What is 5/30 plus 2/7? (Answer: 19/42)

Exact Answer

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Problem: What is 5/30 plus 2/7?
Formula / Expression: 5/30 + 2/7
Final Answer: 19/42
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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 5/30 by 7, and multiply the numerator and denominator of 2/7 by 30 so both fractions share the common base 210.
Working: 5 × 7/30 × 7 = 35/210 and 2 × 30/7 × 30 = 60/210

Step 3: Add the Numerators
Now add the numerators (35 + 60 = 95) and keep the common denominator 210 unchanged.
Working: 35 + 60/210 = 95/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 95 and 210, which is 5. Divide both the numerator and denominator by 5.
Working: 95 ÷ 5/210 ÷ 5 = 19/42

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 42 produces a repeating decimal (approximately 0.452381, or 45.2381%).
Working: 19 ÷ 42 = 0.452381 (45.2381%)

Key Values:
- Simplified Fraction: 19/42
- Mixed Number Form: 19/42
- Decimal Value: 0.452381
- Percentage: 45.2381%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-30-plus-2-7/
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5/30 + 2/7 = 19/42

Simplified Fraction

19/42

Mixed Number

Proper (19/42)

Decimal Value

0.452381

Percentage

45.2381%

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Step-by-Step Solution: 5/30 + 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 5/30 by 7, and multiply the numerator and denominator of 2/7 by 30 so both fractions share the common base 210.

5 × 7/30 × 7 = 35/210 and 2 × 30/7 × 30 = 60/210

Step 3

Add the Numerators

Now add the numerators (35 + 60 = 95) and keep the common denominator 210 unchanged.

35 + 60/210 = 95/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 95 and 210, which is 5. Divide both the numerator and denominator by 5.

95 ÷ 5/210 ÷ 5 = 19/42

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 42 produces a repeating decimal (approximately 0.452381, or 45.2381%).

19 ÷ 42 = 0.452381 (45.2381%)

Visual Representation

The diagram below illustrates 5/30 plus 2/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/42`
Mixed Number Form	`19/42`
Decimal Form	`0.452381`
Percentage	`45.2381%`

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Frequently Asked Questions

What is 5/30 plus 2/7 as a fraction?

5/30 + 2/7 in simplest fraction form is 19/42.

What is 5/30 plus 2/7 as a decimal?

5/30 + 2/7 converted to a decimal is 0.452381.

What is 5/30 plus 2/7 as a percentage?

5/30 + 2/7 expressed as a percentage is 45.2381%.

Does 5/30 plus 2/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.452381...) because the denominator contains prime factors other than 2 and 5.