What is 3/20 plus 2/7? (Answer: 61/140)

Exact Answer

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Problem: What is 3/20 plus 2/7?
Formula / Expression: 3/20 + 2/7
Final Answer: 61/140
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 140
Multiply the numerator and denominator of 3/20 by 7, and multiply the numerator and denominator of 2/7 by 20 so both fractions share the common base 140.
Working: 3 × 7/20 × 7 = 21/140 and 2 × 20/7 × 20 = 40/140

Step 3: Add the Numerators
Now add the numerators (21 + 40 = 61) and keep the common denominator 140 unchanged.
Working: 21 + 40/140 = 61/140

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 61 and 140 is 1, confirming that 61/140 cannot be reduced further—it is already in its simplest irreducible form.
Working: 61/140

Step 5: Decimal & Percentage Representation
Dividing the numerator 61 by denominator 140 produces a repeating decimal (approximately 0.435714, or 43.5714%).
Working: 61 ÷ 140 = 0.435714 (43.5714%)

Key Values:
- Simplified Fraction: 61/140
- Mixed Number Form: 61/140
- Decimal Value: 0.435714
- Percentage: 43.5714%

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3/20 + 2/7 = 61/140

Simplified Fraction

61/140

Mixed Number

Proper (61/140)

Decimal Value

0.435714

Percentage

43.5714%

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Step-by-Step Solution: 3/20 + 2/7

Step 1

Find the Least Common Denominator (LCD)

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

LCD(20, 7) = 140

Step 2

Convert to Equivalent Fractions with Common Denominator 140

Multiply the numerator and denominator of 3/20 by 7, and multiply the numerator and denominator of 2/7 by 20 so both fractions share the common base 140.

3 × 7/20 × 7 = 21/140 and 2 × 20/7 × 20 = 40/140

Step 3

Add the Numerators

Now add the numerators (21 + 40 = 61) and keep the common denominator 140 unchanged.

21 + 40/140 = 61/140

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 61 and 140 is 1, confirming that 61/140 cannot be reduced further—it is already in its simplest irreducible form.

61/140

Step 5

Decimal & Percentage Representation

Dividing the numerator 61 by denominator 140 produces a repeating decimal (approximately 0.435714, or 43.5714%).

61 ÷ 140 = 0.435714 (43.5714%)

Visual Representation

The diagram below illustrates 3/20 plus 2/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`61/140`
Mixed Number Form	`61/140`
Decimal Form	`0.435714`
Percentage	`43.5714%`

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Frequently Asked Questions

What is 3/20 plus 2/7 as a fraction?

3/20 + 2/7 in simplest fraction form is 61/140.

What is 3/20 plus 2/7 as a decimal?

3/20 + 2/7 converted to a decimal is 0.435714.

What is 3/20 plus 2/7 as a percentage?

3/20 + 2/7 expressed as a percentage is 43.5714%.

Does 3/20 plus 2/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.435714...) because the denominator contains prime factors other than 2 and 5.