Solve for the Missing Fraction: 10/7 - ? = 5/7

Q: Why do I rearrange the equation instead of guessing?

Rearranging gives you the exact answer every time! Guessing might work sometimes, but algebra ensures you'll always be correct and understand the process.

Q: What if the denominators were different?

You'd need to find a common denominator first, then subtract the numerators. With same denominators like $ \frac{10}{7} $ and $ \frac{5}{7} $, you can subtract directly!

Q: How do I know which number to subtract from which?

Look at your rearranged equation: $ x = \frac{10}{7} - \frac{5}{7} $. The first number in the original equation minus the result gives you the missing fraction.

Q: Can I check my answer a different way?

Yes! Try substitution: Replace the blank with your answer $ \frac{5}{7} $ in the original equation. Does $ \frac{10}{7} - \frac{5}{7} = \frac{5}{7} $? Perfect!

Q: What if my answer doesn't look right?

Double-check your arithmetic! Make sure you're subtracting numerators (10 - 5 = 5) and keeping the same denominator (7). The missing fraction should always make the equation balanced.

Fraction Subtraction with Missing Terms

Complete the missing fraction
$\frac{10}{7}-_{——}=\frac{5}{7}$

What is the missing fraction?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:10 Let's find the missing fraction.

00:13 If the answer's denominator matches, then the missing denominator matches too.

00:21 Now, let's calculate using the numerators.

00:25 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the missing fraction
$\frac{10}{7}-_{——}=\frac{5}{7}$

What is the missing fraction?

Step-by-step solution

To find the missing fraction in the equation $\frac{10}{7} - \text{missing fraction} = \frac{5}{7}$ , follow these steps:

Step 1: Identify the given equation.
According to the problem, we have:

$\frac{10}{7} - \text{missing fraction} = \frac{5}{7}$

Step 2: Rearrange the equation to solve for the missing fraction.
If we let the missing fraction be $x$ , our equation becomes:

$\frac{10}{7} - x = \frac{5}{7}$

Step 3: Isolate $x$ by subtracting $\frac{5}{7}$ from both sides of the equation:

$x = \frac{10}{7} - \frac{5}{7}$

Step 4: Simplify the subtraction.
Since the denominators are the same, we subtract the numerators directly:

$x = \frac{10 - 5}{7}$

$x = \frac{5}{7}$

Therefore, the missing fraction in the equation is $\frac{5}{7}$ .

Final Answer

$\frac{5}{7}$

Key Points to Remember

Essential concepts to master this topic

Equation Setup: Rearrange to isolate the missing fraction variable
Technique: Subtract $\frac{5}{7}$ from $\frac{10}{7}$ gives $\frac{5}{7}$
Check: Verify $\frac{10}{7} - \frac{5}{7} = \frac{5}{7}$ works perfectly ✓

Common Mistakes

Avoid these frequent errors

Adding instead of subtracting to find the missing fraction
Don't add the known fractions together = $\frac{10}{7} + \frac{5}{7} = \frac{15}{7}$ ! This completely ignores the subtraction operation in the original equation. Always rearrange the equation properly by moving terms to isolate the unknown.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

$\frac{3}{2}-\frac{1}{2}=\text{?}$

FAQ

Everything you need to know about this question

Why do I rearrange the equation instead of guessing?

Rearranging gives you the exact answer every time! Guessing might work sometimes, but algebra ensures you'll always be correct and understand the process.

What if the denominators were different?

You'd need to find a common denominator first, then subtract the numerators. With same denominators like $\frac{10}{7}$ and $\frac{5}{7}$ , you can subtract directly!

How do I know which number to subtract from which?

Look at your rearranged equation: $x = \frac{10}{7} - \frac{5}{7}$ . The first number in the original equation minus the result gives you the missing fraction.

Can I check my answer a different way?

Yes! Try substitution: Replace the blank with your answer $\frac{5}{7}$ in the original equation. Does $\frac{10}{7} - \frac{5}{7} = \frac{5}{7}$ ? Perfect!

What if my answer doesn't look right?

Double-check your arithmetic! Make sure you're subtracting numerators (10 - 5 = 5) and keeping the same denominator (7). The missing fraction should always make the equation balanced.

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