What is 3/46 plus 3/13? (Answer: 177/598)

Exact Answer

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Problem: What is 3/46 plus 3/13?
Formula / Expression: 3/46 + 3/13
Final Answer: 177/598
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 46 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 46 × 13 = 598.
Working: LCD(46, 13) = 598

Step 2: Convert to Equivalent Fractions with Common Denominator 598
Multiply the numerator and denominator of 3/46 by 13, and multiply the numerator and denominator of 3/13 by 46 so both fractions share the common base 598.
Working: 3 × 13/46 × 13 = 39/598 and 3 × 46/13 × 46 = 138/598

Step 3: Add the Numerators
Now add the numerators (39 + 138 = 177) and keep the common denominator 598 unchanged.
Working: 39 + 138/598 = 177/598

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 177 and 598 is 1, confirming that 177/598 cannot be reduced further—it is already in its simplest irreducible form.
Working: 177/598

Step 5: Decimal & Percentage Representation
Dividing the numerator 177 by denominator 598 produces a repeating decimal (approximately 0.295987, or 29.5987%).
Working: 177 ÷ 598 = 0.295987 (29.5987%)

Key Values:
- Simplified Fraction: 177/598
- Mixed Number Form: 177/598
- Decimal Value: 0.295987
- Percentage: 29.5987%

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Solved with FractionsCalc:
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3/46 + 3/13 = 177/598

Simplified Fraction

177/598

Mixed Number

Proper (177/598)

Decimal Value

0.295987

Percentage

29.5987%

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Step-by-Step Solution: 3/46 + 3/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 46 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 46 × 13 = 598.

LCD(46, 13) = 598

Step 2

Convert to Equivalent Fractions with Common Denominator 598

Multiply the numerator and denominator of 3/46 by 13, and multiply the numerator and denominator of 3/13 by 46 so both fractions share the common base 598.

3 × 13/46 × 13 = 39/598 and 3 × 46/13 × 46 = 138/598

Step 3

Add the Numerators

Now add the numerators (39 + 138 = 177) and keep the common denominator 598 unchanged.

39 + 138/598 = 177/598

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 177 and 598 is 1, confirming that 177/598 cannot be reduced further—it is already in its simplest irreducible form.

177/598

Step 5

Decimal & Percentage Representation

Dividing the numerator 177 by denominator 598 produces a repeating decimal (approximately 0.295987, or 29.5987%).

177 ÷ 598 = 0.295987 (29.5987%)

Visual Representation

The diagram below illustrates 3/46 plus 3/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`177/598`
Mixed Number Form	`177/598`
Decimal Form	`0.295987`
Percentage	`29.5987%`

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Frequently Asked Questions

What is 3/46 plus 3/13 as a fraction?

3/46 + 3/13 in simplest fraction form is 177/598.

What is 3/46 plus 3/13 as a decimal?

3/46 + 3/13 converted to a decimal is 0.295987.

What is 3/46 plus 3/13 as a percentage?

3/46 + 3/13 expressed as a percentage is 29.5987%.

Does 3/46 plus 3/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.295987...) because the denominator contains prime factors other than 2 and 5.