What is 11/33 plus 9/13? (Answer: 40/39)

Exact Answer

==================================================
Problem: What is 11/33 plus 9/13?
Formula / Expression: 11/33 + 9/13
Final Answer: 1 1/39 (40/39)
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 33 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 33 × 13 = 429.
Working: LCD(33, 13) = 429

Step 2: Convert to Equivalent Fractions with Common Denominator 429
Multiply the numerator and denominator of 11/33 by 13, and multiply the numerator and denominator of 9/13 by 33 so both fractions share the common base 429.
Working: 11 × 13/33 × 13 = 143/429 and 9 × 33/13 × 33 = 297/429

Step 3: Add the Numerators
Now add the numerators (143 + 297 = 440) and keep the common denominator 429 unchanged.
Working: 143 + 297/429 = 440/429

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 440 and 429, which is 11. Divide both the numerator and denominator by 11.
Working: 440 ÷ 11/429 ÷ 11 = 40/39

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (40) is greater than the denominator (39), divide 40 by 39: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/39.
Working: 40/39 = 1 1/39

Step 6: Decimal & Percentage Representation
Dividing the numerator 40 by denominator 39 produces a repeating decimal (approximately 1.025641, or 102.5641%).
Working: 40 ÷ 39 = 1.025641 (102.5641%)

Key Values:
- Simplified Fraction: 40/39
- Mixed Number Form: 1 1/39
- Decimal Value: 1.025641
- Percentage: 102.5641%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-11-33-plus-9-13/
==================================================

11/33 + 9/13 = 40/39

Simplified Fraction

40/39

Mixed Number

1 1/39

Decimal Value

1.025641

Percentage

102.5641%

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: 11/33 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 33 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 33 × 13 = 429.

LCD(33, 13) = 429

Step 2

Convert to Equivalent Fractions with Common Denominator 429

Multiply the numerator and denominator of 11/33 by 13, and multiply the numerator and denominator of 9/13 by 33 so both fractions share the common base 429.

11 × 13/33 × 13 = 143/429 and 9 × 33/13 × 33 = 297/429

Step 3

Add the Numerators

Now add the numerators (143 + 297 = 440) and keep the common denominator 429 unchanged.

143 + 297/429 = 440/429

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 440 and 429, which is 11. Divide both the numerator and denominator by 11.

440 ÷ 11/429 ÷ 11 = 40/39

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (40) is greater than the denominator (39), divide 40 by 39: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/39.

40/39 = 11/39

Step 6

Decimal & Percentage Representation

Dividing the numerator 40 by denominator 39 produces a repeating decimal (approximately 1.025641, or 102.5641%).

40 ÷ 39 = 1.025641 (102.5641%)

Visual Representation

The diagram below illustrates 11/33 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`40/39`
Mixed Number Form	`1 1/39`
Decimal Form	`1.025641`
Percentage	`102.5641%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 11/33 plus 9/13 as a fraction?

11/33 + 9/13 in simplest fraction form is 40/39 (or 1 1/39 as a mixed number).

What is 11/33 plus 9/13 as a decimal?

11/33 + 9/13 converted to a decimal is 1.025641.

What is 11/33 plus 9/13 as a percentage?

11/33 + 9/13 expressed as a percentage is 102.5641%.

How do you write 11/33 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 40/39 can be written as the mixed number 1 1/39.

Does 11/33 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.025641...) because the denominator contains prime factors other than 2 and 5.