What is 10/52 plus 4/13? (Answer: 1/2)

Exact Answer

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Problem: What is 10/52 plus 4/13?
Formula / Expression: 10/52 + 4/13
Final Answer: 1/2
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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 4/13 by 4 so both fractions share the common base 52.
Working: 10 × 1/52 × 1 = 10/52 and 4 × 4/13 × 4 = 16/52

Step 3: Add the Numerators
Now add the numerators (10 + 16 = 26) and keep the common denominator 52 unchanged.
Working: 10 + 16/52 = 26/52

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 26 and 52, which is 26. Divide both the numerator and denominator by 26.
Working: 26 ÷ 26/52 ÷ 26 = 1/2

Step 5: Decimal & Percentage Representation
Dividing the numerator 1 by denominator 2 yields an exact terminating decimal of 0.5 (or 50%).
Working: 1 ÷ 2 = 0.5 (50%)

Key Values:
- Simplified Fraction: 1/2
- Mixed Number Form: 1/2
- Decimal Value: 0.5
- Percentage: 50%

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Solved with FractionsCalc:
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10/52 + 4/13 = 1/2

Simplified Fraction

1/2

Mixed Number

Proper (1/2)

Decimal Value

0.5

Percentage

50%

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Step-by-Step Solution: 10/52 + 4/13

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 4/13 by 4 so both fractions share the common base 52.

10 × 1/52 × 1 = 10/52 and 4 × 4/13 × 4 = 16/52

Step 3

Add the Numerators

Now add the numerators (10 + 16 = 26) and keep the common denominator 52 unchanged.

10 + 16/52 = 26/52

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 26 and 52, which is 26. Divide both the numerator and denominator by 26.

26 ÷ 26/52 ÷ 26 = 1/2

Step 5

Decimal & Percentage Representation

Dividing the numerator 1 by denominator 2 yields an exact terminating decimal of 0.5 (or 50%).

1 ÷ 2 = 0.5 (50%)

Visual Representation

The diagram below illustrates 10/52 plus 4/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`1/2`
Mixed Number Form	`1/2`
Decimal Form	`0.5`
Percentage	`50%`

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Frequently Asked Questions

What is 10/52 plus 4/13 as a fraction?

10/52 + 4/13 in simplest fraction form is 1/2.

What is 10/52 plus 4/13 as a decimal?

10/52 + 4/13 converted to a decimal is 0.5.

What is 10/52 plus 4/13 as a percentage?

10/52 + 4/13 expressed as a percentage is 50%.

Does 10/52 plus 4/13 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.5) because the denominator in simplest terms contains only prime factors 2 and/or 5.