Common Denominators Practice Problems & Worksheets

Master finding common denominators with step-by-step practice problems. Learn three proven methods to solve fraction addition and subtraction exercises confidently.

📚Master Common Denominators with Interactive Practice

Apply the first case method when one denominator divides another evenly
Find common multiples using the second case multiplication approach
Use the third case method by multiplying denominators together
Convert fractions to equivalent forms with matching denominators
Solve fraction addition and subtraction problems step-by-step
Identify the least common denominator for simplified solutions

Understanding Common Denominators

Complete explanation with examples

A common denominator is a denominator that will be common and equal for all the fractions in the exercise. We will reach such a denominator by reducing or enlarging the fraction - an operation of multiplication or division.
We can arrive at several correct common denominators.

We will divide the search for the common denominator into 3 cases:

The first case: one of the denominators appearing in the original exercise will be the common denominator.
In this case, we will notice that we only have to multiply one denominator by an integer to reach the same denominator as in the other fraction.
The second case: find a number that both denominators in the exercise can reach by multiplication.
The third case: find the common denominator by multiplying the denominators.

Detailed explanation

Practice Common Denominators

Test your knowledge with 26 quizzes

What is the least common multiple of these two numbers?

$\boxed{4}~~~\boxed{8}$

Examples with solutions for Common Denominators

Step-by-step solutions included

Exercise #1

Determine the least common multiple of 8 and 12.

$\boxed 8~~~\boxed{ 12}$

Step-by-Step Solution

To find the least common multiple (LCM) of the numbers 8 and 12, we will list the multiples of each number and find the smallest multiple they have in common.

Multiples of 8: $8, 16, 24, 32, \ldots$

Multiples of 12: $12, 24, 36, 48, \ldots$

The smallest common multiple is $24$ .

Answer:

Exercise #2

Find the least common multiple of 5 and 9.

$\boxed 5~~~\boxed 9$

Step-by-Step Solution

To find the least common multiple (LCM) of 5 and 9, list the multiples of each number and find the smallest multiple they have in common.

Multiples of 5: $5, 10, 15, 20, 25, 30, 35, 40, 45, \ldots$

Multiples of 9: $9, 18, 27, 36, 45, \ldots$

The smallest common multiple is $45$ .

Answer:

Exercise #3

What is the least common multiple (LCM) of the numbers 3 and 7?

$\boxed 3~~~\boxed 7$

Step-by-Step Solution

To find the least common multiple (LCM) of the numbers 3 and 7, we will list the multiples of each number and find the smallest multiple they have in common.

Multiples of 3: $3, 6, 9, 12, 15, 18, 21, \ldots$

Multiples of 7: $7, 14, 21, 28, \ldots$

The smallest common multiple is $21$ .

Answer:

Exercise #4

What is the least common multiple of the numbers 10 and 15?

$\boxed {10}~~~\boxed {15 }$

Step-by-Step Solution

To find the least common multiple (LCM) of 10 and 15, list the multiples of each number and find the smallest multiple they have in common.

Multiples of 10: $10, 20, 30, 40, \ldots$

Multiples of 15: $15, 30, 45, 60, \ldots$

The smallest common multiple is $30$ .

Answer:

Exercise #5

You have a pair of denominators, what is their least common multiple?

$\boxed 3~~~\boxed 4$

Step-by-Step Solution

To find the least common multiple (LCM) of $3$ and $4$ , we list the multiples of each number until we find the smallest multiple they have in common.

Multiples of $3$ : $3, 6, 9, 12, 15, \ldots$

Multiples of $4$ : $4, 8, 12, 16, 20, \ldots$

The smallest common multiple is $12$ .

Answer:

Frequently Asked Questions

Everything you need to know about Common Denominators

What is a common denominator and why do I need it?

A common denominator is a shared denominator that makes all fractions in an exercise equal at the bottom. You need it to add or subtract fractions because you can only combine fractions that have the same denominator, just like you can only add apples to apples.

What are the 3 methods for finding common denominators?

The three methods are: 1) Use one existing denominator if it's a multiple of the other, 2) Find a number both denominators can reach through multiplication, 3) Multiply the denominators together. Always try methods in this order to find the smallest common denominator.

How do I know which method to use for finding common denominators?

Start with the first method: check if one denominator divides evenly into another. If not, try the second method by finding a common multiple. If both fail, use the third method of multiplying denominators - this always works but may not give the smallest answer.

When I change the denominator, do I need to change the numerator too?

Yes, absolutely! When you multiply or divide the denominator, you must do the same operation to the numerator to keep the fraction's value unchanged. For example, if you multiply the denominator by 3, multiply the numerator by 3 too.

What's the difference between common denominator and least common denominator?

A common denominator is any shared denominator that works for your fractions. The least common denominator (LCD) is the smallest possible common denominator. While any common denominator will work, using the LCD makes calculations easier and answers simpler.

How do I find common denominators for fractions like 2/3 and 1/6?

For 2/3 and 1/6, notice that 3 × 2 = 6, so 6 can be your common denominator. Convert 2/3 to 4/6 by multiplying both numerator and denominator by 2. Now you have 4/6 + 1/6, which is much easier to solve.

Can I always multiply denominators together to find a common denominator?

Yes, multiplying denominators always works and is the safest method when you're unsure. For example, with 1/13 + 2/5, multiply 13 × 5 = 65 as your common denominator. However, this might not give you the smallest possible answer.

What common mistakes should I avoid when finding common denominators?

The biggest mistake is forgetting to multiply the numerator when you multiply the denominator. Other common errors include: not checking if a simpler common denominator exists, rushing to multiply denominators without trying easier methods first, and making arithmetic errors in the multiplication steps.

Continue Your Math Journey

Master Common Denominators first, then advance to these related topics that build on your fraction skills

Topics Learned in Later Sections

How do you simplify fractions?Simplification and Expansion of Simple Fractions

Practice by Question Type

Choose your preferred learning style and practice format for fraction problems

Finding a Common Denominator by Multiplying the Denominators More than two fractions One of the denominators is the common denominator The common denominator is smaller than the product of the denominators Worded problems

Common Denominators Practice Problems & Worksheets

Understanding Common Denominators

We will divide the search for the common denominator into 3 cases:

Practice Common Denominators

Examples with solutions for Common Denominators

Frequently Asked Questions

What is a common denominator and why do I need it?

What are the 3 methods for finding common denominators?

How do I know which method to use for finding common denominators?

When I change the denominator, do I need to change the numerator too?

What's the difference between common denominator and least common denominator?

How do I find common denominators for fractions like 2/3 and 1/6?

Can I always multiply denominators together to find a common denominator?

What common mistakes should I avoid when finding common denominators?

More Common Denominators Questions