What is 1/5 plus 9/22? (Answer: 67/110)

Exact Answer

==================================================
Problem: What is 1/5 plus 9/22?
Formula / Expression: 1/5 + 9/22
Final Answer: 67/110
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 5 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 22 = 110.
Working: LCD(5, 22) = 110

Step 2: Convert to Equivalent Fractions with Common Denominator 110
Multiply the numerator and denominator of 1/5 by 22, and multiply the numerator and denominator of 9/22 by 5 so both fractions share the common base 110.
Working: 1 × 22/5 × 22 = 22/110 and 9 × 5/22 × 5 = 45/110

Step 3: Add the Numerators
Now add the numerators (22 + 45 = 67) and keep the common denominator 110 unchanged.
Working: 22 + 45/110 = 67/110

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 67 and 110 is 1, confirming that 67/110 cannot be reduced further—it is already in its simplest irreducible form.
Working: 67/110

Step 5: Decimal & Percentage Representation
Dividing the numerator 67 by denominator 110 produces a repeating decimal (approximately 0.609091, or 60.9091%).
Working: 67 ÷ 110 = 0.609091 (60.9091%)

Key Values:
- Simplified Fraction: 67/110
- Mixed Number Form: 67/110
- Decimal Value: 0.609091
- Percentage: 60.9091%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-5-plus-9-22/
==================================================

1/5 + 9/22 = 67/110

Simplified Fraction

67/110

Mixed Number

Proper (67/110)

Decimal Value

0.609091

Percentage

60.9091%

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: 1/5 + 9/22

Step 1

Find the Least Common Denominator (LCD)

The denominators 5 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 22 = 110.

LCD(5, 22) = 110

Step 2

Convert to Equivalent Fractions with Common Denominator 110

Multiply the numerator and denominator of 1/5 by 22, and multiply the numerator and denominator of 9/22 by 5 so both fractions share the common base 110.

1 × 22/5 × 22 = 22/110 and 9 × 5/22 × 5 = 45/110

Step 3

Add the Numerators

Now add the numerators (22 + 45 = 67) and keep the common denominator 110 unchanged.

22 + 45/110 = 67/110

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 67 and 110 is 1, confirming that 67/110 cannot be reduced further—it is already in its simplest irreducible form.

67/110

Step 5

Decimal & Percentage Representation

Dividing the numerator 67 by denominator 110 produces a repeating decimal (approximately 0.609091, or 60.9091%).

67 ÷ 110 = 0.609091 (60.9091%)

Visual Representation

The diagram below illustrates 1/5 plus 9/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`67/110`
Mixed Number Form	`67/110`
Decimal Form	`0.609091`
Percentage	`60.9091%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 1/5 plus 9/22 as a fraction?

1/5 + 9/22 in simplest fraction form is 67/110.

What is 1/5 plus 9/22 as a decimal?

1/5 + 9/22 converted to a decimal is 0.609091.

What is 1/5 plus 9/22 as a percentage?

1/5 + 9/22 expressed as a percentage is 60.9091%.

Does 1/5 plus 9/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.609091...) because the denominator contains prime factors other than 2 and 5.