What is 2/9 plus 10/20? (Answer: 13/18)

Exact Answer

==================================================
Problem: What is 2/9 plus 10/20?
Formula / Expression: 2/9 + 10/20
Final Answer: 13/18
==================================================

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 10/20 by 9 so both fractions share the common base 180.
Working: 2 × 20/9 × 20 = 40/180 and 10 × 9/20 × 9 = 90/180

Step 3: Add the Numerators
Now add the numerators (40 + 90 = 130) and keep the common denominator 180 unchanged.
Working: 40 + 90/180 = 130/180

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 130 and 180, which is 10. Divide both the numerator and denominator by 10.
Working: 130 ÷ 10/180 ÷ 10 = 13/18

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 18 produces a repeating decimal (approximately 0.722222, or 72.2222%).
Working: 13 ÷ 18 = 0.722222 (72.2222%)

Key Values:
- Simplified Fraction: 13/18
- Mixed Number Form: 13/18
- Decimal Value: 0.722222
- Percentage: 72.2222%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-9-plus-10-20/
==================================================

2/9 + 10/20 = 13/18

Simplified Fraction

13/18

Mixed Number

Proper (13/18)

Decimal Value

0.722222

Percentage

72.2222%

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 + 10/20

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 10/20 by 9 so both fractions share the common base 180.

2 × 20/9 × 20 = 40/180 and 10 × 9/20 × 9 = 90/180

Step 3

Add the Numerators

Now add the numerators (40 + 90 = 130) and keep the common denominator 180 unchanged.

40 + 90/180 = 130/180

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 130 and 180, which is 10. Divide both the numerator and denominator by 10.

130 ÷ 10/180 ÷ 10 = 13/18

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 18 produces a repeating decimal (approximately 0.722222, or 72.2222%).

13 ÷ 18 = 0.722222 (72.2222%)

Visual Representation

The diagram below illustrates 2/9 plus 10/20 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/18`
Mixed Number Form	`13/18`
Decimal Form	`0.722222`
Percentage	`72.2222%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 2/9 plus 10/20 as a fraction?

2/9 + 10/20 in simplest fraction form is 13/18.

What is 2/9 plus 10/20 as a decimal?

2/9 + 10/20 converted to a decimal is 0.722222.

What is 2/9 plus 10/20 as a percentage?

2/9 + 10/20 expressed as a percentage is 72.2222%.

Does 2/9 plus 10/20 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.722222...) because the denominator contains prime factors other than 2 and 5.