What is 10/52 plus 3/13? (Answer: 11/26)

Exact Answer

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Problem: What is 10/52 plus 3/13?
Formula / Expression: 10/52 + 3/13
Final Answer: 11/26
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 52 is an exact multiple of 13 (13 × 4 = 52). The Least Common Denominator (LCD) is simply 52, meaning we only need to scale one fraction.
Working: LCD(52, 13) = 52

Step 2: Convert to Equivalent Fractions with Common Denominator 52
Multiply the numerator and denominator of 10/52 by 1, and multiply the numerator and denominator of 3/13 by 4 so both fractions share the common base 52.
Working: 10 × 1/52 × 1 = 10/52 and 3 × 4/13 × 4 = 12/52

Step 3: Add the Numerators
Now add the numerators (10 + 12 = 22) and keep the common denominator 52 unchanged.
Working: 10 + 12/52 = 22/52

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 22 and 52, which is 2. Divide both the numerator and denominator by 2.
Working: 22 ÷ 2/52 ÷ 2 = 11/26

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 26 produces a repeating decimal (approximately 0.423077, or 42.3077%).
Working: 11 ÷ 26 = 0.423077 (42.3077%)

Key Values:
- Simplified Fraction: 11/26
- Mixed Number Form: 11/26
- Decimal Value: 0.423077
- Percentage: 42.3077%

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Solved with FractionsCalc:
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10/52 + 3/13 = 11/26

Simplified Fraction

11/26

Mixed Number

Proper (11/26)

Decimal Value

0.423077

Percentage

42.3077%

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Step-by-Step Solution: 10/52 + 3/13

Step 1

Find the Least Common Denominator (LCD)

Notice that 52 is an exact multiple of 13 (13 × 4 = 52). The Least Common Denominator (LCD) is simply 52, meaning we only need to scale one fraction.

LCD(52, 13) = 52

Step 2

Convert to Equivalent Fractions with Common Denominator 52

Multiply the numerator and denominator of 10/52 by 1, and multiply the numerator and denominator of 3/13 by 4 so both fractions share the common base 52.

10 × 1/52 × 1 = 10/52 and 3 × 4/13 × 4 = 12/52

Step 3

Add the Numerators

Now add the numerators (10 + 12 = 22) and keep the common denominator 52 unchanged.

10 + 12/52 = 22/52

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 22 and 52, which is 2. Divide both the numerator and denominator by 2.

22 ÷ 2/52 ÷ 2 = 11/26

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 26 produces a repeating decimal (approximately 0.423077, or 42.3077%).

11 ÷ 26 = 0.423077 (42.3077%)

Visual Representation

The diagram below illustrates 10/52 plus 3/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/26`
Mixed Number Form	`11/26`
Decimal Form	`0.423077`
Percentage	`42.3077%`

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Frequently Asked Questions

What is 10/52 plus 3/13 as a fraction?

10/52 + 3/13 in simplest fraction form is 11/26.

What is 10/52 plus 3/13 as a decimal?

10/52 + 3/13 converted to a decimal is 0.423077.

What is 10/52 plus 3/13 as a percentage?

10/52 + 3/13 expressed as a percentage is 42.3077%.

Does 10/52 plus 3/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.423077...) because the denominator contains prime factors other than 2 and 5.