What is 3/13 plus 5/9? (Answer: 92/117)

Exact Answer

==================================================
Problem: What is 3/13 plus 5/9?
Formula / Expression: 3/13 + 5/9
Final Answer: 92/117
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 9 = 117.
Working: LCD(13, 9) = 117

Step 2: Convert to Equivalent Fractions with Common Denominator 117
Multiply the numerator and denominator of 3/13 by 9, and multiply the numerator and denominator of 5/9 by 13 so both fractions share the common base 117.
Working: 3 × 9/13 × 9 = 27/117 and 5 × 13/9 × 13 = 65/117

Step 3: Add the Numerators
Now add the numerators (27 + 65 = 92) and keep the common denominator 117 unchanged.
Working: 27 + 65/117 = 92/117

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 92 and 117 is 1, confirming that 92/117 cannot be reduced further—it is already in its simplest irreducible form.
Working: 92/117

Step 5: Decimal & Percentage Representation
Dividing the numerator 92 by denominator 117 produces a repeating decimal (approximately 0.786325, or 78.6325%).
Working: 92 ÷ 117 = 0.786325 (78.6325%)

Key Values:
- Simplified Fraction: 92/117
- Mixed Number Form: 92/117
- Decimal Value: 0.786325
- Percentage: 78.6325%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-13-plus-5-9/
==================================================

3/13 + 5/9 = 92/117

Simplified Fraction

92/117

Mixed Number

Proper (92/117)

Decimal Value

0.786325

Percentage

78.6325%

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: 3/13 + 5/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 9 = 117.

LCD(13, 9) = 117

Step 2

Convert to Equivalent Fractions with Common Denominator 117

Multiply the numerator and denominator of 3/13 by 9, and multiply the numerator and denominator of 5/9 by 13 so both fractions share the common base 117.

3 × 9/13 × 9 = 27/117 and 5 × 13/9 × 13 = 65/117

Step 3

Add the Numerators

Now add the numerators (27 + 65 = 92) and keep the common denominator 117 unchanged.

27 + 65/117 = 92/117

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 92 and 117 is 1, confirming that 92/117 cannot be reduced further—it is already in its simplest irreducible form.

92/117

Step 5

Decimal & Percentage Representation

Dividing the numerator 92 by denominator 117 produces a repeating decimal (approximately 0.786325, or 78.6325%).

92 ÷ 117 = 0.786325 (78.6325%)

Visual Representation

The diagram below illustrates 3/13 plus 5/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`92/117`
Mixed Number Form	`92/117`
Decimal Form	`0.786325`
Percentage	`78.6325%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 3/13 plus 5/9 as a fraction?

3/13 + 5/9 in simplest fraction form is 92/117.

What is 3/13 plus 5/9 as a decimal?

3/13 + 5/9 converted to a decimal is 0.786325.

What is 3/13 plus 5/9 as a percentage?

3/13 + 5/9 expressed as a percentage is 78.6325%.

Does 3/13 plus 5/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.786325...) because the denominator contains prime factors other than 2 and 5.