What is 16/39 plus 9/21? (Answer: 229/273)

Exact Answer

==================================================
Problem: What is 16/39 plus 9/21?
Formula / Expression: 16/39 + 9/21
Final Answer: 229/273
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 39 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 273 (which is smaller than their product 39 × 21 = 819, keeping the calculation simpler).
Working: LCD(39, 21) = 273

Step 2: Convert to Equivalent Fractions with Common Denominator 273
Multiply the numerator and denominator of 16/39 by 7, and multiply the numerator and denominator of 9/21 by 13 so both fractions share the common base 273.
Working: 16 × 7/39 × 7 = 112/273 and 9 × 13/21 × 13 = 117/273

Step 3: Add the Numerators
Now add the numerators (112 + 117 = 229) and keep the common denominator 273 unchanged.
Working: 112 + 117/273 = 229/273

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 229 and 273 is 1, confirming that 229/273 cannot be reduced further—it is already in its simplest irreducible form.
Working: 229/273

Step 5: Decimal & Percentage Representation
Dividing the numerator 229 by denominator 273 produces a repeating decimal (approximately 0.838828, or 83.8828%).
Working: 229 ÷ 273 = 0.838828 (83.8828%)

Key Values:
- Simplified Fraction: 229/273
- Mixed Number Form: 229/273
- Decimal Value: 0.838828
- Percentage: 83.8828%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-16-39-plus-9-21/
==================================================

16/39 + 9/21 = 229/273

Simplified Fraction

229/273

Mixed Number

Proper (229/273)

Decimal Value

0.838828

Percentage

83.8828%

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: 16/39 + 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 39 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 273 (which is smaller than their product 39 × 21 = 819, keeping the calculation simpler).

LCD(39, 21) = 273

Step 2

Convert to Equivalent Fractions with Common Denominator 273

Multiply the numerator and denominator of 16/39 by 7, and multiply the numerator and denominator of 9/21 by 13 so both fractions share the common base 273.

16 × 7/39 × 7 = 112/273 and 9 × 13/21 × 13 = 117/273

Step 3

Add the Numerators

Now add the numerators (112 + 117 = 229) and keep the common denominator 273 unchanged.

112 + 117/273 = 229/273

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 229 and 273 is 1, confirming that 229/273 cannot be reduced further—it is already in its simplest irreducible form.

229/273

Step 5

Decimal & Percentage Representation

Dividing the numerator 229 by denominator 273 produces a repeating decimal (approximately 0.838828, or 83.8828%).

229 ÷ 273 = 0.838828 (83.8828%)

Visual Representation

The diagram below illustrates 16/39 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`229/273`
Mixed Number Form	`229/273`
Decimal Form	`0.838828`
Percentage	`83.8828%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 16/39 plus 9/21 as a fraction?

16/39 + 9/21 in simplest fraction form is 229/273.

What is 16/39 plus 9/21 as a decimal?

16/39 + 9/21 converted to a decimal is 0.838828.

What is 16/39 plus 9/21 as a percentage?

16/39 + 9/21 expressed as a percentage is 83.8828%.

Does 16/39 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.838828...) because the denominator contains prime factors other than 2 and 5.