What is 18/32 plus 9/13? (Answer: 261/208)

Exact Answer

==================================================
Problem: What is 18/32 plus 9/13?
Formula / Expression: 18/32 + 9/13
Final Answer: 1 53/208 (261/208)
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 32 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 32 × 13 = 416.
Working: LCD(32, 13) = 416

Step 2: Convert to Equivalent Fractions with Common Denominator 416
Multiply the numerator and denominator of 18/32 by 13, and multiply the numerator and denominator of 9/13 by 32 so both fractions share the common base 416.
Working: 18 × 13/32 × 13 = 234/416 and 9 × 32/13 × 32 = 288/416

Step 3: Add the Numerators
Now add the numerators (234 + 288 = 522) and keep the common denominator 416 unchanged.
Working: 234 + 288/416 = 522/416

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 522 and 416, which is 2. Divide both the numerator and denominator by 2.
Working: 522 ÷ 2/416 ÷ 2 = 261/208

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (261) is greater than the denominator (208), divide 261 by 208: it goes in 1 whole time(s) with a remainder of 53, giving the mixed number 1 53/208.
Working: 261/208 = 1 53/208

Step 6: Decimal & Percentage Representation
Dividing the numerator 261 by denominator 208 produces a repeating decimal (approximately 1.254808, or 125.4808%).
Working: 261 ÷ 208 = 1.254808 (125.4808%)

Key Values:
- Simplified Fraction: 261/208
- Mixed Number Form: 1 53/208
- Decimal Value: 1.254808
- Percentage: 125.4808%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-18-32-plus-9-13/
==================================================

18/32 + 9/13 = 261/208

Simplified Fraction

261/208

Mixed Number

1 53/208

Decimal Value

1.254808

Percentage

125.4808%

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: 18/32 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 32 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 32 × 13 = 416.

LCD(32, 13) = 416

Step 2

Convert to Equivalent Fractions with Common Denominator 416

Multiply the numerator and denominator of 18/32 by 13, and multiply the numerator and denominator of 9/13 by 32 so both fractions share the common base 416.

18 × 13/32 × 13 = 234/416 and 9 × 32/13 × 32 = 288/416

Step 3

Add the Numerators

Now add the numerators (234 + 288 = 522) and keep the common denominator 416 unchanged.

234 + 288/416 = 522/416

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 522 and 416, which is 2. Divide both the numerator and denominator by 2.

522 ÷ 2/416 ÷ 2 = 261/208

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (261) is greater than the denominator (208), divide 261 by 208: it goes in 1 whole time(s) with a remainder of 53, giving the mixed number 1 53/208.

261/208 = 153/208

Step 6

Decimal & Percentage Representation

Dividing the numerator 261 by denominator 208 produces a repeating decimal (approximately 1.254808, or 125.4808%).

261 ÷ 208 = 1.254808 (125.4808%)

Visual Representation

The diagram below illustrates 18/32 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`261/208`
Mixed Number Form	`1 53/208`
Decimal Form	`1.254808`
Percentage	`125.4808%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 18/32 plus 9/13 as a fraction?

18/32 + 9/13 in simplest fraction form is 261/208 (or 1 53/208 as a mixed number).

What is 18/32 plus 9/13 as a decimal?

18/32 + 9/13 converted to a decimal is 1.254808.

What is 18/32 plus 9/13 as a percentage?

18/32 + 9/13 expressed as a percentage is 125.4808%.

How do you write 18/32 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 261/208 can be written as the mixed number 1 53/208.

Does 18/32 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.254808...) because the denominator contains prime factors other than 2 and 5.