What is 4/13 plus 2/4? (Answer: 21/26)

Exact Answer

==================================================
Problem: What is 4/13 plus 2/4?
Formula / Expression: 4/13 + 2/4
Final Answer: 21/26
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 4 = 52.
Working: LCD(13, 4) = 52

Step 2: Convert to Equivalent Fractions with Common Denominator 52
Multiply the numerator and denominator of 4/13 by 4, and multiply the numerator and denominator of 2/4 by 13 so both fractions share the common base 52.
Working: 4 × 4/13 × 4 = 16/52 and 2 × 13/4 × 13 = 26/52

Step 3: Add the Numerators
Now add the numerators (16 + 26 = 42) and keep the common denominator 52 unchanged.
Working: 16 + 26/52 = 42/52

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 42 and 52, which is 2. Divide both the numerator and denominator by 2.
Working: 42 ÷ 2/52 ÷ 2 = 21/26

Step 5: Decimal & Percentage Representation
Dividing the numerator 21 by denominator 26 produces a repeating decimal (approximately 0.807692, or 80.7692%).
Working: 21 ÷ 26 = 0.807692 (80.7692%)

Key Values:
- Simplified Fraction: 21/26
- Mixed Number Form: 21/26
- Decimal Value: 0.807692
- Percentage: 80.7692%

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

4/13 + 2/4 = 21/26

Simplified Fraction

21/26

Mixed Number

Proper (21/26)

Decimal Value

0.807692

Percentage

80.7692%

Reduce / Convert Fraction:

Convert Fraction:

Enter Decimal Number:

Enter Percentage: %

What is % of

From Value: To Value:

Simplify Ratio: :

Switch to Proportion / Missing X Solver (A/B = C/D) →

Enter 3 known numbers and leave 1 empty (or type x) to solve:

← Switch to Ratio Simplifier (A:B)

Provide any 2 values below to calculate the remaining:

Price before discount

Discount

Price after discount

You saved

+ Add Sales Tax & Extra Coupon (Optional)

Sales Tax: % Extra Off: %

Provide any 2 values below to calculate the remaining:

Cost

Markup

REVENUE

Gross Profit

Profit Margin

Bill Subtotal

Tip Percentage

Split (People)

👥

Quick Tip:

Total Bill

Split Between

👥

Tip % (Optional)

Include Tip:

Total Price

Quantity

Unit of Measure

← Discount & Sales Tax • Ratio Simplifier (A:B) →

First Number: Second Number:

Find All Factors of:

Dividend: ÷ Divisor:

Number to Round: To Nearest:

Method: Standard (5+ ↑) Always Up (Ceil) Always Down (Floor)

Presets:

√ Square Root of: OR Power (x^y): ^{^}

x² + x + = 0

Number (n! & log):

Circle Radius (r):

Side a: Side b:

Angle (Degrees): °

Numbers (comma separated):

Total Items (n): Choose (r):

Decimal Number:

Number (1–3999):

Step-by-Step Solution: 4/13 + 2/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 4 = 52.

LCD(13, 4) = 52

Step 2

Convert to Equivalent Fractions with Common Denominator 52

Multiply the numerator and denominator of 4/13 by 4, and multiply the numerator and denominator of 2/4 by 13 so both fractions share the common base 52.

4 × 4/13 × 4 = 16/52 and 2 × 13/4 × 13 = 26/52

Step 3

Add the Numerators

Now add the numerators (16 + 26 = 42) and keep the common denominator 52 unchanged.

16 + 26/52 = 42/52

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 42 and 52, which is 2. Divide both the numerator and denominator by 2.

42 ÷ 2/52 ÷ 2 = 21/26

Step 5

Decimal & Percentage Representation

Dividing the numerator 21 by denominator 26 produces a repeating decimal (approximately 0.807692, or 80.7692%).

21 ÷ 26 = 0.807692 (80.7692%)

Visual Representation

The diagram below illustrates 4/13 plus 2/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`21/26`
Mixed Number Form	`21/26`
Decimal Form	`0.807692`
Percentage	`80.7692%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 4/13 plus 2/4 as a fraction?

4/13 + 2/4 in simplest fraction form is 21/26.

What is 4/13 plus 2/4 as a decimal?

4/13 + 2/4 converted to a decimal is 0.807692.

What is 4/13 plus 2/4 as a percentage?

4/13 + 2/4 expressed as a percentage is 80.7692%.

Does 4/13 plus 2/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.807692...) because the denominator contains prime factors other than 2 and 5.