What is 3/52 plus 7/13? (Answer: 31/52)

Exact Answer

==================================================
Problem: What is 3/52 plus 7/13?
Formula / Expression: 3/52 + 7/13
Final Answer: 31/52
==================================================

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 3/52 by 1, and multiply the numerator and denominator of 7/13 by 4 so both fractions share the common base 52.
Working: 3 × 1/52 × 1 = 3/52 and 7 × 4/13 × 4 = 28/52

Step 3: Add the Numerators
Now add the numerators (3 + 28 = 31) and keep the common denominator 52 unchanged.
Working: 3 + 28/52 = 31/52

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 31 and 52 is 1, confirming that 31/52 cannot be reduced further—it is already in its simplest irreducible form.
Working: 31/52

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 52 produces a repeating decimal (approximately 0.596154, or 59.6154%).
Working: 31 ÷ 52 = 0.596154 (59.6154%)

Key Values:
- Simplified Fraction: 31/52
- Mixed Number Form: 31/52
- Decimal Value: 0.596154
- Percentage: 59.6154%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-52-plus-7-13/
==================================================

3/52 + 7/13 = 31/52

Simplified Fraction

31/52

Mixed Number

Proper (31/52)

Decimal Value

0.596154

Percentage

59.6154%

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: 3/52 + 7/13

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 3/52 by 1, and multiply the numerator and denominator of 7/13 by 4 so both fractions share the common base 52.

3 × 1/52 × 1 = 3/52 and 7 × 4/13 × 4 = 28/52

Step 3

Add the Numerators

Now add the numerators (3 + 28 = 31) and keep the common denominator 52 unchanged.

3 + 28/52 = 31/52

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 31 and 52 is 1, confirming that 31/52 cannot be reduced further—it is already in its simplest irreducible form.

31/52

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 52 produces a repeating decimal (approximately 0.596154, or 59.6154%).

31 ÷ 52 = 0.596154 (59.6154%)

Visual Representation

The diagram below illustrates 3/52 plus 7/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/52`
Mixed Number Form	`31/52`
Decimal Form	`0.596154`
Percentage	`59.6154%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 3/52 plus 7/13 as a fraction?

3/52 + 7/13 in simplest fraction form is 31/52.

What is 3/52 plus 7/13 as a decimal?

3/52 + 7/13 converted to a decimal is 0.596154.

What is 3/52 plus 7/13 as a percentage?

3/52 + 7/13 expressed as a percentage is 59.6154%.

Does 3/52 plus 7/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.596154...) because the denominator contains prime factors other than 2 and 5.