What is 3/42 plus 4/13? (Answer: 69/182)

Exact Answer

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Problem: What is 3/42 plus 4/13?
Formula / Expression: 3/42 + 4/13
Final Answer: 69/182
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 42 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 42 × 13 = 546.
Working: LCD(42, 13) = 546

Step 2: Convert to Equivalent Fractions with Common Denominator 546
Multiply the numerator and denominator of 3/42 by 13, and multiply the numerator and denominator of 4/13 by 42 so both fractions share the common base 546.
Working: 3 × 13/42 × 13 = 39/546 and 4 × 42/13 × 42 = 168/546

Step 3: Add the Numerators
Now add the numerators (39 + 168 = 207) and keep the common denominator 546 unchanged.
Working: 39 + 168/546 = 207/546

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 207 and 546, which is 3. Divide both the numerator and denominator by 3.
Working: 207 ÷ 3/546 ÷ 3 = 69/182

Step 5: Decimal & Percentage Representation
Dividing the numerator 69 by denominator 182 produces a repeating decimal (approximately 0.379121, or 37.9121%).
Working: 69 ÷ 182 = 0.379121 (37.9121%)

Key Values:
- Simplified Fraction: 69/182
- Mixed Number Form: 69/182
- Decimal Value: 0.379121
- Percentage: 37.9121%

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Solved with FractionsCalc:
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3/42 + 4/13 = 69/182

Simplified Fraction

69/182

Mixed Number

Proper (69/182)

Decimal Value

0.379121

Percentage

37.9121%

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Step-by-Step Solution: 3/42 + 4/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 42 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 42 × 13 = 546.

LCD(42, 13) = 546

Step 2

Convert to Equivalent Fractions with Common Denominator 546

Multiply the numerator and denominator of 3/42 by 13, and multiply the numerator and denominator of 4/13 by 42 so both fractions share the common base 546.

3 × 13/42 × 13 = 39/546 and 4 × 42/13 × 42 = 168/546

Step 3

Add the Numerators

Now add the numerators (39 + 168 = 207) and keep the common denominator 546 unchanged.

39 + 168/546 = 207/546

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 207 and 546, which is 3. Divide both the numerator and denominator by 3.

207 ÷ 3/546 ÷ 3 = 69/182

Step 5

Decimal & Percentage Representation

Dividing the numerator 69 by denominator 182 produces a repeating decimal (approximately 0.379121, or 37.9121%).

69 ÷ 182 = 0.379121 (37.9121%)

Visual Representation

The diagram below illustrates 3/42 plus 4/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`69/182`
Mixed Number Form	`69/182`
Decimal Form	`0.379121`
Percentage	`37.9121%`

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Frequently Asked Questions

What is 3/42 plus 4/13 as a fraction?

3/42 + 4/13 in simplest fraction form is 69/182.

What is 3/42 plus 4/13 as a decimal?

3/42 + 4/13 converted to a decimal is 0.379121.

What is 3/42 plus 4/13 as a percentage?

3/42 + 4/13 expressed as a percentage is 37.9121%.

Does 3/42 plus 4/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.379121...) because the denominator contains prime factors other than 2 and 5.