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

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the unknown

00:04 Arrange the equation and isolate the unknown

00:13 We want to find the least common denominator

00:20 Multiply each fraction by the other denominator to find the common denominator

00:24 Remember to multiply both numerator and denominator

00:38 Calculate the products

00:44 Add under the common denominator

00:49 Calculate the numerator

00:52 And this is the solution to the question

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

Complete the following exercise:

$\frac{3}{4}:\frac{5}{6}=\text{?}$

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!

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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

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