Adding Fractions: Solve 4/7 + 3/7 Step by Step

Q: Why don't I add the denominators together?

The denominator tells you what size pieces you're working with. Since both fractions use sevenths, you're adding pieces of the same size. Adding denominators would change the piece size, giving you the wrong answer!

Q: How do I know when a fraction equals a whole number?

When the numerator equals the denominator, the fraction equals 1. When the numerator is a multiple of the denominator, you get a whole number. For example: $ \frac{14}{7} = 2 $

Q: What if the fractions had different denominators?

Then you'd need to find a common denominator first! Convert both fractions to equivalent fractions with the same denominator, then add the numerators.

Q: Do I always need to simplify my answer?

Yes, always simplify! Check if the numerator and denominator share any common factors. In this case, $ \frac{7}{7} $ simplifies to the whole number 1.

Fraction Addition with Same Denominators

Solve the following exercise:

$\frac{4}{7}+\frac{3}{7}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Let's add the fractions under a common denominator

00:11 Let's calculate the numerator

00:15 Any fraction where the numerator equals the denominator equals 1

00:18 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:

$\frac{4}{7}+\frac{3}{7}=\text{?}$

Step-by-step solution

To solve the addition of the two fractions $\frac{4}{7} + \frac{3}{7}$ , follow these steps:

Step 1: Since both fractions have the same denominator, add the numerators directly: $4 + 3 = 7$ .
Step 2: Retain the common denominator: $7$ .
Step 3: The resulting fraction after addition is $\frac{7}{7}$ .
Step 4: Simplify the resulting fraction if possible. Since $\frac{7}{7} = 1$ , the simplified result is $1$ .

Therefore, the solution to the problem is 1.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Same Denominator Rule: Add numerators, keep the denominator unchanged
Addition Technique: $\frac{4}{7} + \frac{3}{7} = \frac{4+3}{7} = \frac{7}{7}$
Simplification Check: $\frac{7}{7} = 1$ because numerator equals denominator ✓

Common Mistakes

Avoid these frequent errors

Adding both numerators and denominators
Don't add denominators: $\frac{4}{7} + \frac{3}{7} \neq \frac{7}{14}$ ! This creates a completely different fraction with wrong value. Always keep the same denominator and only add the numerators.

Practice Quiz

Test your knowledge with interactive questions

$$ $\frac{4}{5}+\frac{1}{5}=$

FAQ

Everything you need to know about this question

Why don't I add the denominators together?

The denominator tells you what size pieces you're working with. Since both fractions use sevenths, you're adding pieces of the same size. Adding denominators would change the piece size, giving you the wrong answer!

How do I know when a fraction equals a whole number?

When the numerator equals the denominator, the fraction equals 1. When the numerator is a multiple of the denominator, you get a whole number. For example: $\frac{14}{7} = 2$

What if the fractions had different denominators?

Then you'd need to find a common denominator first! Convert both fractions to equivalent fractions with the same denominator, then add the numerators.

Do I always need to simplify my answer?

Yes, always simplify! Check if the numerator and denominator share any common factors. In this case, $\frac{7}{7}$ simplifies to the whole number 1.

How can I check if my answer is correct?

Convert your answer back to the original denominator and see if it makes sense. Here, 1 = $\frac{7}{7}$ , and 4 + 3 = 7, so our work is correct! ✓

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