What is 3/50 plus 2/21? (Answer: 163/1050)

Exact Answer

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Problem: What is 3/50 plus 2/21?
Formula / Expression: 3/50 + 2/21
Final Answer: 163/1050
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 50 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 50 × 21 = 1050.
Working: LCD(50, 21) = 1050

Step 2: Convert to Equivalent Fractions with Common Denominator 1050
Multiply the numerator and denominator of 3/50 by 21, and multiply the numerator and denominator of 2/21 by 50 so both fractions share the common base 1050.
Working: 3 × 21/50 × 21 = 63/1050 and 2 × 50/21 × 50 = 100/1050

Step 3: Add the Numerators
Now add the numerators (63 + 100 = 163) and keep the common denominator 1050 unchanged.
Working: 63 + 100/1050 = 163/1050

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 163 and 1050 is 1, confirming that 163/1050 cannot be reduced further—it is already in its simplest irreducible form.
Working: 163/1050

Step 5: Decimal & Percentage Representation
Dividing the numerator 163 by denominator 1050 produces a repeating decimal (approximately 0.155238, or 15.5238%).
Working: 163 ÷ 1050 = 0.155238 (15.5238%)

Key Values:
- Simplified Fraction: 163/1050
- Mixed Number Form: 163/1050
- Decimal Value: 0.155238
- Percentage: 15.5238%

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Solved with FractionsCalc:
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3/50 + 2/21 = 163/1050

Simplified Fraction

163/1050

Mixed Number

Proper (163/1050)

Decimal Value

0.155238

Percentage

15.5238%

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Step-by-Step Solution: 3/50 + 2/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 50 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 50 × 21 = 1050.

LCD(50, 21) = 1050

Step 2

Convert to Equivalent Fractions with Common Denominator 1050

Multiply the numerator and denominator of 3/50 by 21, and multiply the numerator and denominator of 2/21 by 50 so both fractions share the common base 1050.

3 × 21/50 × 21 = 63/1050 and 2 × 50/21 × 50 = 100/1050

Step 3

Add the Numerators

Now add the numerators (63 + 100 = 163) and keep the common denominator 1050 unchanged.

63 + 100/1050 = 163/1050

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 163 and 1050 is 1, confirming that 163/1050 cannot be reduced further—it is already in its simplest irreducible form.

163/1050

Step 5

Decimal & Percentage Representation

Dividing the numerator 163 by denominator 1050 produces a repeating decimal (approximately 0.155238, or 15.5238%).

163 ÷ 1050 = 0.155238 (15.5238%)

Visual Representation

The diagram below illustrates 3/50 plus 2/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`163/1050`
Mixed Number Form	`163/1050`
Decimal Form	`0.155238`
Percentage	`15.5238%`

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Frequently Asked Questions

What is 3/50 plus 2/21 as a fraction?

3/50 + 2/21 in simplest fraction form is 163/1050.

What is 3/50 plus 2/21 as a decimal?

3/50 + 2/21 converted to a decimal is 0.155238.

What is 3/50 plus 2/21 as a percentage?

3/50 + 2/21 expressed as a percentage is 15.5238%.

Does 3/50 plus 2/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.155238...) because the denominator contains prime factors other than 2 and 5.