What is 10/33 plus 5/13? (Answer: 295/429)

Exact Answer

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Problem: What is 10/33 plus 5/13?
Formula / Expression: 10/33 + 5/13
Final Answer: 295/429
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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 10/33 by 13, and multiply the numerator and denominator of 5/13 by 33 so both fractions share the common base 429.
Working: 10 × 13/33 × 13 = 130/429 and 5 × 33/13 × 33 = 165/429

Step 3: Add the Numerators
Now add the numerators (130 + 165 = 295) and keep the common denominator 429 unchanged.
Working: 130 + 165/429 = 295/429

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 295 and 429 is 1, confirming that 295/429 cannot be reduced further—it is already in its simplest irreducible form.
Working: 295/429

Step 5: Decimal & Percentage Representation
Dividing the numerator 295 by denominator 429 produces a repeating decimal (approximately 0.687646, or 68.7646%).
Working: 295 ÷ 429 = 0.687646 (68.7646%)

Key Values:
- Simplified Fraction: 295/429
- Mixed Number Form: 295/429
- Decimal Value: 0.687646
- Percentage: 68.7646%

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10/33 + 5/13 = 295/429

Simplified Fraction

295/429

Mixed Number

Proper (295/429)

Decimal Value

0.687646

Percentage

68.7646%

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Step-by-Step Solution: 10/33 + 5/13

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 10/33 by 13, and multiply the numerator and denominator of 5/13 by 33 so both fractions share the common base 429.

10 × 13/33 × 13 = 130/429 and 5 × 33/13 × 33 = 165/429

Step 3

Add the Numerators

Now add the numerators (130 + 165 = 295) and keep the common denominator 429 unchanged.

130 + 165/429 = 295/429

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 295 and 429 is 1, confirming that 295/429 cannot be reduced further—it is already in its simplest irreducible form.

295/429

Step 5

Decimal & Percentage Representation

Dividing the numerator 295 by denominator 429 produces a repeating decimal (approximately 0.687646, or 68.7646%).

295 ÷ 429 = 0.687646 (68.7646%)

Visual Representation

The diagram below illustrates 10/33 plus 5/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`295/429`
Mixed Number Form	`295/429`
Decimal Form	`0.687646`
Percentage	`68.7646%`

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Frequently Asked Questions

What is 10/33 plus 5/13 as a fraction?

10/33 + 5/13 in simplest fraction form is 295/429.

What is 10/33 plus 5/13 as a decimal?

10/33 + 5/13 converted to a decimal is 0.687646.

What is 10/33 plus 5/13 as a percentage?

10/33 + 5/13 expressed as a percentage is 68.7646%.

Does 10/33 plus 5/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.687646...) because the denominator contains prime factors other than 2 and 5.