What is 1/9 plus 5/21? (Answer: 22/63)

Exact Answer

==================================================
Problem: What is 1/9 plus 5/21?
Formula / Expression: 1/9 + 5/21
Final Answer: 22/63
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 63 (which is smaller than their product 9 × 21 = 189, keeping the calculation simpler).
Working: LCD(9, 21) = 63

Step 2: Convert to Equivalent Fractions with Common Denominator 63
Multiply the numerator and denominator of 1/9 by 7, and multiply the numerator and denominator of 5/21 by 3 so both fractions share the common base 63.
Working: 1 × 7/9 × 7 = 7/63 and 5 × 3/21 × 3 = 15/63

Step 3: Add the Numerators
Now add the numerators (7 + 15 = 22) and keep the common denominator 63 unchanged.
Working: 7 + 15/63 = 22/63

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 22 and 63 is 1, confirming that 22/63 cannot be reduced further—it is already in its simplest irreducible form.
Working: 22/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 22 by denominator 63 produces a repeating decimal (approximately 0.349206, or 34.9206%).
Working: 22 ÷ 63 = 0.349206 (34.9206%)

Key Values:
- Simplified Fraction: 22/63
- Mixed Number Form: 22/63
- Decimal Value: 0.349206
- Percentage: 34.9206%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-9-plus-5-21/
==================================================

1/9 + 5/21 = 22/63

Simplified Fraction

22/63

Mixed Number

Proper (22/63)

Decimal Value

0.349206

Percentage

34.9206%

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: 1/9 + 5/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 63 (which is smaller than their product 9 × 21 = 189, keeping the calculation simpler).

LCD(9, 21) = 63

Step 2

Convert to Equivalent Fractions with Common Denominator 63

Multiply the numerator and denominator of 1/9 by 7, and multiply the numerator and denominator of 5/21 by 3 so both fractions share the common base 63.

1 × 7/9 × 7 = 7/63 and 5 × 3/21 × 3 = 15/63

Step 3

Add the Numerators

Now add the numerators (7 + 15 = 22) and keep the common denominator 63 unchanged.

7 + 15/63 = 22/63

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 22 and 63 is 1, confirming that 22/63 cannot be reduced further—it is already in its simplest irreducible form.

22/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 22 by denominator 63 produces a repeating decimal (approximately 0.349206, or 34.9206%).

22 ÷ 63 = 0.349206 (34.9206%)

Visual Representation

The diagram below illustrates 1/9 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`22/63`
Mixed Number Form	`22/63`
Decimal Form	`0.349206`
Percentage	`34.9206%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 1/9 plus 5/21 as a fraction?

1/9 + 5/21 in simplest fraction form is 22/63.

What is 1/9 plus 5/21 as a decimal?

1/9 + 5/21 converted to a decimal is 0.349206.

What is 1/9 plus 5/21 as a percentage?

1/9 + 5/21 expressed as a percentage is 34.9206%.

Does 1/9 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.349206...) because the denominator contains prime factors other than 2 and 5.