Solve the Fraction Subtraction: 7/12 minus 5/12

Q: Why can I subtract the numerators directly?

When fractions have the same denominator, you're working with the same-sized pieces! Think of it like having 7 pizza slices and eating 5 - you have 2 slices left, all from the same pizza cut into 12 pieces.

Q: How do I know when to simplify my answer?

Always check if you can simplify! Look for common factors in the numerator and denominator. For $ \frac{2}{12} $, both 2 and 12 are divisible by 2, so you get $ \frac{1}{6} $.

Q: What if the denominators were different?

Then you'd need to find a common denominator first! But in this problem, both fractions already have denominator 12, so you can subtract directly.

Q: Can the answer be larger than the original fractions?

No! When subtracting fractions, your answer will always be smaller than the first fraction. Here, $ \frac{1}{6} $ is indeed smaller than $ \frac{7}{12} $.

Fraction Subtraction with Same Denominators

Solve the following exercise:

$\frac{7}{12}-\frac{5}{12}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Subtract in the common denominator

00:09 Calculate the numerator

00:12 Reduce the fraction as much as possible

00:16 Make sure to divide both numerator and denominator

00:23 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

Solve the following exercise:

$\frac{7}{12}-\frac{5}{12}=\text{?}$

Step-by-step solution

The problem requires us to subtract the fraction $\frac{5}{12}$ from $\frac{7}{12}$ . Since both fractions have the same denominator, we can directly subtract their numerators while keeping the denominator constant:

The calculation is as follows:

Subtract the numerators: $7 - 5 = 2$ .
Keep the denominator the same: 12.
Thus, $\frac{7}{12} - \frac{5}{12} = \frac{2}{12}$ . Simplifying $\frac{2}{12}$ by dividing both the numerator and denominator by their greatest common divisor, which is 2, we get $\frac{1}{6}$ .

After performing the simplification, the answer to the problem is $\frac{1}{6}$ .

From the answer choices given, $\frac{1}{6}$ corresponds to choice 2.

Therefore, the solution to the problem is $\frac{1}{6}$ .

Final Answer

$\frac{1}{6}$

Key Points to Remember

Essential concepts to master this topic

Rule: Same denominators mean subtract numerators, keep denominator unchanged
Technique: Calculate 7 - 5 = 2, then simplify $\frac{2}{12}$ to lowest terms
Check: Verify $\frac{1}{6} = \frac{2}{12}$ by cross-multiplying: 1×12 = 2×6 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to simplify the final answer
Don't leave $\frac{2}{12}$ as your final answer = incorrect simplified form! This misses the crucial last step and loses points. Always reduce fractions to lowest terms by dividing both numerator and denominator by their GCD.

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 can I subtract the numerators directly?

When fractions have the same denominator, you're working with the same-sized pieces! Think of it like having 7 pizza slices and eating 5 - you have 2 slices left, all from the same pizza cut into 12 pieces.

How do I know when to simplify my answer?

Always check if you can simplify! Look for common factors in the numerator and denominator. For $\frac{2}{12}$ , both 2 and 12 are divisible by 2, so you get $\frac{1}{6}$ .

What if the denominators were different?

Then you'd need to find a common denominator first! But in this problem, both fractions already have denominator 12, so you can subtract directly.

Can the answer be larger than the original fractions?

No! When subtracting fractions, your answer will always be smaller than the first fraction. Here, $\frac{1}{6}$ is indeed smaller than $\frac{7}{12}$ .

How do I find the greatest common divisor to simplify?

List the factors of both numbers and find the largest one they share. For 2 and 12: factors of 2 are {1, 2}, factors of 12 are {1, 2, 3, 4, 6, 12}. The GCD is 2.

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