What is 3/22 plus 3/13? (Answer: 105/286)

Exact Answer

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Problem: What is 3/22 plus 3/13?
Formula / Expression: 3/22 + 3/13
Final Answer: 105/286
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 22 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 22 × 13 = 286.
Working: LCD(22, 13) = 286

Step 2: Convert to Equivalent Fractions with Common Denominator 286
Multiply the numerator and denominator of 3/22 by 13, and multiply the numerator and denominator of 3/13 by 22 so both fractions share the common base 286.
Working: 3 × 13/22 × 13 = 39/286 and 3 × 22/13 × 22 = 66/286

Step 3: Add the Numerators
Now add the numerators (39 + 66 = 105) and keep the common denominator 286 unchanged.
Working: 39 + 66/286 = 105/286

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 105 and 286 is 1, confirming that 105/286 cannot be reduced further—it is already in its simplest irreducible form.
Working: 105/286

Step 5: Decimal & Percentage Representation
Dividing the numerator 105 by denominator 286 produces a repeating decimal (approximately 0.367133, or 36.7133%).
Working: 105 ÷ 286 = 0.367133 (36.7133%)

Key Values:
- Simplified Fraction: 105/286
- Mixed Number Form: 105/286
- Decimal Value: 0.367133
- Percentage: 36.7133%

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Solved with FractionsCalc:
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3/22 + 3/13 = 105/286

Simplified Fraction

105/286

Mixed Number

Proper (105/286)

Decimal Value

0.367133

Percentage

36.7133%

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Step-by-Step Solution: 3/22 + 3/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 22 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 22 × 13 = 286.

LCD(22, 13) = 286

Step 2

Convert to Equivalent Fractions with Common Denominator 286

Multiply the numerator and denominator of 3/22 by 13, and multiply the numerator and denominator of 3/13 by 22 so both fractions share the common base 286.

3 × 13/22 × 13 = 39/286 and 3 × 22/13 × 22 = 66/286

Step 3

Add the Numerators

Now add the numerators (39 + 66 = 105) and keep the common denominator 286 unchanged.

39 + 66/286 = 105/286

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 105 and 286 is 1, confirming that 105/286 cannot be reduced further—it is already in its simplest irreducible form.

105/286

Step 5

Decimal & Percentage Representation

Dividing the numerator 105 by denominator 286 produces a repeating decimal (approximately 0.367133, or 36.7133%).

105 ÷ 286 = 0.367133 (36.7133%)

Visual Representation

The diagram below illustrates 3/22 plus 3/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`105/286`
Mixed Number Form	`105/286`
Decimal Form	`0.367133`
Percentage	`36.7133%`

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Frequently Asked Questions

What is 3/22 plus 3/13 as a fraction?

3/22 + 3/13 in simplest fraction form is 105/286.

What is 3/22 plus 3/13 as a decimal?

3/22 + 3/13 converted to a decimal is 0.367133.

What is 3/22 plus 3/13 as a percentage?

3/22 + 3/13 expressed as a percentage is 36.7133%.

Does 3/22 plus 3/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.367133...) because the denominator contains prime factors other than 2 and 5.