What is 3/39 plus 3/21? (Answer: 20/91)

Exact Answer

==================================================
Problem: What is 3/39 plus 3/21?
Formula / Expression: 3/39 + 3/21
Final Answer: 20/91
==================================================

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 3/39 by 7, and multiply the numerator and denominator of 3/21 by 13 so both fractions share the common base 273.
Working: 3 × 7/39 × 7 = 21/273 and 3 × 13/21 × 13 = 39/273

Step 3: Add the Numerators
Now add the numerators (21 + 39 = 60) and keep the common denominator 273 unchanged.
Working: 21 + 39/273 = 60/273

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 60 and 273, which is 3. Divide both the numerator and denominator by 3.
Working: 60 ÷ 3/273 ÷ 3 = 20/91

Step 5: Decimal & Percentage Representation
Dividing the numerator 20 by denominator 91 produces a repeating decimal (approximately 0.21978, or 21.978%).
Working: 20 ÷ 91 = 0.21978 (21.978%)

Key Values:
- Simplified Fraction: 20/91
- Mixed Number Form: 20/91
- Decimal Value: 0.21978
- Percentage: 21.978%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-39-plus-3-21/
==================================================

3/39 + 3/21 = 20/91

Simplified Fraction

20/91

Mixed Number

Proper (20/91)

Decimal Value

0.21978

Percentage

21.978%

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: 3/39 + 3/21

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 3/39 by 7, and multiply the numerator and denominator of 3/21 by 13 so both fractions share the common base 273.

3 × 7/39 × 7 = 21/273 and 3 × 13/21 × 13 = 39/273

Step 3

Add the Numerators

Now add the numerators (21 + 39 = 60) and keep the common denominator 273 unchanged.

21 + 39/273 = 60/273

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 60 and 273, which is 3. Divide both the numerator and denominator by 3.

60 ÷ 3/273 ÷ 3 = 20/91

Step 5

Decimal & Percentage Representation

Dividing the numerator 20 by denominator 91 produces a repeating decimal (approximately 0.21978, or 21.978%).

20 ÷ 91 = 0.21978 (21.978%)

Visual Representation

The diagram below illustrates 3/39 plus 3/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`20/91`
Mixed Number Form	`20/91`
Decimal Form	`0.21978`
Percentage	`21.978%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 3/39 plus 3/21 as a fraction?

3/39 + 3/21 in simplest fraction form is 20/91.

What is 3/39 plus 3/21 as a decimal?

3/39 + 3/21 converted to a decimal is 0.21978.

What is 3/39 plus 3/21 as a percentage?

3/39 + 3/21 expressed as a percentage is 21.978%.

Does 3/39 plus 3/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.21978...) because the denominator contains prime factors other than 2 and 5.