What is 1/6 plus 3/5? (Answer: 23/30)

Exact Answer

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Problem: What is 1/6 plus 3/5?
Formula / Expression: 1/6 + 3/5
Final Answer: 23/30
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 6 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 6 × 5 = 30.
Working: LCD(6, 5) = 30

Step 2: Convert to Equivalent Fractions with Common Denominator 30
Multiply the numerator and denominator of 1/6 by 5, and multiply the numerator and denominator of 3/5 by 6 so both fractions share the common base 30.
Working: 1 × 5/6 × 5 = 5/30 and 3 × 6/5 × 6 = 18/30

Step 3: Add the Numerators
Now add the numerators (5 + 18 = 23) and keep the common denominator 30 unchanged.
Working: 5 + 18/30 = 23/30

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 23 and 30 is 1, confirming that 23/30 cannot be reduced further—it is already in its simplest irreducible form.
Working: 23/30

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 30 produces a repeating decimal (approximately 0.766667, or 76.6667%).
Working: 23 ÷ 30 = 0.766667 (76.6667%)

Key Values:
- Simplified Fraction: 23/30
- Mixed Number Form: 23/30
- Decimal Value: 0.766667
- Percentage: 76.6667%

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1/6 + 3/5 = 23/30

Simplified Fraction

23/30

Mixed Number

Proper (23/30)

Decimal Value

0.766667

Percentage

76.6667%

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Step-by-Step Solution: 1/6 + 3/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 6 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 6 × 5 = 30.

LCD(6, 5) = 30

Step 2

Convert to Equivalent Fractions with Common Denominator 30

Multiply the numerator and denominator of 1/6 by 5, and multiply the numerator and denominator of 3/5 by 6 so both fractions share the common base 30.

1 × 5/6 × 5 = 5/30 and 3 × 6/5 × 6 = 18/30

Step 3

Add the Numerators

Now add the numerators (5 + 18 = 23) and keep the common denominator 30 unchanged.

5 + 18/30 = 23/30

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 23 and 30 is 1, confirming that 23/30 cannot be reduced further—it is already in its simplest irreducible form.

23/30

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 30 produces a repeating decimal (approximately 0.766667, or 76.6667%).

23 ÷ 30 = 0.766667 (76.6667%)

Visual Representation

The diagram below illustrates 1/6 plus 3/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/30`
Mixed Number Form	`23/30`
Decimal Form	`0.766667`
Percentage	`76.6667%`

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Frequently Asked Questions

What is 1/6 plus 3/5 as a fraction?

1/6 + 3/5 in simplest fraction form is 23/30.

What is 1/6 plus 3/5 as a decimal?

1/6 + 3/5 converted to a decimal is 0.766667.

What is 1/6 plus 3/5 as a percentage?

1/6 + 3/5 expressed as a percentage is 76.6667%.

Does 1/6 plus 3/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.766667...) because the denominator contains prime factors other than 2 and 5.