What is 13/27 plus 9/13? (Answer: 412/351)

Exact Answer

==================================================
Problem: What is 13/27 plus 9/13?
Formula / Expression: 13/27 + 9/13
Final Answer: 1 61/351 (412/351)
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 27 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 27 × 13 = 351.
Working: LCD(27, 13) = 351

Step 2: Convert to Equivalent Fractions with Common Denominator 351
Multiply the numerator and denominator of 13/27 by 13, and multiply the numerator and denominator of 9/13 by 27 so both fractions share the common base 351.
Working: 13 × 13/27 × 13 = 169/351 and 9 × 27/13 × 27 = 243/351

Step 3: Add the Numerators
Now add the numerators (169 + 243 = 412) and keep the common denominator 351 unchanged.
Working: 169 + 243/351 = 412/351

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 412 and 351 is 1, confirming that 412/351 cannot be reduced further—it is already in its simplest irreducible form.
Working: 412/351

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (412) is greater than the denominator (351), divide 412 by 351: it goes in 1 whole time(s) with a remainder of 61, giving the mixed number 1 61/351.
Working: 412/351 = 1 61/351

Step 6: Decimal & Percentage Representation
Dividing the numerator 412 by denominator 351 produces a repeating decimal (approximately 1.173789, or 117.3789%).
Working: 412 ÷ 351 = 1.173789 (117.3789%)

Key Values:
- Simplified Fraction: 412/351
- Mixed Number Form: 1 61/351
- Decimal Value: 1.173789
- Percentage: 117.3789%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-27-plus-9-13/
==================================================

13/27 + 9/13 = 412/351

Simplified Fraction

412/351

Mixed Number

1 61/351

Decimal Value

1.173789

Percentage

117.3789%

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: 13/27 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 27 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 27 × 13 = 351.

LCD(27, 13) = 351

Step 2

Convert to Equivalent Fractions with Common Denominator 351

Multiply the numerator and denominator of 13/27 by 13, and multiply the numerator and denominator of 9/13 by 27 so both fractions share the common base 351.

13 × 13/27 × 13 = 169/351 and 9 × 27/13 × 27 = 243/351

Step 3

Add the Numerators

Now add the numerators (169 + 243 = 412) and keep the common denominator 351 unchanged.

169 + 243/351 = 412/351

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 412 and 351 is 1, confirming that 412/351 cannot be reduced further—it is already in its simplest irreducible form.

412/351

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (412) is greater than the denominator (351), divide 412 by 351: it goes in 1 whole time(s) with a remainder of 61, giving the mixed number 1 61/351.

412/351 = 161/351

Step 6

Decimal & Percentage Representation

Dividing the numerator 412 by denominator 351 produces a repeating decimal (approximately 1.173789, or 117.3789%).

412 ÷ 351 = 1.173789 (117.3789%)

Visual Representation

The diagram below illustrates 13/27 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`412/351`
Mixed Number Form	`1 61/351`
Decimal Form	`1.173789`
Percentage	`117.3789%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 13/27 plus 9/13 as a fraction?

13/27 + 9/13 in simplest fraction form is 412/351 (or 1 61/351 as a mixed number).

What is 13/27 plus 9/13 as a decimal?

13/27 + 9/13 converted to a decimal is 1.173789.

What is 13/27 plus 9/13 as a percentage?

13/27 + 9/13 expressed as a percentage is 117.3789%.

How do you write 13/27 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 412/351 can be written as the mixed number 1 61/351.

Does 13/27 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.173789...) because the denominator contains prime factors other than 2 and 5.