What is 9/20 plus 2/3? (Answer: 67/60)

Exact Answer

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Problem: What is 9/20 plus 2/3?
Formula / Expression: 9/20 + 2/3
Final Answer: 1 7/60 (67/60)
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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 9/20 by 3, and multiply the numerator and denominator of 2/3 by 20 so both fractions share the common base 60.
Working: 9 × 3/20 × 3 = 27/60 and 2 × 20/3 × 20 = 40/60

Step 3: Add the Numerators
Now add the numerators (27 + 40 = 67) and keep the common denominator 60 unchanged.
Working: 27 + 40/60 = 67/60

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 67 and 60 is 1, confirming that 67/60 cannot be reduced further—it is already in its simplest irreducible form.
Working: 67/60

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (67) is greater than the denominator (60), divide 67 by 60: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/60.
Working: 67/60 = 1 7/60

Step 6: Decimal & Percentage Representation
Dividing the numerator 67 by denominator 60 produces a repeating decimal (approximately 1.116667, or 111.6667%).
Working: 67 ÷ 60 = 1.116667 (111.6667%)

Key Values:
- Simplified Fraction: 67/60
- Mixed Number Form: 1 7/60
- Decimal Value: 1.116667
- Percentage: 111.6667%

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Solved with FractionsCalc:
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9/20 + 2/3 = 67/60

Simplified Fraction

67/60

Mixed Number

1 7/60

Decimal Value

1.116667

Percentage

111.6667%

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Step-by-Step Solution: 9/20 + 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 9/20 by 3, and multiply the numerator and denominator of 2/3 by 20 so both fractions share the common base 60.

9 × 3/20 × 3 = 27/60 and 2 × 20/3 × 20 = 40/60

Step 3

Add the Numerators

Now add the numerators (27 + 40 = 67) and keep the common denominator 60 unchanged.

27 + 40/60 = 67/60

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 67 and 60 is 1, confirming that 67/60 cannot be reduced further—it is already in its simplest irreducible form.

67/60

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (67) is greater than the denominator (60), divide 67 by 60: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/60.

67/60 = 17/60

Step 6

Decimal & Percentage Representation

Dividing the numerator 67 by denominator 60 produces a repeating decimal (approximately 1.116667, or 111.6667%).

67 ÷ 60 = 1.116667 (111.6667%)

Visual Representation

The diagram below illustrates 9/20 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`67/60`
Mixed Number Form	`1 7/60`
Decimal Form	`1.116667`
Percentage	`111.6667%`

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Frequently Asked Questions

What is 9/20 plus 2/3 as a fraction?

9/20 + 2/3 in simplest fraction form is 67/60 (or 1 7/60 as a mixed number).

What is 9/20 plus 2/3 as a decimal?

9/20 + 2/3 converted to a decimal is 1.116667.

What is 9/20 plus 2/3 as a percentage?

9/20 + 2/3 expressed as a percentage is 111.6667%.

How do you write 9/20 plus 2/3 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 67/60 can be written as the mixed number 1 7/60.

Does 9/20 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.116667...) because the denominator contains prime factors other than 2 and 5.