What is 13/19 plus 15/21? (Answer: 186/133)

Exact Answer

==================================================
Problem: What is 13/19 plus 15/21?
Formula / Expression: 13/19 + 15/21
Final Answer: 1 53/133 (186/133)
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 19 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 21 = 399.
Working: LCD(19, 21) = 399

Step 2: Convert to Equivalent Fractions with Common Denominator 399
Multiply the numerator and denominator of 13/19 by 21, and multiply the numerator and denominator of 15/21 by 19 so both fractions share the common base 399.
Working: 13 × 21/19 × 21 = 273/399 and 15 × 19/21 × 19 = 285/399

Step 3: Add the Numerators
Now add the numerators (273 + 285 = 558) and keep the common denominator 399 unchanged.
Working: 273 + 285/399 = 558/399

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 558 and 399, which is 3. Divide both the numerator and denominator by 3.
Working: 558 ÷ 3/399 ÷ 3 = 186/133

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (186) is greater than the denominator (133), divide 186 by 133: it goes in 1 whole time(s) with a remainder of 53, giving the mixed number 1 53/133.
Working: 186/133 = 1 53/133

Step 6: Decimal & Percentage Representation
Dividing the numerator 186 by denominator 133 produces a repeating decimal (approximately 1.398496, or 139.8496%).
Working: 186 ÷ 133 = 1.398496 (139.8496%)

Key Values:
- Simplified Fraction: 186/133
- Mixed Number Form: 1 53/133
- Decimal Value: 1.398496
- Percentage: 139.8496%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-19-plus-15-21/
==================================================

13/19 + 15/21 = 186/133

Simplified Fraction

186/133

Mixed Number

1 53/133

Decimal Value

1.398496

Percentage

139.8496%

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: 13/19 + 15/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 19 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 21 = 399.

LCD(19, 21) = 399

Step 2

Convert to Equivalent Fractions with Common Denominator 399

Multiply the numerator and denominator of 13/19 by 21, and multiply the numerator and denominator of 15/21 by 19 so both fractions share the common base 399.

13 × 21/19 × 21 = 273/399 and 15 × 19/21 × 19 = 285/399

Step 3

Add the Numerators

Now add the numerators (273 + 285 = 558) and keep the common denominator 399 unchanged.

273 + 285/399 = 558/399

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 558 and 399, which is 3. Divide both the numerator and denominator by 3.

558 ÷ 3/399 ÷ 3 = 186/133

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (186) is greater than the denominator (133), divide 186 by 133: it goes in 1 whole time(s) with a remainder of 53, giving the mixed number 1 53/133.

186/133 = 153/133

Step 6

Decimal & Percentage Representation

Dividing the numerator 186 by denominator 133 produces a repeating decimal (approximately 1.398496, or 139.8496%).

186 ÷ 133 = 1.398496 (139.8496%)

Visual Representation

The diagram below illustrates 13/19 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`186/133`
Mixed Number Form	`1 53/133`
Decimal Form	`1.398496`
Percentage	`139.8496%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 13/19 plus 15/21 as a fraction?

13/19 + 15/21 in simplest fraction form is 186/133 (or 1 53/133 as a mixed number).

What is 13/19 plus 15/21 as a decimal?

13/19 + 15/21 converted to a decimal is 1.398496.

What is 13/19 plus 15/21 as a percentage?

13/19 + 15/21 expressed as a percentage is 139.8496%.

How do you write 13/19 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 186/133 can be written as the mixed number 1 53/133.

Does 13/19 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.398496...) because the denominator contains prime factors other than 2 and 5.