What is 2/7 plus 9/20? (Answer: 103/140)

Exact Answer

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Problem: What is 2/7 plus 9/20?
Formula / Expression: 2/7 + 9/20
Final Answer: 103/140
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 20 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 20 = 140.
Working: LCD(7, 20) = 140

Step 2: Convert to Equivalent Fractions with Common Denominator 140
Multiply the numerator and denominator of 2/7 by 20, and multiply the numerator and denominator of 9/20 by 7 so both fractions share the common base 140.
Working: 2 × 20/7 × 20 = 40/140 and 9 × 7/20 × 7 = 63/140

Step 3: Add the Numerators
Now add the numerators (40 + 63 = 103) and keep the common denominator 140 unchanged.
Working: 40 + 63/140 = 103/140

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 103 and 140 is 1, confirming that 103/140 cannot be reduced further—it is already in its simplest irreducible form.
Working: 103/140

Step 5: Decimal & Percentage Representation
Dividing the numerator 103 by denominator 140 produces a repeating decimal (approximately 0.735714, or 73.5714%).
Working: 103 ÷ 140 = 0.735714 (73.5714%)

Key Values:
- Simplified Fraction: 103/140
- Mixed Number Form: 103/140
- Decimal Value: 0.735714
- Percentage: 73.5714%

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Solved with FractionsCalc:
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2/7 + 9/20 = 103/140

Simplified Fraction

103/140

Mixed Number

Proper (103/140)

Decimal Value

0.735714

Percentage

73.5714%

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Step-by-Step Solution: 2/7 + 9/20

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 20 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 20 = 140.

LCD(7, 20) = 140

Step 2

Convert to Equivalent Fractions with Common Denominator 140

Multiply the numerator and denominator of 2/7 by 20, and multiply the numerator and denominator of 9/20 by 7 so both fractions share the common base 140.

2 × 20/7 × 20 = 40/140 and 9 × 7/20 × 7 = 63/140

Step 3

Add the Numerators

Now add the numerators (40 + 63 = 103) and keep the common denominator 140 unchanged.

40 + 63/140 = 103/140

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 103 and 140 is 1, confirming that 103/140 cannot be reduced further—it is already in its simplest irreducible form.

103/140

Step 5

Decimal & Percentage Representation

Dividing the numerator 103 by denominator 140 produces a repeating decimal (approximately 0.735714, or 73.5714%).

103 ÷ 140 = 0.735714 (73.5714%)

Visual Representation

The diagram below illustrates 2/7 plus 9/20 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`103/140`
Mixed Number Form	`103/140`
Decimal Form	`0.735714`
Percentage	`73.5714%`

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Frequently Asked Questions

What is 2/7 plus 9/20 as a fraction?

2/7 + 9/20 in simplest fraction form is 103/140.

What is 2/7 plus 9/20 as a decimal?

2/7 + 9/20 converted to a decimal is 0.735714.

What is 2/7 plus 9/20 as a percentage?

2/7 + 9/20 expressed as a percentage is 73.5714%.

Does 2/7 plus 9/20 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.735714...) because the denominator contains prime factors other than 2 and 5.