Division of Fractions

Definition

Division of fractions is the process of dividing one fraction by another fraction. It involves inverting the divisor fraction and then multiplying it by the dividend fraction to find the quotient.

5 Must Know Facts For Your Next Test

1. To divide one fraction by another, you invert the divisor fraction and then multiply it by the dividend fraction.
2. Dividing a fraction by a whole number is the same as multiplying the fraction by the reciprocal of the whole number.
3. When dividing fractions with different denominators, it is often helpful to first convert the fractions to equivalent fractions with a common denominator.
4. Division of fractions is the inverse operation of multiplication of fractions, just as division of whole numbers is the inverse of multiplication of whole numbers.
5. Dividing by a fraction is the same as multiplying by the reciprocal of that fraction.

Review Questions

• Explain the process of dividing one fraction by another fraction.
  • To divide one fraction by another fraction, you first find the reciprocal of the divisor fraction by swapping the numerator and denominator. Then, you multiply the dividend fraction by the reciprocal of the divisor fraction. This effectively inverts the division operation and transforms it into a multiplication operation, which is easier to perform. For example, to divide $\frac{1}{2}$ by $\frac{1}{4}$, you would first find the reciprocal of $\frac{1}{4}$, which is $\frac{4}{1}$, and then multiply $\frac{1}{2}$ by $\frac{4}{1}$ to get the final answer of $\frac{4}{2}$ or 2.
• Describe how dividing a fraction by a whole number is different from dividing a fraction by another fraction.
  • Dividing a fraction by a whole number is the same as multiplying the fraction by the reciprocal of the whole number. For example, to divide $\frac{1}{2}$ by 4, you would multiply $\frac{1}{2}$ by $\frac{1}{4}$, which is the reciprocal of 4. This is different from dividing a fraction by another fraction, where you would invert the divisor fraction and then multiply it by the dividend fraction. The key difference is that with a whole number divisor, you can simply take the reciprocal, but with a fraction divisor, you need to invert the entire fraction.
• Analyze the relationship between division of fractions and multiplication of fractions, and explain how this relationship can be used to simplify division of fractions.
  • Division of fractions is the inverse operation of multiplication of fractions, just as division of whole numbers is the inverse of multiplication of whole numbers. This means that dividing a fraction by another fraction is equivalent to multiplying the dividend fraction by the reciprocal of the divisor fraction. This relationship can be used to simplify division of fractions by first converting the division operation into a multiplication operation. For example, to divide $\frac{1}{2}$ by $\frac{1}{4}$, you can instead multiply $\frac{1}{2}$ by the reciprocal of $\frac{1}{4}$, which is $\frac{4}{1}$, to get the final answer of $\frac{4}{2}$ or 2. This approach allows you to leverage your understanding of fraction multiplication to perform division of fractions more efficiently.

Related terms

Reciprocal:

The reciprocal of a fraction is the fraction with its numerator and denominator swapped, such that when multiplied by the original fraction, the product is 1.

Equivalent Fractions:

Equivalent fractions are fractions that represent the same value, even though the numerator and denominator may be different.

Least Common Denominator (LCD):

The least common denominator is the smallest positive integer that is divisible by all the denominators of the fractions being operated on.