whole and denominator is whole right then why is opposite. why 7/8 is numerator but its total

Answer: $5$ full containers can be filled (with $\frac{1}{4}$ of a container remaining). $\frac{7}{8}$ is in the numerator because it is the total quantity (dividend) being divided by the unit capacity (divisor $\frac{1}{6}$ ).

Step-by-step solution

Step 1: Distinguish single fractions from division of quantities

In a single fraction like $\frac{7}{8}$ , the number $8$ represents the whole divided into equal parts, and $7$ represents the parts taken. However, when finding how many containers can be filled from a total amount, we are performing division across two different quantities. Just like dividing $20\text{ kg}$ by $4\text{ kg}$ gives $\frac{20}{4}$ , the total amount available, $\frac{7}{8}\text{ kg}$ , is the dividend (the top or numerator of the overall division), and the container capacity, $\frac{1}{6}\text{ kg}$ , is the divisor (the denominator of the overall division).

Step 2: Set up the division expression

To determine how many groups of size $\frac{1}{6}\text{ kg}$ fit into the total of $\frac{7}{8}\text{ kg}$ , we divide the total rice by the capacity of one container. This forms a complex fraction where the dividend $\frac{7}{8}$ is in the numerator of the division, and the divisor $\frac{1}{6}$ is in the denominator.

Step 3: Multiply by the reciprocal of the divisor

Dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of $\frac{1}{6}$ is $\frac{6}{1}$ . Multiplying the numerators gives $7 \times 6 = 42$ , and multiplying the denominators gives $8 \times 1 = 8$ .

Step 4: Simplify and determine full containers

Dividing the numerator and denominator by their common factor $2$ yields $\frac{21}{4}$ . Converting this improper fraction to a mixed number gives $5$ and $\frac{1}{4}$ , which means $5$ full containers can be filled, with $\frac{1}{4}$ of a container left over.

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