What is 2/13 plus 10/60? (Answer: 25/78)

Exact Answer

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Problem: What is 2/13 plus 10/60?
Formula / Expression: 2/13 + 10/60
Final Answer: 25/78
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 60 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 60 = 780.
Working: LCD(13, 60) = 780

Step 2: Convert to Equivalent Fractions with Common Denominator 780
Multiply the numerator and denominator of 2/13 by 60, and multiply the numerator and denominator of 10/60 by 13 so both fractions share the common base 780.
Working: 2 × 60/13 × 60 = 120/780 and 10 × 13/60 × 13 = 130/780

Step 3: Add the Numerators
Now add the numerators (120 + 130 = 250) and keep the common denominator 780 unchanged.
Working: 120 + 130/780 = 250/780

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 250 and 780, which is 10. Divide both the numerator and denominator by 10.
Working: 250 ÷ 10/780 ÷ 10 = 25/78

Step 5: Decimal & Percentage Representation
Dividing the numerator 25 by denominator 78 produces a repeating decimal (approximately 0.320513, or 32.0513%).
Working: 25 ÷ 78 = 0.320513 (32.0513%)

Key Values:
- Simplified Fraction: 25/78
- Mixed Number Form: 25/78
- Decimal Value: 0.320513
- Percentage: 32.0513%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-13-plus-10-60/
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2/13 + 10/60 = 25/78

Simplified Fraction

25/78

Mixed Number

Proper (25/78)

Decimal Value

0.320513

Percentage

32.0513%

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Step-by-Step Solution: 2/13 + 10/60

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 60 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 60 = 780.

LCD(13, 60) = 780

Step 2

Convert to Equivalent Fractions with Common Denominator 780

Multiply the numerator and denominator of 2/13 by 60, and multiply the numerator and denominator of 10/60 by 13 so both fractions share the common base 780.

2 × 60/13 × 60 = 120/780 and 10 × 13/60 × 13 = 130/780

Step 3

Add the Numerators

Now add the numerators (120 + 130 = 250) and keep the common denominator 780 unchanged.

120 + 130/780 = 250/780

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 250 and 780, which is 10. Divide both the numerator and denominator by 10.

250 ÷ 10/780 ÷ 10 = 25/78

Step 5

Decimal & Percentage Representation

Dividing the numerator 25 by denominator 78 produces a repeating decimal (approximately 0.320513, or 32.0513%).

25 ÷ 78 = 0.320513 (32.0513%)

Visual Representation

The diagram below illustrates 2/13 plus 10/60 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`25/78`
Mixed Number Form	`25/78`
Decimal Form	`0.320513`
Percentage	`32.0513%`

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Frequently Asked Questions

What is 2/13 plus 10/60 as a fraction?

2/13 + 10/60 in simplest fraction form is 25/78.

What is 2/13 plus 10/60 as a decimal?

2/13 + 10/60 converted to a decimal is 0.320513.

What is 2/13 plus 10/60 as a percentage?

2/13 + 10/60 expressed as a percentage is 32.0513%.

Does 2/13 plus 10/60 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.320513...) because the denominator contains prime factors other than 2 and 5.