What is 6/20 plus 2/3? (Answer: 29/30)

Exact Answer

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Problem: What is 6/20 plus 2/3?
Formula / Expression: 6/20 + 2/3
Final Answer: 29/30
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 20 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 20 × 3 = 60.
Working: LCD(20, 3) = 60

Step 2: Convert to Equivalent Fractions with Common Denominator 60
Multiply the numerator and denominator of 6/20 by 3, and multiply the numerator and denominator of 2/3 by 20 so both fractions share the common base 60.
Working: 6 × 3/20 × 3 = 18/60 and 2 × 20/3 × 20 = 40/60

Step 3: Add the Numerators
Now add the numerators (18 + 40 = 58) and keep the common denominator 60 unchanged.
Working: 18 + 40/60 = 58/60

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 58 and 60, which is 2. Divide both the numerator and denominator by 2.
Working: 58 ÷ 2/60 ÷ 2 = 29/30

Step 5: Decimal & Percentage Representation
Dividing the numerator 29 by denominator 30 produces a repeating decimal (approximately 0.966667, or 96.6667%).
Working: 29 ÷ 30 = 0.966667 (96.6667%)

Key Values:
- Simplified Fraction: 29/30
- Mixed Number Form: 29/30
- Decimal Value: 0.966667
- Percentage: 96.6667%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-6-20-plus-2-3/
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6/20 + 2/3 = 29/30

Simplified Fraction

29/30

Mixed Number

Proper (29/30)

Decimal Value

0.966667

Percentage

96.6667%

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Step-by-Step Solution: 6/20 + 2/3

Step 1

Find the Least Common Denominator (LCD)

The denominators 20 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 20 × 3 = 60.

LCD(20, 3) = 60

Step 2

Convert to Equivalent Fractions with Common Denominator 60

Multiply the numerator and denominator of 6/20 by 3, and multiply the numerator and denominator of 2/3 by 20 so both fractions share the common base 60.

6 × 3/20 × 3 = 18/60 and 2 × 20/3 × 20 = 40/60

Step 3

Add the Numerators

Now add the numerators (18 + 40 = 58) and keep the common denominator 60 unchanged.

18 + 40/60 = 58/60

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 58 and 60, which is 2. Divide both the numerator and denominator by 2.

58 ÷ 2/60 ÷ 2 = 29/30

Step 5

Decimal & Percentage Representation

Dividing the numerator 29 by denominator 30 produces a repeating decimal (approximately 0.966667, or 96.6667%).

29 ÷ 30 = 0.966667 (96.6667%)

Visual Representation

The diagram below illustrates 6/20 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`29/30`
Mixed Number Form	`29/30`
Decimal Form	`0.966667`
Percentage	`96.6667%`

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Frequently Asked Questions

What is 6/20 plus 2/3 as a fraction?

6/20 + 2/3 in simplest fraction form is 29/30.

What is 6/20 plus 2/3 as a decimal?

6/20 + 2/3 converted to a decimal is 0.966667.

What is 6/20 plus 2/3 as a percentage?

6/20 + 2/3 expressed as a percentage is 96.6667%.

Does 6/20 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.966667...) because the denominator contains prime factors other than 2 and 5.