Solve the Fraction Equation: Finding the Missing Number in ? + 3/4 = 4/5

Q: Why can't I just subtract 4-3 and 5-4 to get 1/1?

Fractions don't work like that! You can only subtract the numerators when denominators are the same. Think of it like trying to subtract 4 apples from 5 oranges - they need to be the same "type" first.

Q: How do I find the least common denominator of 4 and 5?

Since 4 and 5 share no common factors (they're relatively prime), multiply them together: 4 × 5 = 20. This gives you the LCD you need!

Q: What if my answer seems too small?

Small answers like $ \frac{1}{20} $ are normal! Remember that $ \frac{3}{4} = 0.75 $ and $ \frac{4}{5} = 0.8 $, so the difference is only 0.05 = $ \frac{1}{20} $.

Q: Can I convert to decimals instead?

You could, but you might get rounding errors! $ \frac{3}{4} = 0.75 $ and $ \frac{4}{5} = 0.8 $, so x = 0.8 - 0.75 = 0.05. Converting back: 0.05 = $ \frac{5}{100} = \frac{1}{20} $.

Fraction Equations with Common Denominators

$?+\frac{3}{4}=\frac{4}{5}$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's find the unknown value.

00:09 First, arrange the equation and isolate the variable.

00:18 Next, find the least common denominator.

00:25 Multiply each fraction by the other fraction's denominator.

00:29 Be sure to multiply both the top, the numerator, and the bottom, t he denominator.

00:43 Now, calculate the products.

00:49 Add them together under the common denominator.

00:54 Finally, calculate the final numerator.

00:57 And that's how you solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$?+\frac{3}{4}=\frac{4}{5}$

Step-by-step solution

To solve this problem, we aim to find $x$ in the equation $x + \frac{3}{4} = \frac{4}{5}$ .

Step 1: Isolate $x$ by subtracting $\frac{3}{4}$ from both sides.

$x = \frac{4}{5} - \frac{3}{4}$

Step 2: Find a common denominator for the fractions $\frac{4}{5}$ and $\frac{3}{4}$ . The least common denominator of 5 and 4 is 20.

Convert $\frac{4}{5}$ to a fraction with a denominator of 20:

$\frac{4}{5} = \frac{4 \times 4}{5 \times 4} = \frac{16}{20}$

Convert $\frac{3}{4}$ to a fraction with a denominator of 20:

$\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}$

Step 3: Subtract the two fractions:

$x = \frac{16}{20} - \frac{15}{20} = \frac{16 - 15}{20} = \frac{1}{20}$

Therefore, the missing fraction $x$ is $\frac{1}{20}$ .

Final Answer

$\frac{1}{20}$

Key Points to Remember

Essential concepts to master this topic

Isolation: Subtract fractions from both sides to isolate variable
Common Denominator: Convert $\frac{4}{5}$ to $\frac{16}{20}$ and $\frac{3}{4}$ to $\frac{15}{20}$
Verification: Check that $\frac{1}{20} + \frac{3}{4} = \frac{1}{20} + \frac{15}{20} = \frac{16}{20} = \frac{4}{5}$ ✓

Common Mistakes

Avoid these frequent errors

Subtracting numerators without common denominators
Don't subtract $\frac{4}{5} - \frac{3}{4}$ as $\frac{4-3}{5-4} = \frac{1}{1} = 1$ ! You can't subtract fractions with different denominators directly. Always find the LCD (20) first, then convert both fractions before subtracting.

Practice Quiz

Test your knowledge with interactive questions

$\frac{1}{4}\times\frac{3}{2}=$

FAQ

Everything you need to know about this question

Why can't I just subtract 4-3 and 5-4 to get 1/1?

Fractions don't work like that! You can only subtract the numerators when denominators are the same. Think of it like trying to subtract 4 apples from 5 oranges - they need to be the same "type" first.

How do I find the least common denominator of 4 and 5?

Since 4 and 5 share no common factors (they're relatively prime), multiply them together: 4 × 5 = 20. This gives you the LCD you need!

What if my answer seems too small?

Small answers like $\frac{1}{20}$ are normal! Remember that $\frac{3}{4} = 0.75$ and $\frac{4}{5} = 0.8$ , so the difference is only 0.05 = $\frac{1}{20}$ .

Can I convert to decimals instead?

You could, but you might get rounding errors! $\frac{3}{4} = 0.75$ and $\frac{4}{5} = 0.8$ , so x = 0.8 - 0.75 = 0.05. Converting back: 0.05 = $\frac{5}{100} = \frac{1}{20}$ .

How do I check if 1/20 is in simplest form?

Check if 1 and 20 have any common factors besides 1. Since 1 only has itself as a factor, $\frac{1}{20}$ is already in simplest form!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Operations with Fractions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

Solve the Fraction Equation: Finding the Missing Number in ? + 3/4 = 4/5

Fraction Equations with Common Denominators

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why can't I just subtract 4-3 and 5-4 to get 1/1?

How do I find the least common denominator of 4 and 5?

What if my answer seems too small?

Can I convert to decimals instead?

How do I check if 1/20 is in simplest form?

🌟 Unlock Your Math Potential

More Questions

Addition of Fractions

Solve the Fraction Equation: Finding the Number Plus 1/6 = 2/3

Solve the Fraction Equation: Finding the Missing Number in ? + 1/3 = 2/5

Solve the Fraction Equation: Finding the Missing Number in 7/14 + ? = 1/2

Solve the Fraction Expression: 3/6 + 2/4 - 1/12

All Operations in Fractions

Solve the Fraction Equation: Finding the Missing Addend in 1/6 + ? = 1/2

Solve: Adding Fractions 3/5 + 2/7 Step by Step

Solve the Fraction Equation: Finding the Missing Addend in 2/9 + ? = 2/3

Solve the Fraction Equation: Find the Missing Addend in 1/10 + ? = 3/4