What is 2/39 plus 10/13? (Answer: 32/39)

Exact Answer

==================================================
Problem: What is 2/39 plus 10/13?
Formula / Expression: 2/39 + 10/13
Final Answer: 32/39
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 39 is an exact multiple of 13 (13 × 3 = 39). The Least Common Denominator (LCD) is simply 39, meaning we only need to scale one fraction.
Working: LCD(39, 13) = 39

Step 2: Convert to Equivalent Fractions with Common Denominator 39
Multiply the numerator and denominator of 2/39 by 1, and multiply the numerator and denominator of 10/13 by 3 so both fractions share the common base 39.
Working: 2 × 1/39 × 1 = 2/39 and 10 × 3/13 × 3 = 30/39

Step 3: Add the Numerators
Now add the numerators (2 + 30 = 32) and keep the common denominator 39 unchanged.
Working: 2 + 30/39 = 32/39

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 32 and 39 is 1, confirming that 32/39 cannot be reduced further—it is already in its simplest irreducible form.
Working: 32/39

Step 5: Decimal & Percentage Representation
Dividing the numerator 32 by denominator 39 produces a repeating decimal (approximately 0.820513, or 82.0513%).
Working: 32 ÷ 39 = 0.820513 (82.0513%)

Key Values:
- Simplified Fraction: 32/39
- Mixed Number Form: 32/39
- Decimal Value: 0.820513
- Percentage: 82.0513%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-39-plus-10-13/
==================================================

2/39 + 10/13 = 32/39

Simplified Fraction

32/39

Mixed Number

Proper (32/39)

Decimal Value

0.820513

Percentage

82.0513%

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: 2/39 + 10/13

Step 1

Find the Least Common Denominator (LCD)

Notice that 39 is an exact multiple of 13 (13 × 3 = 39). The Least Common Denominator (LCD) is simply 39, meaning we only need to scale one fraction.

LCD(39, 13) = 39

Step 2

Convert to Equivalent Fractions with Common Denominator 39

Multiply the numerator and denominator of 2/39 by 1, and multiply the numerator and denominator of 10/13 by 3 so both fractions share the common base 39.

2 × 1/39 × 1 = 2/39 and 10 × 3/13 × 3 = 30/39

Step 3

Add the Numerators

Now add the numerators (2 + 30 = 32) and keep the common denominator 39 unchanged.

2 + 30/39 = 32/39

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 32 and 39 is 1, confirming that 32/39 cannot be reduced further—it is already in its simplest irreducible form.

32/39

Step 5

Decimal & Percentage Representation

Dividing the numerator 32 by denominator 39 produces a repeating decimal (approximately 0.820513, or 82.0513%).

32 ÷ 39 = 0.820513 (82.0513%)

Visual Representation

The diagram below illustrates 2/39 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`32/39`
Mixed Number Form	`32/39`
Decimal Form	`0.820513`
Percentage	`82.0513%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 2/39 plus 10/13 as a fraction?

2/39 + 10/13 in simplest fraction form is 32/39.

What is 2/39 plus 10/13 as a decimal?

2/39 + 10/13 converted to a decimal is 0.820513.

What is 2/39 plus 10/13 as a percentage?

2/39 + 10/13 expressed as a percentage is 82.0513%.

Does 2/39 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.820513...) because the denominator contains prime factors other than 2 and 5.