What is 2/30 plus 2/7? (Answer: 37/105)

Exact Answer

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Problem: What is 2/30 plus 2/7?
Formula / Expression: 2/30 + 2/7
Final Answer: 37/105
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 30 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 30 × 7 = 210.
Working: LCD(30, 7) = 210

Step 2: Convert to Equivalent Fractions with Common Denominator 210
Multiply the numerator and denominator of 2/30 by 7, and multiply the numerator and denominator of 2/7 by 30 so both fractions share the common base 210.
Working: 2 × 7/30 × 7 = 14/210 and 2 × 30/7 × 30 = 60/210

Step 3: Add the Numerators
Now add the numerators (14 + 60 = 74) and keep the common denominator 210 unchanged.
Working: 14 + 60/210 = 74/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 74 and 210, which is 2. Divide both the numerator and denominator by 2.
Working: 74 ÷ 2/210 ÷ 2 = 37/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 105 produces a repeating decimal (approximately 0.352381, or 35.2381%).
Working: 37 ÷ 105 = 0.352381 (35.2381%)

Key Values:
- Simplified Fraction: 37/105
- Mixed Number Form: 37/105
- Decimal Value: 0.352381
- Percentage: 35.2381%

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Solved with FractionsCalc:
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2/30 + 2/7 = 37/105

Simplified Fraction

37/105

Mixed Number

Proper (37/105)

Decimal Value

0.352381

Percentage

35.2381%

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Step-by-Step Solution: 2/30 + 2/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 30 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 30 × 7 = 210.

LCD(30, 7) = 210

Step 2

Convert to Equivalent Fractions with Common Denominator 210

Multiply the numerator and denominator of 2/30 by 7, and multiply the numerator and denominator of 2/7 by 30 so both fractions share the common base 210.

2 × 7/30 × 7 = 14/210 and 2 × 30/7 × 30 = 60/210

Step 3

Add the Numerators

Now add the numerators (14 + 60 = 74) and keep the common denominator 210 unchanged.

14 + 60/210 = 74/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 74 and 210, which is 2. Divide both the numerator and denominator by 2.

74 ÷ 2/210 ÷ 2 = 37/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 105 produces a repeating decimal (approximately 0.352381, or 35.2381%).

37 ÷ 105 = 0.352381 (35.2381%)

Visual Representation

The diagram below illustrates 2/30 plus 2/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/105`
Mixed Number Form	`37/105`
Decimal Form	`0.352381`
Percentage	`35.2381%`

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Frequently Asked Questions

What is 2/30 plus 2/7 as a fraction?

2/30 + 2/7 in simplest fraction form is 37/105.

What is 2/30 plus 2/7 as a decimal?

2/30 + 2/7 converted to a decimal is 0.352381.

What is 2/30 plus 2/7 as a percentage?

2/30 + 2/7 expressed as a percentage is 35.2381%.

Does 2/30 plus 2/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.352381...) because the denominator contains prime factors other than 2 and 5.