What is 1/2 plus 7/13? (Answer: 27/26)

Exact Answer

==================================================
Problem: What is 1/2 plus 7/13?
Formula / Expression: 1/2 + 7/13
Final Answer: 1 1/26 (27/26)
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 2 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 2 × 13 = 26.
Working: LCD(2, 13) = 26

Step 2: Convert to Equivalent Fractions with Common Denominator 26
Multiply the numerator and denominator of 1/2 by 13, and multiply the numerator and denominator of 7/13 by 2 so both fractions share the common base 26.
Working: 1 × 13/2 × 13 = 13/26 and 7 × 2/13 × 2 = 14/26

Step 3: Add the Numerators
Now add the numerators (13 + 14 = 27) and keep the common denominator 26 unchanged.
Working: 13 + 14/26 = 27/26

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 27 and 26 is 1, confirming that 27/26 cannot be reduced further—it is already in its simplest irreducible form.
Working: 27/26

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (27) is greater than the denominator (26), divide 27 by 26: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/26.
Working: 27/26 = 1 1/26

Step 6: Decimal & Percentage Representation
Dividing the numerator 27 by denominator 26 produces a repeating decimal (approximately 1.038462, or 103.8462%).
Working: 27 ÷ 26 = 1.038462 (103.8462%)

Key Values:
- Simplified Fraction: 27/26
- Mixed Number Form: 1 1/26
- Decimal Value: 1.038462
- Percentage: 103.8462%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-2-plus-7-13/
==================================================

1/2 + 7/13 = 27/26

Simplified Fraction

27/26

Mixed Number

1 1/26

Decimal Value

1.038462

Percentage

103.8462%

Reduce / Convert Fraction:

Convert Fraction:

Enter Decimal Number:

Enter Percentage: %

What is % of

From Value: To Value:

Simplify Ratio: :

Switch to Proportion / Missing X Solver (A/B = C/D) →

Enter 3 known numbers and leave 1 empty (or type x) to solve:

← Switch to Ratio Simplifier (A:B)

Provide any 2 values below to calculate the remaining:

Price before discount

Discount

Price after discount

You saved

+ Add Sales Tax & Extra Coupon (Optional)

Sales Tax: % Extra Off: %

Provide any 2 values below to calculate the remaining:

Cost

Markup

REVENUE

Gross Profit

Profit Margin

Bill Subtotal

Tip Percentage

Split (People)

👥

Quick Tip:

Total Bill

Split Between

👥

Tip % (Optional)

Include Tip:

Total Price

Quantity

Unit of Measure

← Discount & Sales Tax • Ratio Simplifier (A:B) →

First Number: Second Number:

Find All Factors of:

Dividend: ÷ Divisor:

Number to Round: To Nearest:

Method: Standard (5+ ↑) Always Up (Ceil) Always Down (Floor)

Presets:

√ Square Root of: OR Power (x^y): ^{^}

x² + x + = 0

Number (n! & log):

Circle Radius (r):

Side a: Side b:

Angle (Degrees): °

Numbers (comma separated):

Total Items (n): Choose (r):

Decimal Number:

Number (1–3999):

Step-by-Step Solution: 1/2 + 7/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 2 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 2 × 13 = 26.

LCD(2, 13) = 26

Step 2

Convert to Equivalent Fractions with Common Denominator 26

Multiply the numerator and denominator of 1/2 by 13, and multiply the numerator and denominator of 7/13 by 2 so both fractions share the common base 26.

1 × 13/2 × 13 = 13/26 and 7 × 2/13 × 2 = 14/26

Step 3

Add the Numerators

Now add the numerators (13 + 14 = 27) and keep the common denominator 26 unchanged.

13 + 14/26 = 27/26

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 27 and 26 is 1, confirming that 27/26 cannot be reduced further—it is already in its simplest irreducible form.

27/26

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (27) is greater than the denominator (26), divide 27 by 26: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/26.

27/26 = 11/26

Step 6

Decimal & Percentage Representation

Dividing the numerator 27 by denominator 26 produces a repeating decimal (approximately 1.038462, or 103.8462%).

27 ÷ 26 = 1.038462 (103.8462%)

Visual Representation

The diagram below illustrates 1/2 plus 7/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`27/26`
Mixed Number Form	`1 1/26`
Decimal Form	`1.038462`
Percentage	`103.8462%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 1/2 plus 7/13 as a fraction?

1/2 + 7/13 in simplest fraction form is 27/26 (or 1 1/26 as a mixed number).

What is 1/2 plus 7/13 as a decimal?

1/2 + 7/13 converted to a decimal is 1.038462.

What is 1/2 plus 7/13 as a percentage?

1/2 + 7/13 expressed as a percentage is 103.8462%.

How do you write 1/2 plus 7/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 27/26 can be written as the mixed number 1 1/26.

Does 1/2 plus 7/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.038462...) because the denominator contains prime factors other than 2 and 5.