What is 4/52 plus 4/13? (Answer: 5/13)

Exact Answer

==================================================
Problem: What is 4/52 plus 4/13?
Formula / Expression: 4/52 + 4/13
Final Answer: 5/13
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 52 is an exact multiple of 13 (13 × 4 = 52). The Least Common Denominator (LCD) is simply 52, meaning we only need to scale one fraction.
Working: LCD(52, 13) = 52

Step 2: Convert to Equivalent Fractions with Common Denominator 52
Multiply the numerator and denominator of 4/52 by 1, and multiply the numerator and denominator of 4/13 by 4 so both fractions share the common base 52.
Working: 4 × 1/52 × 1 = 4/52 and 4 × 4/13 × 4 = 16/52

Step 3: Add the Numerators
Now add the numerators (4 + 16 = 20) and keep the common denominator 52 unchanged.
Working: 4 + 16/52 = 20/52

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 20 and 52, which is 4. Divide both the numerator and denominator by 4.
Working: 20 ÷ 4/52 ÷ 4 = 5/13

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 13 produces a repeating decimal (approximately 0.384615, or 38.4615%).
Working: 5 ÷ 13 = 0.384615 (38.4615%)

Key Values:
- Simplified Fraction: 5/13
- Mixed Number Form: 5/13
- Decimal Value: 0.384615
- Percentage: 38.4615%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-52-plus-4-13/
==================================================

4/52 + 4/13 = 5/13

Simplified Fraction

5/13

Mixed Number

Proper (5/13)

Decimal Value

0.384615

Percentage

38.4615%

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: 4/52 + 4/13

Step 1

Find the Least Common Denominator (LCD)

Notice that 52 is an exact multiple of 13 (13 × 4 = 52). The Least Common Denominator (LCD) is simply 52, meaning we only need to scale one fraction.

LCD(52, 13) = 52

Step 2

Convert to Equivalent Fractions with Common Denominator 52

Multiply the numerator and denominator of 4/52 by 1, and multiply the numerator and denominator of 4/13 by 4 so both fractions share the common base 52.

4 × 1/52 × 1 = 4/52 and 4 × 4/13 × 4 = 16/52

Step 3

Add the Numerators

Now add the numerators (4 + 16 = 20) and keep the common denominator 52 unchanged.

4 + 16/52 = 20/52

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 20 and 52, which is 4. Divide both the numerator and denominator by 4.

20 ÷ 4/52 ÷ 4 = 5/13

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 13 produces a repeating decimal (approximately 0.384615, or 38.4615%).

5 ÷ 13 = 0.384615 (38.4615%)

Visual Representation

The diagram below illustrates 4/52 plus 4/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/13`
Mixed Number Form	`5/13`
Decimal Form	`0.384615`
Percentage	`38.4615%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 4/52 plus 4/13 as a fraction?

4/52 + 4/13 in simplest fraction form is 5/13.

What is 4/52 plus 4/13 as a decimal?

4/52 + 4/13 converted to a decimal is 0.384615.

What is 4/52 plus 4/13 as a percentage?

4/52 + 4/13 expressed as a percentage is 38.4615%.

Does 4/52 plus 4/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.384615...) because the denominator contains prime factors other than 2 and 5.