What is 8/33 plus 10/13? (Answer: 434/429)

Exact Answer

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Problem: What is 8/33 plus 10/13?
Formula / Expression: 8/33 + 10/13
Final Answer: 1 5/429 (434/429)
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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 8/33 by 13, and multiply the numerator and denominator of 10/13 by 33 so both fractions share the common base 429.
Working: 8 × 13/33 × 13 = 104/429 and 10 × 33/13 × 33 = 330/429

Step 3: Add the Numerators
Now add the numerators (104 + 330 = 434) and keep the common denominator 429 unchanged.
Working: 104 + 330/429 = 434/429

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 434 and 429 is 1, confirming that 434/429 cannot be reduced further—it is already in its simplest irreducible form.
Working: 434/429

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (434) is greater than the denominator (429), divide 434 by 429: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/429.
Working: 434/429 = 1 5/429

Step 6: Decimal & Percentage Representation
Dividing the numerator 434 by denominator 429 produces a repeating decimal (approximately 1.011655, or 101.1655%).
Working: 434 ÷ 429 = 1.011655 (101.1655%)

Key Values:
- Simplified Fraction: 434/429
- Mixed Number Form: 1 5/429
- Decimal Value: 1.011655
- Percentage: 101.1655%

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Solved with FractionsCalc:
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8/33 + 10/13 = 434/429

Simplified Fraction

434/429

Mixed Number

1 5/429

Decimal Value

1.011655

Percentage

101.1655%

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Step-by-Step Solution: 8/33 + 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 8/33 by 13, and multiply the numerator and denominator of 10/13 by 33 so both fractions share the common base 429.

8 × 13/33 × 13 = 104/429 and 10 × 33/13 × 33 = 330/429

Step 3

Add the Numerators

Now add the numerators (104 + 330 = 434) and keep the common denominator 429 unchanged.

104 + 330/429 = 434/429

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 434 and 429 is 1, confirming that 434/429 cannot be reduced further—it is already in its simplest irreducible form.

434/429

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (434) is greater than the denominator (429), divide 434 by 429: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/429.

434/429 = 15/429

Step 6

Decimal & Percentage Representation

Dividing the numerator 434 by denominator 429 produces a repeating decimal (approximately 1.011655, or 101.1655%).

434 ÷ 429 = 1.011655 (101.1655%)

Visual Representation

The diagram below illustrates 8/33 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`434/429`
Mixed Number Form	`1 5/429`
Decimal Form	`1.011655`
Percentage	`101.1655%`

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Frequently Asked Questions

What is 8/33 plus 10/13 as a fraction?

8/33 + 10/13 in simplest fraction form is 434/429 (or 1 5/429 as a mixed number).

What is 8/33 plus 10/13 as a decimal?

8/33 + 10/13 converted to a decimal is 1.011655.

What is 8/33 plus 10/13 as a percentage?

8/33 + 10/13 expressed as a percentage is 101.1655%.

How do you write 8/33 plus 10/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 434/429 can be written as the mixed number 1 5/429.

Does 8/33 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.011655...) because the denominator contains prime factors other than 2 and 5.