What is 2/9 plus 9/12? (Answer: 35/36)

Exact Answer

==================================================
Problem: What is 2/9 plus 9/12?
Formula / Expression: 2/9 + 9/12
Final Answer: 35/36
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 12 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 36 (which is smaller than their product 9 × 12 = 108, keeping the calculation simpler).
Working: LCD(9, 12) = 36

Step 2: Convert to Equivalent Fractions with Common Denominator 36
Multiply the numerator and denominator of 2/9 by 4, and multiply the numerator and denominator of 9/12 by 3 so both fractions share the common base 36.
Working: 2 × 4/9 × 4 = 8/36 and 9 × 3/12 × 3 = 27/36

Step 3: Add the Numerators
Now add the numerators (8 + 27 = 35) and keep the common denominator 36 unchanged.
Working: 8 + 27/36 = 35/36

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 35 and 36 is 1, confirming that 35/36 cannot be reduced further—it is already in its simplest irreducible form.
Working: 35/36

Step 5: Decimal & Percentage Representation
Dividing the numerator 35 by denominator 36 produces a repeating decimal (approximately 0.972222, or 97.2222%).
Working: 35 ÷ 36 = 0.972222 (97.2222%)

Key Values:
- Simplified Fraction: 35/36
- Mixed Number Form: 35/36
- Decimal Value: 0.972222
- Percentage: 97.2222%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-9-plus-9-12/
==================================================

2/9 + 9/12 = 35/36

Simplified Fraction

35/36

Mixed Number

Proper (35/36)

Decimal Value

0.972222

Percentage

97.2222%

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 + 9/12

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 12 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 36 (which is smaller than their product 9 × 12 = 108, keeping the calculation simpler).

LCD(9, 12) = 36

Step 2

Convert to Equivalent Fractions with Common Denominator 36

Multiply the numerator and denominator of 2/9 by 4, and multiply the numerator and denominator of 9/12 by 3 so both fractions share the common base 36.

2 × 4/9 × 4 = 8/36 and 9 × 3/12 × 3 = 27/36

Step 3

Add the Numerators

Now add the numerators (8 + 27 = 35) and keep the common denominator 36 unchanged.

8 + 27/36 = 35/36

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 35 and 36 is 1, confirming that 35/36 cannot be reduced further—it is already in its simplest irreducible form.

35/36

Step 5

Decimal & Percentage Representation

Dividing the numerator 35 by denominator 36 produces a repeating decimal (approximately 0.972222, or 97.2222%).

35 ÷ 36 = 0.972222 (97.2222%)

Visual Representation

The diagram below illustrates 2/9 plus 9/12 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`35/36`
Mixed Number Form	`35/36`
Decimal Form	`0.972222`
Percentage	`97.2222%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 2/9 plus 9/12 as a fraction?

2/9 + 9/12 in simplest fraction form is 35/36.

What is 2/9 plus 9/12 as a decimal?

2/9 + 9/12 converted to a decimal is 0.972222.

What is 2/9 plus 9/12 as a percentage?

2/9 + 9/12 expressed as a percentage is 97.2222%.

Does 2/9 plus 9/12 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.972222...) because the denominator contains prime factors other than 2 and 5.