What is 9/21 plus 5/9? (Answer: 62/63)

Exact Answer

==================================================
Problem: What is 9/21 plus 5/9?
Formula / Expression: 9/21 + 5/9
Final Answer: 62/63
==================================================

Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 63
Multiply the numerator and denominator of 9/21 by 3, and multiply the numerator and denominator of 5/9 by 7 so both fractions share the common base 63.
Working: 9 × 3/21 × 3 = 27/63 and 5 × 7/9 × 7 = 35/63

Step 3: Add the Numerators
Now add the numerators (27 + 35 = 62) and keep the common denominator 63 unchanged.
Working: 27 + 35/63 = 62/63

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 62 and 63 is 1, confirming that 62/63 cannot be reduced further—it is already in its simplest irreducible form.
Working: 62/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 62 by denominator 63 produces a repeating decimal (approximately 0.984127, or 98.4127%).
Working: 62 ÷ 63 = 0.984127 (98.4127%)

Key Values:
- Simplified Fraction: 62/63
- Mixed Number Form: 62/63
- Decimal Value: 0.984127
- Percentage: 98.4127%

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

9/21 + 5/9 = 62/63

Simplified Fraction

62/63

Mixed Number

Proper (62/63)

Decimal Value

0.984127

Percentage

98.4127%

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: 9/21 + 5/9

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 9) = 63

Step 2

Convert to Equivalent Fractions with Common Denominator 63

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

9 × 3/21 × 3 = 27/63 and 5 × 7/9 × 7 = 35/63

Step 3

Add the Numerators

Now add the numerators (27 + 35 = 62) and keep the common denominator 63 unchanged.

27 + 35/63 = 62/63

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 62 and 63 is 1, confirming that 62/63 cannot be reduced further—it is already in its simplest irreducible form.

62/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 62 by denominator 63 produces a repeating decimal (approximately 0.984127, or 98.4127%).

62 ÷ 63 = 0.984127 (98.4127%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`62/63`
Mixed Number Form	`62/63`
Decimal Form	`0.984127`
Percentage	`98.4127%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

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

9/21 + 5/9 in simplest fraction form is 62/63.

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

9/21 + 5/9 converted to a decimal is 0.984127.

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

9/21 + 5/9 expressed as a percentage is 98.4127%.

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

It results in a repeating decimal (approximately 0.984127...) because the denominator contains prime factors other than 2 and 5.