What is 2/20 plus 2/15? (Answer: 7/30)

Exact Answer

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Problem: What is 2/20 plus 2/15?
Formula / Expression: 2/20 + 2/15
Final Answer: 7/30
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 20 and 15 share a common factor (GCD = 5). Finding their Least Common Multiple gives an LCD of 60 (which is smaller than their product 20 × 15 = 300, keeping the calculation simpler).
Working: LCD(20, 15) = 60

Step 2: Convert to Equivalent Fractions with Common Denominator 60
Multiply the numerator and denominator of 2/20 by 3, and multiply the numerator and denominator of 2/15 by 4 so both fractions share the common base 60.
Working: 2 × 3/20 × 3 = 6/60 and 2 × 4/15 × 4 = 8/60

Step 3: Add the Numerators
Now add the numerators (6 + 8 = 14) and keep the common denominator 60 unchanged.
Working: 6 + 8/60 = 14/60

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 14 and 60, which is 2. Divide both the numerator and denominator by 2.
Working: 14 ÷ 2/60 ÷ 2 = 7/30

Step 5: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 30 produces a repeating decimal (approximately 0.233333, or 23.3333%).
Working: 7 ÷ 30 = 0.233333 (23.3333%)

Key Values:
- Simplified Fraction: 7/30
- Mixed Number Form: 7/30
- Decimal Value: 0.233333
- Percentage: 23.3333%

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Solved with FractionsCalc:
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2/20 + 2/15 = 7/30

Simplified Fraction

7/30

Mixed Number

Proper (7/30)

Decimal Value

0.233333

Percentage

23.3333%

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Step-by-Step Solution: 2/20 + 2/15

Step 1

Find the Least Common Denominator (LCD)

The denominators 20 and 15 share a common factor (GCD = 5). Finding their Least Common Multiple gives an LCD of 60 (which is smaller than their product 20 × 15 = 300, keeping the calculation simpler).

LCD(20, 15) = 60

Step 2

Convert to Equivalent Fractions with Common Denominator 60

Multiply the numerator and denominator of 2/20 by 3, and multiply the numerator and denominator of 2/15 by 4 so both fractions share the common base 60.

2 × 3/20 × 3 = 6/60 and 2 × 4/15 × 4 = 8/60

Step 3

Add the Numerators

Now add the numerators (6 + 8 = 14) and keep the common denominator 60 unchanged.

6 + 8/60 = 14/60

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 14 and 60, which is 2. Divide both the numerator and denominator by 2.

14 ÷ 2/60 ÷ 2 = 7/30

Step 5

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 30 produces a repeating decimal (approximately 0.233333, or 23.3333%).

7 ÷ 30 = 0.233333 (23.3333%)

Visual Representation

The diagram below illustrates 2/20 plus 2/15 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/30`
Mixed Number Form	`7/30`
Decimal Form	`0.233333`
Percentage	`23.3333%`

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Frequently Asked Questions

What is 2/20 plus 2/15 as a fraction?

2/20 + 2/15 in simplest fraction form is 7/30.

What is 2/20 plus 2/15 as a decimal?

2/20 + 2/15 converted to a decimal is 0.233333.

What is 2/20 plus 2/15 as a percentage?

2/20 + 2/15 expressed as a percentage is 23.3333%.

Does 2/20 plus 2/15 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.233333...) because the denominator contains prime factors other than 2 and 5.