What is 3/9 plus 10/22? (Answer: 26/33)

Exact Answer

==================================================
Problem: What is 3/9 plus 10/22?
Formula / Expression: 3/9 + 10/22
Final Answer: 26/33
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 22 = 198.
Working: LCD(9, 22) = 198

Step 2: Convert to Equivalent Fractions with Common Denominator 198
Multiply the numerator and denominator of 3/9 by 22, and multiply the numerator and denominator of 10/22 by 9 so both fractions share the common base 198.
Working: 3 × 22/9 × 22 = 66/198 and 10 × 9/22 × 9 = 90/198

Step 3: Add the Numerators
Now add the numerators (66 + 90 = 156) and keep the common denominator 198 unchanged.
Working: 66 + 90/198 = 156/198

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 156 and 198, which is 6. Divide both the numerator and denominator by 6.
Working: 156 ÷ 6/198 ÷ 6 = 26/33

Step 5: Decimal & Percentage Representation
Dividing the numerator 26 by denominator 33 produces a repeating decimal (approximately 0.787879, or 78.7879%).
Working: 26 ÷ 33 = 0.787879 (78.7879%)

Key Values:
- Simplified Fraction: 26/33
- Mixed Number Form: 26/33
- Decimal Value: 0.787879
- Percentage: 78.7879%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-9-plus-10-22/
==================================================

3/9 + 10/22 = 26/33

Simplified Fraction

26/33

Mixed Number

Proper (26/33)

Decimal Value

0.787879

Percentage

78.7879%

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: 3/9 + 10/22

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 22 = 198.

LCD(9, 22) = 198

Step 2

Convert to Equivalent Fractions with Common Denominator 198

Multiply the numerator and denominator of 3/9 by 22, and multiply the numerator and denominator of 10/22 by 9 so both fractions share the common base 198.

3 × 22/9 × 22 = 66/198 and 10 × 9/22 × 9 = 90/198

Step 3

Add the Numerators

Now add the numerators (66 + 90 = 156) and keep the common denominator 198 unchanged.

66 + 90/198 = 156/198

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 156 and 198, which is 6. Divide both the numerator and denominator by 6.

156 ÷ 6/198 ÷ 6 = 26/33

Step 5

Decimal & Percentage Representation

Dividing the numerator 26 by denominator 33 produces a repeating decimal (approximately 0.787879, or 78.7879%).

26 ÷ 33 = 0.787879 (78.7879%)

Visual Representation

The diagram below illustrates 3/9 plus 10/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`26/33`
Mixed Number Form	`26/33`
Decimal Form	`0.787879`
Percentage	`78.7879%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 3/9 plus 10/22 as a fraction?

3/9 + 10/22 in simplest fraction form is 26/33.

What is 3/9 plus 10/22 as a decimal?

3/9 + 10/22 converted to a decimal is 0.787879.

What is 3/9 plus 10/22 as a percentage?

3/9 + 10/22 expressed as a percentage is 78.7879%.

Does 3/9 plus 10/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.787879...) because the denominator contains prime factors other than 2 and 5.