What is 2/7 plus 7/20? (Answer: 89/140)

Exact Answer

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Problem: What is 2/7 plus 7/20?
Formula / Expression: 2/7 + 7/20
Final Answer: 89/140
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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 7/20 by 7 so both fractions share the common base 140.
Working: 2 × 20/7 × 20 = 40/140 and 7 × 7/20 × 7 = 49/140

Step 3: Add the Numerators
Now add the numerators (40 + 49 = 89) and keep the common denominator 140 unchanged.
Working: 40 + 49/140 = 89/140

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 89 and 140 is 1, confirming that 89/140 cannot be reduced further—it is already in its simplest irreducible form.
Working: 89/140

Step 5: Decimal & Percentage Representation
Dividing the numerator 89 by denominator 140 produces a repeating decimal (approximately 0.635714, or 63.5714%).
Working: 89 ÷ 140 = 0.635714 (63.5714%)

Key Values:
- Simplified Fraction: 89/140
- Mixed Number Form: 89/140
- Decimal Value: 0.635714
- Percentage: 63.5714%

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Solved with FractionsCalc:
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2/7 + 7/20 = 89/140

Simplified Fraction

89/140

Mixed Number

Proper (89/140)

Decimal Value

0.635714

Percentage

63.5714%

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

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 7/20 by 7 so both fractions share the common base 140.

2 × 20/7 × 20 = 40/140 and 7 × 7/20 × 7 = 49/140

Step 3

Add the Numerators

Now add the numerators (40 + 49 = 89) and keep the common denominator 140 unchanged.

40 + 49/140 = 89/140

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 89 and 140 is 1, confirming that 89/140 cannot be reduced further—it is already in its simplest irreducible form.

89/140

Step 5

Decimal & Percentage Representation

Dividing the numerator 89 by denominator 140 produces a repeating decimal (approximately 0.635714, or 63.5714%).

89 ÷ 140 = 0.635714 (63.5714%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`89/140`
Mixed Number Form	`89/140`
Decimal Form	`0.635714`
Percentage	`63.5714%`

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Frequently Asked Questions

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

2/7 + 7/20 in simplest fraction form is 89/140.

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

2/7 + 7/20 converted to a decimal is 0.635714.

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

2/7 + 7/20 expressed as a percentage is 63.5714%.

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

It results in a repeating decimal (approximately 0.635714...) because the denominator contains prime factors other than 2 and 5.