What is 2/42 plus 2/9? (Answer: 17/63)

Exact Answer

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Problem: What is 2/42 plus 2/9?
Formula / Expression: 2/42 + 2/9
Final Answer: 17/63
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 42 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 126 (which is smaller than their product 42 × 9 = 378, keeping the calculation simpler).
Working: LCD(42, 9) = 126

Step 2: Convert to Equivalent Fractions with Common Denominator 126
Multiply the numerator and denominator of 2/42 by 3, and multiply the numerator and denominator of 2/9 by 14 so both fractions share the common base 126.
Working: 2 × 3/42 × 3 = 6/126 and 2 × 14/9 × 14 = 28/126

Step 3: Add the Numerators
Now add the numerators (6 + 28 = 34) and keep the common denominator 126 unchanged.
Working: 6 + 28/126 = 34/126

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 34 and 126, which is 2. Divide both the numerator and denominator by 2.
Working: 34 ÷ 2/126 ÷ 2 = 17/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 63 produces a repeating decimal (approximately 0.269841, or 26.9841%).
Working: 17 ÷ 63 = 0.269841 (26.9841%)

Key Values:
- Simplified Fraction: 17/63
- Mixed Number Form: 17/63
- Decimal Value: 0.269841
- Percentage: 26.9841%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-42-plus-2-9/
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2/42 + 2/9 = 17/63

Simplified Fraction

17/63

Mixed Number

Proper (17/63)

Decimal Value

0.269841

Percentage

26.9841%

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Step-by-Step Solution: 2/42 + 2/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 42 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 126 (which is smaller than their product 42 × 9 = 378, keeping the calculation simpler).

LCD(42, 9) = 126

Step 2

Convert to Equivalent Fractions with Common Denominator 126

Multiply the numerator and denominator of 2/42 by 3, and multiply the numerator and denominator of 2/9 by 14 so both fractions share the common base 126.

2 × 3/42 × 3 = 6/126 and 2 × 14/9 × 14 = 28/126

Step 3

Add the Numerators

Now add the numerators (6 + 28 = 34) and keep the common denominator 126 unchanged.

6 + 28/126 = 34/126

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 34 and 126, which is 2. Divide both the numerator and denominator by 2.

34 ÷ 2/126 ÷ 2 = 17/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 63 produces a repeating decimal (approximately 0.269841, or 26.9841%).

17 ÷ 63 = 0.269841 (26.9841%)

Visual Representation

The diagram below illustrates 2/42 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/63`
Mixed Number Form	`17/63`
Decimal Form	`0.269841`
Percentage	`26.9841%`

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Frequently Asked Questions

What is 2/42 plus 2/9 as a fraction?

2/42 + 2/9 in simplest fraction form is 17/63.

What is 2/42 plus 2/9 as a decimal?

2/42 + 2/9 converted to a decimal is 0.269841.

What is 2/42 plus 2/9 as a percentage?

2/42 + 2/9 expressed as a percentage is 26.9841%.

Does 2/42 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.269841...) because the denominator contains prime factors other than 2 and 5.