What is 2/6 plus 7/20? (Answer: 41/60)

Exact Answer

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Problem: What is 2/6 plus 7/20?
Formula / Expression: 2/6 + 7/20
Final Answer: 41/60
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 6 and 20 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 60 (which is smaller than their product 6 × 20 = 120, keeping the calculation simpler).
Working: LCD(6, 20) = 60

Step 2: Convert to Equivalent Fractions with Common Denominator 60
Multiply the numerator and denominator of 2/6 by 10, and multiply the numerator and denominator of 7/20 by 3 so both fractions share the common base 60.
Working: 2 × 10/6 × 10 = 20/60 and 7 × 3/20 × 3 = 21/60

Step 3: Add the Numerators
Now add the numerators (20 + 21 = 41) and keep the common denominator 60 unchanged.
Working: 20 + 21/60 = 41/60

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 41 and 60 is 1, confirming that 41/60 cannot be reduced further—it is already in its simplest irreducible form.
Working: 41/60

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 60 produces a repeating decimal (approximately 0.683333, or 68.3333%).
Working: 41 ÷ 60 = 0.683333 (68.3333%)

Key Values:
- Simplified Fraction: 41/60
- Mixed Number Form: 41/60
- Decimal Value: 0.683333
- Percentage: 68.3333%

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Solved with FractionsCalc:
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2/6 + 7/20 = 41/60

Simplified Fraction

41/60

Mixed Number

Proper (41/60)

Decimal Value

0.683333

Percentage

68.3333%

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Step-by-Step Solution: 2/6 + 7/20

Step 1

Find the Least Common Denominator (LCD)

The denominators 6 and 20 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 60 (which is smaller than their product 6 × 20 = 120, keeping the calculation simpler).

LCD(6, 20) = 60

Step 2

Convert to Equivalent Fractions with Common Denominator 60

Multiply the numerator and denominator of 2/6 by 10, and multiply the numerator and denominator of 7/20 by 3 so both fractions share the common base 60.

2 × 10/6 × 10 = 20/60 and 7 × 3/20 × 3 = 21/60

Step 3

Add the Numerators

Now add the numerators (20 + 21 = 41) and keep the common denominator 60 unchanged.

20 + 21/60 = 41/60

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 41 and 60 is 1, confirming that 41/60 cannot be reduced further—it is already in its simplest irreducible form.

41/60

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 60 produces a repeating decimal (approximately 0.683333, or 68.3333%).

41 ÷ 60 = 0.683333 (68.3333%)

Visual Representation

The diagram below illustrates 2/6 plus 7/20 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/60`
Mixed Number Form	`41/60`
Decimal Form	`0.683333`
Percentage	`68.3333%`

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Frequently Asked Questions

What is 2/6 plus 7/20 as a fraction?

2/6 + 7/20 in simplest fraction form is 41/60.

What is 2/6 plus 7/20 as a decimal?

2/6 + 7/20 converted to a decimal is 0.683333.

What is 2/6 plus 7/20 as a percentage?

2/6 + 7/20 expressed as a percentage is 68.3333%.

Does 2/6 plus 7/20 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.683333...) because the denominator contains prime factors other than 2 and 5.