Students can undoubtedly benefit from the Reciprocal questions and solutions provided here in order to gain a better understanding of the idea. Finding the reciprocal of a number is an important concept taught in both primary and secondary education. Reciprocal questions can be found practically in almost all examinations. Students can use these questions to acquire a quick overview of the themes and practice them to improve their understanding of the subject. You can also check your answer against the solutions on this page. Click here to learn more about Reciprocal.

What are Reciprocals?

According to the reciprocal definition in Mathematics, the reciprocal of a number is the formula that generates 1 when multiplied by the number. In other words, if the product of two numbers is 1, they are considered reciprocals. The reciprocal of a given integer is defined as the division of 1 by that given integer.

For example, the reciprocal of 5 is 1/5.

In other words, the product of 5 and ⅕ gives 1/5.

Reciprocal Questions With Solutions

1. Find the reciprocal of 10.

Solution:

Given number: 10

As we know, the reciprocal of a number is defined as one over that number.

It means that, if “n” is the given number, then its reciprocal is 1/n.

Hence, the reciprocal of 10 is 1/10.

2. Compute the reciprocal of 17 and justify your answer.

Solution:

Given number: 17.

We know that, the reciprocal of a number is 1 divided by the given number.

Therefore, the reciprocal of 17 is 1/17.

Verification:

As we know, the product of the given number and its reciprocal results in 1.

Thus, 17 × (1/17) = 1.

So, LHS = RHS.

Hence, verified.

3. What is the reciprocal of 1?

Solution:

The reciprocal of 1 is 1.

We know that the product of the given number and its reciprocal should be equal to 1.

Hence, 1 × 1 = 1.

Finding the reciprocal of Negative Numbers:

To find the reciprocal of any negative integer, follow the procedures below:

Step 1: Write the given integer in the form of an improper fraction (Ignore minus sign).

Step 2: Swap the denominator and numerator.

Step 3: Finally, add the minus symbol to the resultant value.

4. Find the reciprocal of -14.

Solution:

Given Number:

Step 1: Write the number in the form of an improper fraction (ignore minus sign)

Thus, 14 = 14/1.

Step 2: Now, swap the numerator and denominator values. Hence, 14/1 becomes 1/14.

Step 3: Now add the minus sign to the result obtained in step 2.

Hence, the reciprocal of -14 is -1/14.

5. Find the reciprocal of -⅙ and justify your answer.

Solution:

Given fraction: -1/6.

Step 1: Ignore minus sign. Hence, the fraction now obtained is ⅙.

Step 2: Now, swap the numerator and denominator. So, ⅙ becomes 6/1.

Step 3: Finally, add the minus sign to the result obtained in step 2.

Hence, the reciprocal of -1/6 is -6/1.

Verification:

The product of -⅙ and (-6/1) should give 1.

So, (-⅙) × (-6/1) = 1

1 = 1

Thus, LHS = RHS.

Hence, verified.

Reciprocal of a Decimal Number:

Simply write one divided by the decimal number to find the reciprocal of a decimal number.

For instance, the reciprocal of 4.3 is 1 / 4.3.

6. Find the reciprocal of 0.34.

Solution:

Given decimal number: 0.34.

We know that the reciprocal of a number can be written as one over that number.

I.e., Reciprocal of 0.34 = 1/0.34.

Reciprocal of a Fraction:

Step 1: Interchange the numerator and denominator to find the reciprocal of a fraction. Thus, the obtained fraction is the reciprocal of the fraction. Similarly, we can find the reciprocal of a fraction if it contains variables.

For instance, the reciprocal of 19/12 is 12/19 and the reciprocal of x/y is y/x.

7. Find the reciprocal of the fraction 6/11.

Solution:

As we know, the reciprocal of a fraction can be determined by swapping the numerator and denominator of the given fraction.

Here, the given fraction is 6/11.

After swapping the numerator and denominator of 6/11, we get 11/6.

Hence, the reciprocal of the fraction 6/11 is 11/6.

8. Find the reciprocal of -12/17, and verify the answer.

Solution:

Given fraction: -12/17.

Hence, the reciprocal of -12/17 is written as follows:

Reciprocal of -12/17 = 1/(-12/17)

Reciprocal of -12/17 = -17/12

Verification:

We know that the product of the given number and its reciprocal equals 1.

Thus,

(-12/17) × (-17/12) = 1

1 = 1

Hence, LHS = RHS.

Reciprocal of a Mixed Fraction:

The steps shown below can be used to determine the reciprocal of a mixed fraction.

Step 1: First, convert the mixed number into an improper fraction.

Step 2: Now, swap the denominator and numerator. The resulting fraction is the required reciprocal.

9. Determine the reciprocal of 3 ½.

Solution:

Given Number: 3 ½.

Step 1: Convert 3 ½ into an improper fraction.

Hence, 3 ½ = 7/2

Step 2: Now, swap the numerator and denominator values, we get the reciprocal.

Thus, 7/2 becomes 2/7.

Hence, the reciprocal of 3 ½ is 2/7.

10. Find the reciprocal of 4 ⅔ .

Solution:

Given Number: 4 ⅔.

Step 1: Convert 4 ⅔ into an improper fraction.

Hence, 4 ⅔ = 14/3

Step 2: Now, interchange the numerator and denominator, and we get the reciprocal.

Thus, 14/3 becomes 3/14.

Hence, the reciprocal of 4 ⅔ is 3/14.

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Practice Questions

Answer the following reciprocal questions:

Determine the reciprocal of 9.
Find the reciprocal of -4.
Determine the reciprocal of 12/23.
Determine the reciprocal of 0.46.
Find the reciprocal 6 ½.

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