What is 7/20 plus 3/7? (Answer: 109/140)

Exact Answer

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Problem: What is 7/20 plus 3/7?
Formula / Expression: 7/20 + 3/7
Final Answer: 109/140
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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 7/20 by 7, and multiply the numerator and denominator of 3/7 by 20 so both fractions share the common base 140.
Working: 7 × 7/20 × 7 = 49/140 and 3 × 20/7 × 20 = 60/140

Step 3: Add the Numerators
Now add the numerators (49 + 60 = 109) and keep the common denominator 140 unchanged.
Working: 49 + 60/140 = 109/140

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 109 and 140 is 1, confirming that 109/140 cannot be reduced further—it is already in its simplest irreducible form.
Working: 109/140

Step 5: Decimal & Percentage Representation
Dividing the numerator 109 by denominator 140 produces a repeating decimal (approximately 0.778571, or 77.8571%).
Working: 109 ÷ 140 = 0.778571 (77.8571%)

Key Values:
- Simplified Fraction: 109/140
- Mixed Number Form: 109/140
- Decimal Value: 0.778571
- Percentage: 77.8571%

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7/20 + 3/7 = 109/140

Simplified Fraction

109/140

Mixed Number

Proper (109/140)

Decimal Value

0.778571

Percentage

77.8571%

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Step-by-Step Solution: 7/20 + 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 7/20 by 7, and multiply the numerator and denominator of 3/7 by 20 so both fractions share the common base 140.

7 × 7/20 × 7 = 49/140 and 3 × 20/7 × 20 = 60/140

Step 3

Add the Numerators

Now add the numerators (49 + 60 = 109) and keep the common denominator 140 unchanged.

49 + 60/140 = 109/140

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 109 and 140 is 1, confirming that 109/140 cannot be reduced further—it is already in its simplest irreducible form.

109/140

Step 5

Decimal & Percentage Representation

Dividing the numerator 109 by denominator 140 produces a repeating decimal (approximately 0.778571, or 77.8571%).

109 ÷ 140 = 0.778571 (77.8571%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`109/140`
Mixed Number Form	`109/140`
Decimal Form	`0.778571`
Percentage	`77.8571%`

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Frequently Asked Questions

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

7/20 + 3/7 in simplest fraction form is 109/140.

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

7/20 + 3/7 converted to a decimal is 0.778571.

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

7/20 + 3/7 expressed as a percentage is 77.8571%.

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

It results in a repeating decimal (approximately 0.778571...) because the denominator contains prime factors other than 2 and 5.