What is 2/45 plus 2/9? (Answer: 4/15)

Exact Answer

==================================================
Problem: What is 2/45 plus 2/9?
Formula / Expression: 2/45 + 2/9
Final Answer: 4/15
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 45 is an exact multiple of 9 (9 × 5 = 45). The Least Common Denominator (LCD) is simply 45, meaning we only need to scale one fraction.
Working: LCD(45, 9) = 45

Step 2: Convert to Equivalent Fractions with Common Denominator 45
Multiply the numerator and denominator of 2/45 by 1, and multiply the numerator and denominator of 2/9 by 5 so both fractions share the common base 45.
Working: 2 × 1/45 × 1 = 2/45 and 2 × 5/9 × 5 = 10/45

Step 3: Add the Numerators
Now add the numerators (2 + 10 = 12) and keep the common denominator 45 unchanged.
Working: 2 + 10/45 = 12/45

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 12 and 45, which is 3. Divide both the numerator and denominator by 3.
Working: 12 ÷ 3/45 ÷ 3 = 4/15

Step 5: Decimal & Percentage Representation
Dividing the numerator 4 by denominator 15 produces a repeating decimal (approximately 0.266667, or 26.6667%).
Working: 4 ÷ 15 = 0.266667 (26.6667%)

Key Values:
- Simplified Fraction: 4/15
- Mixed Number Form: 4/15
- Decimal Value: 0.266667
- Percentage: 26.6667%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-45-plus-2-9/
==================================================

2/45 + 2/9 = 4/15

Simplified Fraction

4/15

Mixed Number

Proper (4/15)

Decimal Value

0.266667

Percentage

26.6667%

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: 2/45 + 2/9

Step 1

Find the Least Common Denominator (LCD)

Notice that 45 is an exact multiple of 9 (9 × 5 = 45). The Least Common Denominator (LCD) is simply 45, meaning we only need to scale one fraction.

LCD(45, 9) = 45

Step 2

Convert to Equivalent Fractions with Common Denominator 45

Multiply the numerator and denominator of 2/45 by 1, and multiply the numerator and denominator of 2/9 by 5 so both fractions share the common base 45.

2 × 1/45 × 1 = 2/45 and 2 × 5/9 × 5 = 10/45

Step 3

Add the Numerators

Now add the numerators (2 + 10 = 12) and keep the common denominator 45 unchanged.

2 + 10/45 = 12/45

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 12 and 45, which is 3. Divide both the numerator and denominator by 3.

12 ÷ 3/45 ÷ 3 = 4/15

Step 5

Decimal & Percentage Representation

Dividing the numerator 4 by denominator 15 produces a repeating decimal (approximately 0.266667, or 26.6667%).

4 ÷ 15 = 0.266667 (26.6667%)

Visual Representation

The diagram below illustrates 2/45 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`4/15`
Mixed Number Form	`4/15`
Decimal Form	`0.266667`
Percentage	`26.6667%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 2/45 plus 2/9 as a fraction?

2/45 + 2/9 in simplest fraction form is 4/15.

What is 2/45 plus 2/9 as a decimal?

2/45 + 2/9 converted to a decimal is 0.266667.

What is 2/45 plus 2/9 as a percentage?

2/45 + 2/9 expressed as a percentage is 26.6667%.

Does 2/45 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.266667...) because the denominator contains prime factors other than 2 and 5.