What is 3/20 plus 7/13? (Answer: 179/260)

Exact Answer

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Problem: What is 3/20 plus 7/13?
Formula / Expression: 3/20 + 7/13
Final Answer: 179/260
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 20 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 20 × 13 = 260.
Working: LCD(20, 13) = 260

Step 2: Convert to Equivalent Fractions with Common Denominator 260
Multiply the numerator and denominator of 3/20 by 13, and multiply the numerator and denominator of 7/13 by 20 so both fractions share the common base 260.
Working: 3 × 13/20 × 13 = 39/260 and 7 × 20/13 × 20 = 140/260

Step 3: Add the Numerators
Now add the numerators (39 + 140 = 179) and keep the common denominator 260 unchanged.
Working: 39 + 140/260 = 179/260

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 179 and 260 is 1, confirming that 179/260 cannot be reduced further—it is already in its simplest irreducible form.
Working: 179/260

Step 5: Decimal & Percentage Representation
Dividing the numerator 179 by denominator 260 produces a repeating decimal (approximately 0.688462, or 68.8462%).
Working: 179 ÷ 260 = 0.688462 (68.8462%)

Key Values:
- Simplified Fraction: 179/260
- Mixed Number Form: 179/260
- Decimal Value: 0.688462
- Percentage: 68.8462%

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3/20 + 7/13 = 179/260

Simplified Fraction

179/260

Mixed Number

Proper (179/260)

Decimal Value

0.688462

Percentage

68.8462%

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Step-by-Step Solution: 3/20 + 7/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 20 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 20 × 13 = 260.

LCD(20, 13) = 260

Step 2

Convert to Equivalent Fractions with Common Denominator 260

Multiply the numerator and denominator of 3/20 by 13, and multiply the numerator and denominator of 7/13 by 20 so both fractions share the common base 260.

3 × 13/20 × 13 = 39/260 and 7 × 20/13 × 20 = 140/260

Step 3

Add the Numerators

Now add the numerators (39 + 140 = 179) and keep the common denominator 260 unchanged.

39 + 140/260 = 179/260

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 179 and 260 is 1, confirming that 179/260 cannot be reduced further—it is already in its simplest irreducible form.

179/260

Step 5

Decimal & Percentage Representation

Dividing the numerator 179 by denominator 260 produces a repeating decimal (approximately 0.688462, or 68.8462%).

179 ÷ 260 = 0.688462 (68.8462%)

Visual Representation

The diagram below illustrates 3/20 plus 7/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`179/260`
Mixed Number Form	`179/260`
Decimal Form	`0.688462`
Percentage	`68.8462%`

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Frequently Asked Questions

What is 3/20 plus 7/13 as a fraction?

3/20 + 7/13 in simplest fraction form is 179/260.

What is 3/20 plus 7/13 as a decimal?

3/20 + 7/13 converted to a decimal is 0.688462.

What is 3/20 plus 7/13 as a percentage?

3/20 + 7/13 expressed as a percentage is 68.8462%.

Does 3/20 plus 7/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.688462...) because the denominator contains prime factors other than 2 and 5.