What is 10/18 plus 2/3? (Answer: 11/9)

Exact Answer

==================================================
Problem: What is 10/18 plus 2/3?
Formula / Expression: 10/18 + 2/3
Final Answer: 1 2/9 (11/9)
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 18 is an exact multiple of 3 (3 × 6 = 18). The Least Common Denominator (LCD) is simply 18, meaning we only need to scale one fraction.
Working: LCD(18, 3) = 18

Step 2: Convert to Equivalent Fractions with Common Denominator 18
Multiply the numerator and denominator of 10/18 by 1, and multiply the numerator and denominator of 2/3 by 6 so both fractions share the common base 18.
Working: 10 × 1/18 × 1 = 10/18 and 2 × 6/3 × 6 = 12/18

Step 3: Add the Numerators
Now add the numerators (10 + 12 = 22) and keep the common denominator 18 unchanged.
Working: 10 + 12/18 = 22/18

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 22 and 18, which is 2. Divide both the numerator and denominator by 2.
Working: 22 ÷ 2/18 ÷ 2 = 11/9

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (11) is greater than the denominator (9), divide 11 by 9: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/9.
Working: 11/9 = 1 2/9

Step 6: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 9 produces a repeating decimal (approximately 1.222222, or 122.2222%).
Working: 11 ÷ 9 = 1.222222 (122.2222%)

Key Values:
- Simplified Fraction: 11/9
- Mixed Number Form: 1 2/9
- Decimal Value: 1.222222
- Percentage: 122.2222%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-18-plus-2-3/
==================================================

10/18 + 2/3 = 11/9

Simplified Fraction

11/9

Mixed Number

1 2/9

Decimal Value

1.222222

Percentage

122.2222%

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: 10/18 + 2/3

Step 1

Find the Least Common Denominator (LCD)

Notice that 18 is an exact multiple of 3 (3 × 6 = 18). The Least Common Denominator (LCD) is simply 18, meaning we only need to scale one fraction.

LCD(18, 3) = 18

Step 2

Convert to Equivalent Fractions with Common Denominator 18

Multiply the numerator and denominator of 10/18 by 1, and multiply the numerator and denominator of 2/3 by 6 so both fractions share the common base 18.

10 × 1/18 × 1 = 10/18 and 2 × 6/3 × 6 = 12/18

Step 3

Add the Numerators

Now add the numerators (10 + 12 = 22) and keep the common denominator 18 unchanged.

10 + 12/18 = 22/18

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 22 and 18, which is 2. Divide both the numerator and denominator by 2.

22 ÷ 2/18 ÷ 2 = 11/9

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (11) is greater than the denominator (9), divide 11 by 9: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/9.

11/9 = 12/9

Step 6

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 9 produces a repeating decimal (approximately 1.222222, or 122.2222%).

11 ÷ 9 = 1.222222 (122.2222%)

Visual Representation

The diagram below illustrates 10/18 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/9`
Mixed Number Form	`1 2/9`
Decimal Form	`1.222222`
Percentage	`122.2222%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 10/18 plus 2/3 as a fraction?

10/18 + 2/3 in simplest fraction form is 11/9 (or 1 2/9 as a mixed number).

What is 10/18 plus 2/3 as a decimal?

10/18 + 2/3 converted to a decimal is 1.222222.

What is 10/18 plus 2/3 as a percentage?

10/18 + 2/3 expressed as a percentage is 122.2222%.

How do you write 10/18 plus 2/3 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 11/9 can be written as the mixed number 1 2/9.

Does 10/18 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.222222...) because the denominator contains prime factors other than 2 and 5.