Divide fractions

Division of fractions means determining the size or number of equal groups when the dividend and nonzero divisor are nonnegative fractions, mixed numbers, or whole numbers; quotients can be interpreted through measurement, grouping, number-line, or area representations. The relationship $a \div b=a \times \frac{1}{b}$ is understood through the inverse relationship between multiplication and division, including why a quotient may exceed either input, while division by zero is undefined; signed-number and symbolic generalizations are outside this scope.

Detailed Explanation: Divide fractions

To divide fractions, use the relationship

a\div b=a\times \frac{1}{b}.

The number $\frac{1}{b}$ is called the reciprocal of $b$ . So, to divide by a fraction, multiply by its reciprocal.

Example

Solve:

2\frac14\div\frac38

Step 1: Convert the mixed number to an improper fraction.

2\frac14=\frac{2\cdot4+1}{4}=\frac94

So the problem becomes

\frac94\div\frac38.

Step 2: Keep the first fraction, change division to multiplication, and flip the second fraction.

\frac94\div\frac38 = \frac94\times\frac83

Step 3: Multiply and simplify.

\frac{9\cdot8}{4\cdot3} = \frac{72}{12} = 6

Therefore,

\boxed{2\frac14\div\frac38=6}.

This means there are six groups of size $\frac38$ in $2\frac14$ . The quotient can be larger than the numbers being divided because $\frac38$ is less than $1$ . Dividing by zero is not defined.

Learn by doing: Divide fractions

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Fraction Division - Whole by Simple

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