- Multiply and Divide Fractions
- Home
- Product of a Unit Fraction and a Whole Number
- Product of a Fraction and a Whole Number: Problem Type 1
- Introduction to Fraction Multiplication
- Fraction Multiplication
- Product of a Fraction and a Whole Number Problem Type 2
- Determining if a Quantity is Increased or Decreased When Multiplied by a Fraction
- Modeling Multiplication of Proper Fractions
- Multiplication of 3 Fractions
- Word Problem Involving Fractions and Multiplication
- The Reciprocal of a Number
- Division Involving a Whole Number and a Fraction
- Fraction Division
- Fact Families for Multiplication and Division of Fractions
- Modeling Division of a Whole Number by a Fraction
- Word Problem Involving Fractions and Division

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- UPSC IAS Exams Notes
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The **reciprocal** of a number is 1 divided by the number.

- The reciprocal of a number is also called its multiplicative inverse.
- The product of a number and its reciprocal is 1.
- All numbers except 0 have a reciprocal.
- The reciprocal of a fraction is found by flipping its numerator and denominator.

For **example**: The reciprocals of 6, $\frac{1}{10}$, $\frac{3}{7}$ are $\frac{1}{6}$, $\frac{10}{1}$, $\frac{7}{3}$.

**Example**

Find the reciprocal of 3

**Solution**

**Step 1:**

To find the reciprocal of 3, we write 1 over 3 i.e., $\frac{1}{3}$.

**Step 2:**

So the reciprocal of 3 is $\frac{1}{3}$

Find the reciprocal of $\frac{1}{4}$

**Step 1:**

To find the reciprocal of $\frac{1}{4}$, its numerator and denominator are flipped

**Step 2:**

The reciprocal of $\frac{1}{4}$ = $\frac{4}{1}$ or 4.

So, the reciprocal of $\frac{1}{4}$= 4.

Find the reciprocal of 7

**Step 1:**

To find the reciprocal of 7, first it is re-written as $\frac{7}{1}$. Then its numerator and denominator are flipped and the reciprocal = $\frac{1}{7}$.

**Step 2:**

So the reciprocal of 7 is $\frac{1}{7}$

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