What is 1/4 plus 10/13? (Answer: 53/52)

Exact Answer

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Problem: What is 1/4 plus 10/13?
Formula / Expression: 1/4 + 10/13
Final Answer: 1 1/52 (53/52)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 4 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 4 × 13 = 52.
Working: LCD(4, 13) = 52

Step 2: Convert to Equivalent Fractions with Common Denominator 52
Multiply the numerator and denominator of 1/4 by 13, and multiply the numerator and denominator of 10/13 by 4 so both fractions share the common base 52.
Working: 1 × 13/4 × 13 = 13/52 and 10 × 4/13 × 4 = 40/52

Step 3: Add the Numerators
Now add the numerators (13 + 40 = 53) and keep the common denominator 52 unchanged.
Working: 13 + 40/52 = 53/52

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 53 and 52 is 1, confirming that 53/52 cannot be reduced further—it is already in its simplest irreducible form.
Working: 53/52

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (53) is greater than the denominator (52), divide 53 by 52: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/52.
Working: 53/52 = 1 1/52

Step 6: Decimal & Percentage Representation
Dividing the numerator 53 by denominator 52 produces a repeating decimal (approximately 1.019231, or 101.9231%).
Working: 53 ÷ 52 = 1.019231 (101.9231%)

Key Values:
- Simplified Fraction: 53/52
- Mixed Number Form: 1 1/52
- Decimal Value: 1.019231
- Percentage: 101.9231%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-4-plus-10-13/
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1/4 + 10/13 = 53/52

Simplified Fraction

53/52

Mixed Number

1 1/52

Decimal Value

1.019231

Percentage

101.9231%

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Step-by-Step Solution: 1/4 + 10/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 4 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 4 × 13 = 52.

LCD(4, 13) = 52

Step 2

Convert to Equivalent Fractions with Common Denominator 52

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

1 × 13/4 × 13 = 13/52 and 10 × 4/13 × 4 = 40/52

Step 3

Add the Numerators

Now add the numerators (13 + 40 = 53) and keep the common denominator 52 unchanged.

13 + 40/52 = 53/52

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 53 and 52 is 1, confirming that 53/52 cannot be reduced further—it is already in its simplest irreducible form.

53/52

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (53) is greater than the denominator (52), divide 53 by 52: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/52.

53/52 = 11/52

Step 6

Decimal & Percentage Representation

Dividing the numerator 53 by denominator 52 produces a repeating decimal (approximately 1.019231, or 101.9231%).

53 ÷ 52 = 1.019231 (101.9231%)

Visual Representation

The diagram below illustrates 1/4 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`53/52`
Mixed Number Form	`1 1/52`
Decimal Form	`1.019231`
Percentage	`101.9231%`

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Frequently Asked Questions

What is 1/4 plus 10/13 as a fraction?

1/4 + 10/13 in simplest fraction form is 53/52 (or 1 1/52 as a mixed number).

What is 1/4 plus 10/13 as a decimal?

1/4 + 10/13 converted to a decimal is 1.019231.

What is 1/4 plus 10/13 as a percentage?

1/4 + 10/13 expressed as a percentage is 101.9231%.

How do you write 1/4 plus 10/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 53/52 can be written as the mixed number 1 1/52.

Does 1/4 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.019231...) because the denominator contains prime factors other than 2 and 5.