What is 11/33 plus 8/13? (Answer: 37/39)

Exact Answer

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Problem: What is 11/33 plus 8/13?
Formula / Expression: 11/33 + 8/13
Final Answer: 37/39
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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 8/13 by 33 so both fractions share the common base 429.
Working: 11 × 13/33 × 13 = 143/429 and 8 × 33/13 × 33 = 264/429

Step 3: Add the Numerators
Now add the numerators (143 + 264 = 407) and keep the common denominator 429 unchanged.
Working: 143 + 264/429 = 407/429

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 407 and 429, which is 11. Divide both the numerator and denominator by 11.
Working: 407 ÷ 11/429 ÷ 11 = 37/39

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 39 produces a repeating decimal (approximately 0.948718, or 94.8718%).
Working: 37 ÷ 39 = 0.948718 (94.8718%)

Key Values:
- Simplified Fraction: 37/39
- Mixed Number Form: 37/39
- Decimal Value: 0.948718
- Percentage: 94.8718%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-11-33-plus-8-13/
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11/33 + 8/13 = 37/39

Simplified Fraction

37/39

Mixed Number

Proper (37/39)

Decimal Value

0.948718

Percentage

94.8718%

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Step-by-Step Solution: 11/33 + 8/13

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 8/13 by 33 so both fractions share the common base 429.

11 × 13/33 × 13 = 143/429 and 8 × 33/13 × 33 = 264/429

Step 3

Add the Numerators

Now add the numerators (143 + 264 = 407) and keep the common denominator 429 unchanged.

143 + 264/429 = 407/429

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 407 and 429, which is 11. Divide both the numerator and denominator by 11.

407 ÷ 11/429 ÷ 11 = 37/39

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 39 produces a repeating decimal (approximately 0.948718, or 94.8718%).

37 ÷ 39 = 0.948718 (94.8718%)

Visual Representation

The diagram below illustrates 11/33 plus 8/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/39`
Mixed Number Form	`37/39`
Decimal Form	`0.948718`
Percentage	`94.8718%`

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Frequently Asked Questions

What is 11/33 plus 8/13 as a fraction?

11/33 + 8/13 in simplest fraction form is 37/39.

What is 11/33 plus 8/13 as a decimal?

11/33 + 8/13 converted to a decimal is 0.948718.

What is 11/33 plus 8/13 as a percentage?

11/33 + 8/13 expressed as a percentage is 94.8718%.

Does 11/33 plus 8/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.948718...) because the denominator contains prime factors other than 2 and 5.