What is 3/5 plus 11/13? (Answer: 94/65)

Exact Answer

==================================================
Problem: What is 3/5 plus 11/13?
Formula / Expression: 3/5 + 11/13
Final Answer: 1 29/65 (94/65)
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 5 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 13 = 65.
Working: LCD(5, 13) = 65

Step 2: Convert to Equivalent Fractions with Common Denominator 65
Multiply the numerator and denominator of 3/5 by 13, and multiply the numerator and denominator of 11/13 by 5 so both fractions share the common base 65.
Working: 3 × 13/5 × 13 = 39/65 and 11 × 5/13 × 5 = 55/65

Step 3: Add the Numerators
Now add the numerators (39 + 55 = 94) and keep the common denominator 65 unchanged.
Working: 39 + 55/65 = 94/65

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 94 and 65 is 1, confirming that 94/65 cannot be reduced further—it is already in its simplest irreducible form.
Working: 94/65

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (94) is greater than the denominator (65), divide 94 by 65: it goes in 1 whole time(s) with a remainder of 29, giving the mixed number 1 29/65.
Working: 94/65 = 1 29/65

Step 6: Decimal & Percentage Representation
Dividing the numerator 94 by denominator 65 produces a repeating decimal (approximately 1.446154, or 144.6154%).
Working: 94 ÷ 65 = 1.446154 (144.6154%)

Key Values:
- Simplified Fraction: 94/65
- Mixed Number Form: 1 29/65
- Decimal Value: 1.446154
- Percentage: 144.6154%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-5-plus-11-13/
==================================================

3/5 + 11/13 = 94/65

Simplified Fraction

94/65

Mixed Number

1 29/65

Decimal Value

1.446154

Percentage

144.6154%

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: 3/5 + 11/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 5 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 13 = 65.

LCD(5, 13) = 65

Step 2

Convert to Equivalent Fractions with Common Denominator 65

Multiply the numerator and denominator of 3/5 by 13, and multiply the numerator and denominator of 11/13 by 5 so both fractions share the common base 65.

3 × 13/5 × 13 = 39/65 and 11 × 5/13 × 5 = 55/65

Step 3

Add the Numerators

Now add the numerators (39 + 55 = 94) and keep the common denominator 65 unchanged.

39 + 55/65 = 94/65

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 94 and 65 is 1, confirming that 94/65 cannot be reduced further—it is already in its simplest irreducible form.

94/65

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (94) is greater than the denominator (65), divide 94 by 65: it goes in 1 whole time(s) with a remainder of 29, giving the mixed number 1 29/65.

94/65 = 129/65

Step 6

Decimal & Percentage Representation

Dividing the numerator 94 by denominator 65 produces a repeating decimal (approximately 1.446154, or 144.6154%).

94 ÷ 65 = 1.446154 (144.6154%)

Visual Representation

The diagram below illustrates 3/5 plus 11/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`94/65`
Mixed Number Form	`1 29/65`
Decimal Form	`1.446154`
Percentage	`144.6154%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 3/5 plus 11/13 as a fraction?

3/5 + 11/13 in simplest fraction form is 94/65 (or 1 29/65 as a mixed number).

What is 3/5 plus 11/13 as a decimal?

3/5 + 11/13 converted to a decimal is 1.446154.

What is 3/5 plus 11/13 as a percentage?

3/5 + 11/13 expressed as a percentage is 144.6154%.

How do you write 3/5 plus 11/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 94/65 can be written as the mixed number 1 29/65.

Does 3/5 plus 11/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.446154...) because the denominator contains prime factors other than 2 and 5.