What is 2/20 plus 3/7? (Answer: 37/70)

Exact Answer

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Problem: What is 2/20 plus 3/7?
Formula / Expression: 2/20 + 3/7
Final Answer: 37/70
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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 2/20 by 7, and multiply the numerator and denominator of 3/7 by 20 so both fractions share the common base 140.
Working: 2 × 7/20 × 7 = 14/140 and 3 × 20/7 × 20 = 60/140

Step 3: Add the Numerators
Now add the numerators (14 + 60 = 74) and keep the common denominator 140 unchanged.
Working: 14 + 60/140 = 74/140

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 74 and 140, which is 2. Divide both the numerator and denominator by 2.
Working: 74 ÷ 2/140 ÷ 2 = 37/70

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 70 produces a repeating decimal (approximately 0.528571, or 52.8571%).
Working: 37 ÷ 70 = 0.528571 (52.8571%)

Key Values:
- Simplified Fraction: 37/70
- Mixed Number Form: 37/70
- Decimal Value: 0.528571
- Percentage: 52.8571%

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Solved with FractionsCalc:
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2/20 + 3/7 = 37/70

Simplified Fraction

37/70

Mixed Number

Proper (37/70)

Decimal Value

0.528571

Percentage

52.8571%

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

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

2 × 7/20 × 7 = 14/140 and 3 × 20/7 × 20 = 60/140

Step 3

Add the Numerators

Now add the numerators (14 + 60 = 74) and keep the common denominator 140 unchanged.

14 + 60/140 = 74/140

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 74 and 140, which is 2. Divide both the numerator and denominator by 2.

74 ÷ 2/140 ÷ 2 = 37/70

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 70 produces a repeating decimal (approximately 0.528571, or 52.8571%).

37 ÷ 70 = 0.528571 (52.8571%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/70`
Mixed Number Form	`37/70`
Decimal Form	`0.528571`
Percentage	`52.8571%`

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Frequently Asked Questions

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

2/20 + 3/7 in simplest fraction form is 37/70.

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

2/20 + 3/7 converted to a decimal is 0.528571.

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

2/20 + 3/7 expressed as a percentage is 52.8571%.

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

It results in a repeating decimal (approximately 0.528571...) because the denominator contains prime factors other than 2 and 5.