What is 2/9 plus 8/20? (Answer: 28/45)

Exact Answer

==================================================
Problem: What is 2/9 plus 8/20?
Formula / Expression: 2/9 + 8/20
Final Answer: 28/45
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 20 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 20 = 180.
Working: LCD(9, 20) = 180

Step 2: Convert to Equivalent Fractions with Common Denominator 180
Multiply the numerator and denominator of 2/9 by 20, and multiply the numerator and denominator of 8/20 by 9 so both fractions share the common base 180.
Working: 2 × 20/9 × 20 = 40/180 and 8 × 9/20 × 9 = 72/180

Step 3: Add the Numerators
Now add the numerators (40 + 72 = 112) and keep the common denominator 180 unchanged.
Working: 40 + 72/180 = 112/180

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 112 and 180, which is 4. Divide both the numerator and denominator by 4.
Working: 112 ÷ 4/180 ÷ 4 = 28/45

Step 5: Decimal & Percentage Representation
Dividing the numerator 28 by denominator 45 produces a repeating decimal (approximately 0.622222, or 62.2222%).
Working: 28 ÷ 45 = 0.622222 (62.2222%)

Key Values:
- Simplified Fraction: 28/45
- Mixed Number Form: 28/45
- Decimal Value: 0.622222
- Percentage: 62.2222%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-9-plus-8-20/
==================================================

2/9 + 8/20 = 28/45

Simplified Fraction

28/45

Mixed Number

Proper (28/45)

Decimal Value

0.622222

Percentage

62.2222%

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 + 8/20

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 20 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 20 = 180.

LCD(9, 20) = 180

Step 2

Convert to Equivalent Fractions with Common Denominator 180

Multiply the numerator and denominator of 2/9 by 20, and multiply the numerator and denominator of 8/20 by 9 so both fractions share the common base 180.

2 × 20/9 × 20 = 40/180 and 8 × 9/20 × 9 = 72/180

Step 3

Add the Numerators

Now add the numerators (40 + 72 = 112) and keep the common denominator 180 unchanged.

40 + 72/180 = 112/180

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 112 and 180, which is 4. Divide both the numerator and denominator by 4.

112 ÷ 4/180 ÷ 4 = 28/45

Step 5

Decimal & Percentage Representation

Dividing the numerator 28 by denominator 45 produces a repeating decimal (approximately 0.622222, or 62.2222%).

28 ÷ 45 = 0.622222 (62.2222%)

Visual Representation

The diagram below illustrates 2/9 plus 8/20 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`28/45`
Mixed Number Form	`28/45`
Decimal Form	`0.622222`
Percentage	`62.2222%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 2/9 plus 8/20 as a fraction?

2/9 + 8/20 in simplest fraction form is 28/45.

What is 2/9 plus 8/20 as a decimal?

2/9 + 8/20 converted to a decimal is 0.622222.

What is 2/9 plus 8/20 as a percentage?

2/9 + 8/20 expressed as a percentage is 62.2222%.

Does 2/9 plus 8/20 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.622222...) because the denominator contains prime factors other than 2 and 5.