Solve Fraction Addition: 1/4 + 4/9 Step-by-Step

Q: Why can't I just add 1/4 + 4/9 directly?

You can only add fractions when they have the same denominator. Think of it like adding different sized pieces - you need to make them the same size first!

Q: What's the pattern when multiplying to get equivalent fractions?

When converting to LCD 36: multiply $ \frac{1}{4} $ by $ \frac{9}{9} $ and $ \frac{4}{9} $ by $ \frac{4}{4} $. Notice: 36 ÷ 4 = 9 and 36 ÷ 9 = 4!

Fraction Addition with Different Denominators

Solve the following exercise:

$\frac{1}{4}+\frac{4}{9}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's solve this problem together.

00:08 First, multiply each fraction by the second denominator, to find a common denominator.

00:14 Remember, multiply both the top number, called the numerator, and the bottom number, called the denominator.

00:21 Now, go ahead. Calculate these multiplications.

00:27 Great job! Now, add the fractions using the common denominator.

00:33 Next, calculate the total for the numerators.

00:37 And there you have it. That's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$\frac{1}{4}+\frac{4}{9}=$

Step-by-step solution

Let's try to find the lowest common denominator between 4 and 9

To find the lowest common denominator, we need to find a number that is divisible by both 4 and 9

In this case, the common denominator is 36

Now we'll multiply each fraction by the appropriate number to reach the denominator 36

We'll multiply the first fraction by 9

We'll multiply the second fraction by 4

$\frac{1\times9}{4\times9}+\frac{4\times4}{9\times4}=\frac{9}{36}+\frac{16}{36}$

Now we'll combine and get:

$\frac{9+16}{36}=\frac{25}{36}$

Final Answer

$\frac{25}{36}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find LCD before adding fractions with different denominators
Technique: Multiply $\frac{1}{4}$ by 9 and $\frac{4}{9}$ by 4 for LCD 36
Check: Verify numerator addition: 9 + 16 = 25, so $\frac{25}{36}$ ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add 1+4=5 and 4+9=13 to get $\frac{5}{13}$ ! This ignores the fundamental rule that fractions must have the same denominator before adding. Always find the LCD first, then convert both fractions.

Practice Quiz

Test your knowledge with interactive questions

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

$$ 5:6= $$

FAQ

Everything you need to know about this question

How do I find the LCD of 4 and 9?

List the multiples of each number: 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36... and 9 = 9, 18, 27, 36... The first number that appears in both lists is your LCD!

Why can't I just add 1/4 + 4/9 directly?

You can only add fractions when they have the same denominator. Think of it like adding different sized pieces - you need to make them the same size first!

What if 36 isn't the smallest common denominator?

Great thinking! Always check: 36 ÷ 4 = 9 and 36 ÷ 9 = 4. Since 4 and 9 share no common factors except 1, their LCD is indeed 4 × 9 = 36.

Do I need to simplify 25/36?

Check if 25 and 36 share any common factors. Since 25 = 5² and 36 = 2² × 3², they have no common factors. So $\frac{25}{36}$ is already in simplest form!

What's the pattern when multiplying to get equivalent fractions?

When converting to LCD 36: multiply $\frac{1}{4}$ by $\frac{9}{9}$ and $\frac{4}{9}$ by $\frac{4}{4}$ . Notice: 36 ÷ 4 = 9 and 36 ÷ 9 = 4!

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