What is 3/9 plus 5/13? (Answer: 28/39)

Exact Answer

==================================================
Problem: What is 3/9 plus 5/13?
Formula / Expression: 3/9 + 5/13
Final Answer: 28/39
==================================================

Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 117
Multiply the numerator and denominator of 3/9 by 13, and multiply the numerator and denominator of 5/13 by 9 so both fractions share the common base 117.
Working: 3 × 13/9 × 13 = 39/117 and 5 × 9/13 × 9 = 45/117

Step 3: Add the Numerators
Now add the numerators (39 + 45 = 84) and keep the common denominator 117 unchanged.
Working: 39 + 45/117 = 84/117

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 84 and 117, which is 3. Divide both the numerator and denominator by 3.
Working: 84 ÷ 3/117 ÷ 3 = 28/39

Step 5: Decimal & Percentage Representation
Dividing the numerator 28 by denominator 39 produces a repeating decimal (approximately 0.717949, or 71.7949%).
Working: 28 ÷ 39 = 0.717949 (71.7949%)

Key Values:
- Simplified Fraction: 28/39
- Mixed Number Form: 28/39
- Decimal Value: 0.717949
- Percentage: 71.7949%

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

3/9 + 5/13 = 28/39

Simplified Fraction

28/39

Mixed Number

Proper (28/39)

Decimal Value

0.717949

Percentage

71.7949%

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: 3/9 + 5/13

Step 1

Find the Least Common Denominator (LCD)

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

LCD(9, 13) = 117

Step 2

Convert to Equivalent Fractions with Common Denominator 117

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

3 × 13/9 × 13 = 39/117 and 5 × 9/13 × 9 = 45/117

Step 3

Add the Numerators

Now add the numerators (39 + 45 = 84) and keep the common denominator 117 unchanged.

39 + 45/117 = 84/117

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 84 and 117, which is 3. Divide both the numerator and denominator by 3.

84 ÷ 3/117 ÷ 3 = 28/39

Step 5

Decimal & Percentage Representation

Dividing the numerator 28 by denominator 39 produces a repeating decimal (approximately 0.717949, or 71.7949%).

28 ÷ 39 = 0.717949 (71.7949%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`28/39`
Mixed Number Form	`28/39`
Decimal Form	`0.717949`
Percentage	`71.7949%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

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

3/9 + 5/13 in simplest fraction form is 28/39.

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

3/9 + 5/13 converted to a decimal is 0.717949.

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

3/9 + 5/13 expressed as a percentage is 71.7949%.

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

It results in a repeating decimal (approximately 0.717949...) because the denominator contains prime factors other than 2 and 5.