What is 10/23 plus 10/13? (Answer: 360/299)

Exact Answer

==================================================
Problem: What is 10/23 plus 10/13?
Formula / Expression: 10/23 + 10/13
Final Answer: 1 61/299 (360/299)
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 23 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 13 = 299.
Working: LCD(23, 13) = 299

Step 2: Convert to Equivalent Fractions with Common Denominator 299
Multiply the numerator and denominator of 10/23 by 13, and multiply the numerator and denominator of 10/13 by 23 so both fractions share the common base 299.
Working: 10 × 13/23 × 13 = 130/299 and 10 × 23/13 × 23 = 230/299

Step 3: Add the Numerators
Now add the numerators (130 + 230 = 360) and keep the common denominator 299 unchanged.
Working: 130 + 230/299 = 360/299

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 360 and 299 is 1, confirming that 360/299 cannot be reduced further—it is already in its simplest irreducible form.
Working: 360/299

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (360) is greater than the denominator (299), divide 360 by 299: it goes in 1 whole time(s) with a remainder of 61, giving the mixed number 1 61/299.
Working: 360/299 = 1 61/299

Step 6: Decimal & Percentage Representation
Dividing the numerator 360 by denominator 299 produces a repeating decimal (approximately 1.204013, or 120.4013%).
Working: 360 ÷ 299 = 1.204013 (120.4013%)

Key Values:
- Simplified Fraction: 360/299
- Mixed Number Form: 1 61/299
- Decimal Value: 1.204013
- Percentage: 120.4013%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-23-plus-10-13/
==================================================

10/23 + 10/13 = 360/299

Simplified Fraction

360/299

Mixed Number

1 61/299

Decimal Value

1.204013

Percentage

120.4013%

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: 10/23 + 10/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 23 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 13 = 299.

LCD(23, 13) = 299

Step 2

Convert to Equivalent Fractions with Common Denominator 299

Multiply the numerator and denominator of 10/23 by 13, and multiply the numerator and denominator of 10/13 by 23 so both fractions share the common base 299.

10 × 13/23 × 13 = 130/299 and 10 × 23/13 × 23 = 230/299

Step 3

Add the Numerators

Now add the numerators (130 + 230 = 360) and keep the common denominator 299 unchanged.

130 + 230/299 = 360/299

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 360 and 299 is 1, confirming that 360/299 cannot be reduced further—it is already in its simplest irreducible form.

360/299

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (360) is greater than the denominator (299), divide 360 by 299: it goes in 1 whole time(s) with a remainder of 61, giving the mixed number 1 61/299.

360/299 = 161/299

Step 6

Decimal & Percentage Representation

Dividing the numerator 360 by denominator 299 produces a repeating decimal (approximately 1.204013, or 120.4013%).

360 ÷ 299 = 1.204013 (120.4013%)

Visual Representation

The diagram below illustrates 10/23 plus 10/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`360/299`
Mixed Number Form	`1 61/299`
Decimal Form	`1.204013`
Percentage	`120.4013%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 10/23 plus 10/13 as a fraction?

10/23 + 10/13 in simplest fraction form is 360/299 (or 1 61/299 as a mixed number).

What is 10/23 plus 10/13 as a decimal?

10/23 + 10/13 converted to a decimal is 1.204013.

What is 10/23 plus 10/13 as a percentage?

10/23 + 10/13 expressed as a percentage is 120.4013%.

How do you write 10/23 plus 10/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 360/299 can be written as the mixed number 1 61/299.

Does 10/23 plus 10/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.204013...) because the denominator contains prime factors other than 2 and 5.