What is 3/7 plus 9/20? (Answer: 123/140)

Exact Answer

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Problem: What is 3/7 plus 9/20?
Formula / Expression: 3/7 + 9/20
Final Answer: 123/140
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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 3/7 by 20, and multiply the numerator and denominator of 9/20 by 7 so both fractions share the common base 140.
Working: 3 × 20/7 × 20 = 60/140 and 9 × 7/20 × 7 = 63/140

Step 3: Add the Numerators
Now add the numerators (60 + 63 = 123) and keep the common denominator 140 unchanged.
Working: 60 + 63/140 = 123/140

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 123 and 140 is 1, confirming that 123/140 cannot be reduced further—it is already in its simplest irreducible form.
Working: 123/140

Step 5: Decimal & Percentage Representation
Dividing the numerator 123 by denominator 140 produces a repeating decimal (approximately 0.878571, or 87.8571%).
Working: 123 ÷ 140 = 0.878571 (87.8571%)

Key Values:
- Simplified Fraction: 123/140
- Mixed Number Form: 123/140
- Decimal Value: 0.878571
- Percentage: 87.8571%

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3/7 + 9/20 = 123/140

Simplified Fraction

123/140

Mixed Number

Proper (123/140)

Decimal Value

0.878571

Percentage

87.8571%

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Step-by-Step Solution: 3/7 + 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 3/7 by 20, and multiply the numerator and denominator of 9/20 by 7 so both fractions share the common base 140.

3 × 20/7 × 20 = 60/140 and 9 × 7/20 × 7 = 63/140

Step 3

Add the Numerators

Now add the numerators (60 + 63 = 123) and keep the common denominator 140 unchanged.

60 + 63/140 = 123/140

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 123 and 140 is 1, confirming that 123/140 cannot be reduced further—it is already in its simplest irreducible form.

123/140

Step 5

Decimal & Percentage Representation

Dividing the numerator 123 by denominator 140 produces a repeating decimal (approximately 0.878571, or 87.8571%).

123 ÷ 140 = 0.878571 (87.8571%)

Visual Representation

The diagram below illustrates 3/7 plus 9/20 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`123/140`
Mixed Number Form	`123/140`
Decimal Form	`0.878571`
Percentage	`87.8571%`

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Frequently Asked Questions

What is 3/7 plus 9/20 as a fraction?

3/7 + 9/20 in simplest fraction form is 123/140.

What is 3/7 plus 9/20 as a decimal?

3/7 + 9/20 converted to a decimal is 0.878571.

What is 3/7 plus 9/20 as a percentage?

3/7 + 9/20 expressed as a percentage is 87.8571%.

Does 3/7 plus 9/20 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.878571...) because the denominator contains prime factors other than 2 and 5.