What is 3/33 plus 10/13? (Answer: 123/143)

Exact Answer

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Problem: What is 3/33 plus 10/13?
Formula / Expression: 3/33 + 10/13
Final Answer: 123/143
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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 3/33 by 13, and multiply the numerator and denominator of 10/13 by 33 so both fractions share the common base 429.
Working: 3 × 13/33 × 13 = 39/429 and 10 × 33/13 × 33 = 330/429

Step 3: Add the Numerators
Now add the numerators (39 + 330 = 369) and keep the common denominator 429 unchanged.
Working: 39 + 330/429 = 369/429

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 369 and 429, which is 3. Divide both the numerator and denominator by 3.
Working: 369 ÷ 3/429 ÷ 3 = 123/143

Step 5: Decimal & Percentage Representation
Dividing the numerator 123 by denominator 143 produces a repeating decimal (approximately 0.86014, or 86.014%).
Working: 123 ÷ 143 = 0.86014 (86.014%)

Key Values:
- Simplified Fraction: 123/143
- Mixed Number Form: 123/143
- Decimal Value: 0.86014
- Percentage: 86.014%

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Solved with FractionsCalc:
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3/33 + 10/13 = 123/143

Simplified Fraction

123/143

Mixed Number

Proper (123/143)

Decimal Value

0.86014

Percentage

86.014%

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Step-by-Step Solution: 3/33 + 10/13

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 3/33 by 13, and multiply the numerator and denominator of 10/13 by 33 so both fractions share the common base 429.

3 × 13/33 × 13 = 39/429 and 10 × 33/13 × 33 = 330/429

Step 3

Add the Numerators

Now add the numerators (39 + 330 = 369) and keep the common denominator 429 unchanged.

39 + 330/429 = 369/429

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 369 and 429, which is 3. Divide both the numerator and denominator by 3.

369 ÷ 3/429 ÷ 3 = 123/143

Step 5

Decimal & Percentage Representation

Dividing the numerator 123 by denominator 143 produces a repeating decimal (approximately 0.86014, or 86.014%).

123 ÷ 143 = 0.86014 (86.014%)

Visual Representation

The diagram below illustrates 3/33 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`123/143`
Mixed Number Form	`123/143`
Decimal Form	`0.86014`
Percentage	`86.014%`

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Frequently Asked Questions

What is 3/33 plus 10/13 as a fraction?

3/33 + 10/13 in simplest fraction form is 123/143.

What is 3/33 plus 10/13 as a decimal?

3/33 + 10/13 converted to a decimal is 0.86014.

What is 3/33 plus 10/13 as a percentage?

3/33 + 10/13 expressed as a percentage is 86.014%.

Does 3/33 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.86014...) because the denominator contains prime factors other than 2 and 5.