What is 3/7 plus 2/4? (Answer: 13/14)

Exact Answer

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Problem: What is 3/7 plus 2/4?
Formula / Expression: 3/7 + 2/4
Final Answer: 13/14
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 4 = 28.
Working: LCD(7, 4) = 28

Step 2: Convert to Equivalent Fractions with Common Denominator 28
Multiply the numerator and denominator of 3/7 by 4, and multiply the numerator and denominator of 2/4 by 7 so both fractions share the common base 28.
Working: 3 × 4/7 × 4 = 12/28 and 2 × 7/4 × 7 = 14/28

Step 3: Add the Numerators
Now add the numerators (12 + 14 = 26) and keep the common denominator 28 unchanged.
Working: 12 + 14/28 = 26/28

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 26 and 28, which is 2. Divide both the numerator and denominator by 2.
Working: 26 ÷ 2/28 ÷ 2 = 13/14

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 14 produces a repeating decimal (approximately 0.928571, or 92.8571%).
Working: 13 ÷ 14 = 0.928571 (92.8571%)

Key Values:
- Simplified Fraction: 13/14
- Mixed Number Form: 13/14
- Decimal Value: 0.928571
- Percentage: 92.8571%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-7-plus-2-4/
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3/7 + 2/4 = 13/14

Simplified Fraction

13/14

Mixed Number

Proper (13/14)

Decimal Value

0.928571

Percentage

92.8571%

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Step-by-Step Solution: 3/7 + 2/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 4 = 28.

LCD(7, 4) = 28

Step 2

Convert to Equivalent Fractions with Common Denominator 28

Multiply the numerator and denominator of 3/7 by 4, and multiply the numerator and denominator of 2/4 by 7 so both fractions share the common base 28.

3 × 4/7 × 4 = 12/28 and 2 × 7/4 × 7 = 14/28

Step 3

Add the Numerators

Now add the numerators (12 + 14 = 26) and keep the common denominator 28 unchanged.

12 + 14/28 = 26/28

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 26 and 28, which is 2. Divide both the numerator and denominator by 2.

26 ÷ 2/28 ÷ 2 = 13/14

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 14 produces a repeating decimal (approximately 0.928571, or 92.8571%).

13 ÷ 14 = 0.928571 (92.8571%)

Visual Representation

The diagram below illustrates 3/7 plus 2/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/14`
Mixed Number Form	`13/14`
Decimal Form	`0.928571`
Percentage	`92.8571%`

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Frequently Asked Questions

What is 3/7 plus 2/4 as a fraction?

3/7 + 2/4 in simplest fraction form is 13/14.

What is 3/7 plus 2/4 as a decimal?

3/7 + 2/4 converted to a decimal is 0.928571.

What is 3/7 plus 2/4 as a percentage?

3/7 + 2/4 expressed as a percentage is 92.8571%.

Does 3/7 plus 2/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.928571...) because the denominator contains prime factors other than 2 and 5.