What is 2/21 plus 2/5? (Answer: 52/105)

Exact Answer

==================================================
Problem: What is 2/21 plus 2/5?
Formula / Expression: 2/21 + 2/5
Final Answer: 52/105
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 5 = 105.
Working: LCD(21, 5) = 105

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 2/21 by 5, and multiply the numerator and denominator of 2/5 by 21 so both fractions share the common base 105.
Working: 2 × 5/21 × 5 = 10/105 and 2 × 21/5 × 21 = 42/105

Step 3: Add the Numerators
Now add the numerators (10 + 42 = 52) and keep the common denominator 105 unchanged.
Working: 10 + 42/105 = 52/105

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 52 and 105 is 1, confirming that 52/105 cannot be reduced further—it is already in its simplest irreducible form.
Working: 52/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 52 by denominator 105 produces a repeating decimal (approximately 0.495238, or 49.5238%).
Working: 52 ÷ 105 = 0.495238 (49.5238%)

Key Values:
- Simplified Fraction: 52/105
- Mixed Number Form: 52/105
- Decimal Value: 0.495238
- Percentage: 49.5238%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-21-plus-2-5/
==================================================

2/21 + 2/5 = 52/105

Simplified Fraction

52/105

Mixed Number

Proper (52/105)

Decimal Value

0.495238

Percentage

49.5238%

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: 2/21 + 2/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 5 = 105.

LCD(21, 5) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 2/21 by 5, and multiply the numerator and denominator of 2/5 by 21 so both fractions share the common base 105.

2 × 5/21 × 5 = 10/105 and 2 × 21/5 × 21 = 42/105

Step 3

Add the Numerators

Now add the numerators (10 + 42 = 52) and keep the common denominator 105 unchanged.

10 + 42/105 = 52/105

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 52 and 105 is 1, confirming that 52/105 cannot be reduced further—it is already in its simplest irreducible form.

52/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 52 by denominator 105 produces a repeating decimal (approximately 0.495238, or 49.5238%).

52 ÷ 105 = 0.495238 (49.5238%)

Visual Representation

The diagram below illustrates 2/21 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`52/105`
Mixed Number Form	`52/105`
Decimal Form	`0.495238`
Percentage	`49.5238%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 2/21 plus 2/5 as a fraction?

2/21 + 2/5 in simplest fraction form is 52/105.

What is 2/21 plus 2/5 as a decimal?

2/21 + 2/5 converted to a decimal is 0.495238.

What is 2/21 plus 2/5 as a percentage?

2/21 + 2/5 expressed as a percentage is 49.5238%.

Does 2/21 plus 2/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.495238...) because the denominator contains prime factors other than 2 and 5.