What is 3/20 plus 2/3? (Answer: 49/60)

Exact Answer

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Problem: What is 3/20 plus 2/3?
Formula / Expression: 3/20 + 2/3
Final Answer: 49/60
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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 3/20 by 3, and multiply the numerator and denominator of 2/3 by 20 so both fractions share the common base 60.
Working: 3 × 3/20 × 3 = 9/60 and 2 × 20/3 × 20 = 40/60

Step 3: Add the Numerators
Now add the numerators (9 + 40 = 49) and keep the common denominator 60 unchanged.
Working: 9 + 40/60 = 49/60

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 49 and 60 is 1, confirming that 49/60 cannot be reduced further—it is already in its simplest irreducible form.
Working: 49/60

Step 5: Decimal & Percentage Representation
Dividing the numerator 49 by denominator 60 produces a repeating decimal (approximately 0.816667, or 81.6667%).
Working: 49 ÷ 60 = 0.816667 (81.6667%)

Key Values:
- Simplified Fraction: 49/60
- Mixed Number Form: 49/60
- Decimal Value: 0.816667
- Percentage: 81.6667%

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Solved with FractionsCalc:
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3/20 + 2/3 = 49/60

Simplified Fraction

49/60

Mixed Number

Proper (49/60)

Decimal Value

0.816667

Percentage

81.6667%

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Step-by-Step Solution: 3/20 + 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 3/20 by 3, and multiply the numerator and denominator of 2/3 by 20 so both fractions share the common base 60.

3 × 3/20 × 3 = 9/60 and 2 × 20/3 × 20 = 40/60

Step 3

Add the Numerators

Now add the numerators (9 + 40 = 49) and keep the common denominator 60 unchanged.

9 + 40/60 = 49/60

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 49 and 60 is 1, confirming that 49/60 cannot be reduced further—it is already in its simplest irreducible form.

49/60

Step 5

Decimal & Percentage Representation

Dividing the numerator 49 by denominator 60 produces a repeating decimal (approximately 0.816667, or 81.6667%).

49 ÷ 60 = 0.816667 (81.6667%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`49/60`
Mixed Number Form	`49/60`
Decimal Form	`0.816667`
Percentage	`81.6667%`

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Frequently Asked Questions

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

3/20 + 2/3 in simplest fraction form is 49/60.

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

3/20 + 2/3 converted to a decimal is 0.816667.

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

3/20 + 2/3 expressed as a percentage is 81.6667%.

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

It results in a repeating decimal (approximately 0.816667...) because the denominator contains prime factors other than 2 and 5.