What is 5/13 plus 3/7? (Answer: 74/91)

Exact Answer

==================================================
Problem: What is 5/13 plus 3/7?
Formula / Expression: 5/13 + 3/7
Final Answer: 74/91
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 7 = 91.
Working: LCD(13, 7) = 91

Step 2: Convert to Equivalent Fractions with Common Denominator 91
Multiply the numerator and denominator of 5/13 by 7, and multiply the numerator and denominator of 3/7 by 13 so both fractions share the common base 91.
Working: 5 × 7/13 × 7 = 35/91 and 3 × 13/7 × 13 = 39/91

Step 3: Add the Numerators
Now add the numerators (35 + 39 = 74) and keep the common denominator 91 unchanged.
Working: 35 + 39/91 = 74/91

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 74 and 91 is 1, confirming that 74/91 cannot be reduced further—it is already in its simplest irreducible form.
Working: 74/91

Step 5: Decimal & Percentage Representation
Dividing the numerator 74 by denominator 91 produces a repeating decimal (approximately 0.813187, or 81.3187%).
Working: 74 ÷ 91 = 0.813187 (81.3187%)

Key Values:
- Simplified Fraction: 74/91
- Mixed Number Form: 74/91
- Decimal Value: 0.813187
- Percentage: 81.3187%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-13-plus-3-7/
==================================================

5/13 + 3/7 = 74/91

Simplified Fraction

74/91

Mixed Number

Proper (74/91)

Decimal Value

0.813187

Percentage

81.3187%

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: 5/13 + 3/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 7 = 91.

LCD(13, 7) = 91

Step 2

Convert to Equivalent Fractions with Common Denominator 91

Multiply the numerator and denominator of 5/13 by 7, and multiply the numerator and denominator of 3/7 by 13 so both fractions share the common base 91.

5 × 7/13 × 7 = 35/91 and 3 × 13/7 × 13 = 39/91

Step 3

Add the Numerators

Now add the numerators (35 + 39 = 74) and keep the common denominator 91 unchanged.

35 + 39/91 = 74/91

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 74 and 91 is 1, confirming that 74/91 cannot be reduced further—it is already in its simplest irreducible form.

74/91

Step 5

Decimal & Percentage Representation

Dividing the numerator 74 by denominator 91 produces a repeating decimal (approximately 0.813187, or 81.3187%).

74 ÷ 91 = 0.813187 (81.3187%)

Visual Representation

The diagram below illustrates 5/13 plus 3/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`74/91`
Mixed Number Form	`74/91`
Decimal Form	`0.813187`
Percentage	`81.3187%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 5/13 plus 3/7 as a fraction?

5/13 + 3/7 in simplest fraction form is 74/91.

What is 5/13 plus 3/7 as a decimal?

5/13 + 3/7 converted to a decimal is 0.813187.

What is 5/13 plus 3/7 as a percentage?

5/13 + 3/7 expressed as a percentage is 81.3187%.

Does 5/13 plus 3/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.813187...) because the denominator contains prime factors other than 2 and 5.