What is 2/9 plus 9/32? (Answer: 145/288)

Exact Answer

==================================================
Problem: What is 2/9 plus 9/32?
Formula / Expression: 2/9 + 9/32
Final Answer: 145/288
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 32 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 32 = 288.
Working: LCD(9, 32) = 288

Step 2: Convert to Equivalent Fractions with Common Denominator 288
Multiply the numerator and denominator of 2/9 by 32, and multiply the numerator and denominator of 9/32 by 9 so both fractions share the common base 288.
Working: 2 × 32/9 × 32 = 64/288 and 9 × 9/32 × 9 = 81/288

Step 3: Add the Numerators
Now add the numerators (64 + 81 = 145) and keep the common denominator 288 unchanged.
Working: 64 + 81/288 = 145/288

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 145 and 288 is 1, confirming that 145/288 cannot be reduced further—it is already in its simplest irreducible form.
Working: 145/288

Step 5: Decimal & Percentage Representation
Dividing the numerator 145 by denominator 288 produces a repeating decimal (approximately 0.503472, or 50.3472%).
Working: 145 ÷ 288 = 0.503472 (50.3472%)

Key Values:
- Simplified Fraction: 145/288
- Mixed Number Form: 145/288
- Decimal Value: 0.503472
- Percentage: 50.3472%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-9-plus-9-32/
==================================================

2/9 + 9/32 = 145/288

Simplified Fraction

145/288

Mixed Number

Proper (145/288)

Decimal Value

0.503472

Percentage

50.3472%

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: 2/9 + 9/32

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 32 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 32 = 288.

LCD(9, 32) = 288

Step 2

Convert to Equivalent Fractions with Common Denominator 288

Multiply the numerator and denominator of 2/9 by 32, and multiply the numerator and denominator of 9/32 by 9 so both fractions share the common base 288.

2 × 32/9 × 32 = 64/288 and 9 × 9/32 × 9 = 81/288

Step 3

Add the Numerators

Now add the numerators (64 + 81 = 145) and keep the common denominator 288 unchanged.

64 + 81/288 = 145/288

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 145 and 288 is 1, confirming that 145/288 cannot be reduced further—it is already in its simplest irreducible form.

145/288

Step 5

Decimal & Percentage Representation

Dividing the numerator 145 by denominator 288 produces a repeating decimal (approximately 0.503472, or 50.3472%).

145 ÷ 288 = 0.503472 (50.3472%)

Visual Representation

The diagram below illustrates 2/9 plus 9/32 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`145/288`
Mixed Number Form	`145/288`
Decimal Form	`0.503472`
Percentage	`50.3472%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 2/9 plus 9/32 as a fraction?

2/9 + 9/32 in simplest fraction form is 145/288.

What is 2/9 plus 9/32 as a decimal?

2/9 + 9/32 converted to a decimal is 0.503472.

What is 2/9 plus 9/32 as a percentage?

2/9 + 9/32 expressed as a percentage is 50.3472%.

Does 2/9 plus 9/32 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.503472...) because the denominator contains prime factors other than 2 and 5.