What is 3/43 plus 2/21? (Answer: 149/903)

Exact Answer

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Problem: What is 3/43 plus 2/21?
Formula / Expression: 3/43 + 2/21
Final Answer: 149/903
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 43 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 43 × 21 = 903.
Working: LCD(43, 21) = 903

Step 2: Convert to Equivalent Fractions with Common Denominator 903
Multiply the numerator and denominator of 3/43 by 21, and multiply the numerator and denominator of 2/21 by 43 so both fractions share the common base 903.
Working: 3 × 21/43 × 21 = 63/903 and 2 × 43/21 × 43 = 86/903

Step 3: Add the Numerators
Now add the numerators (63 + 86 = 149) and keep the common denominator 903 unchanged.
Working: 63 + 86/903 = 149/903

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 149 and 903 is 1, confirming that 149/903 cannot be reduced further—it is already in its simplest irreducible form.
Working: 149/903

Step 5: Decimal & Percentage Representation
Dividing the numerator 149 by denominator 903 produces a repeating decimal (approximately 0.165006, or 16.5006%).
Working: 149 ÷ 903 = 0.165006 (16.5006%)

Key Values:
- Simplified Fraction: 149/903
- Mixed Number Form: 149/903
- Decimal Value: 0.165006
- Percentage: 16.5006%

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Solved with FractionsCalc:
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3/43 + 2/21 = 149/903

Simplified Fraction

149/903

Mixed Number

Proper (149/903)

Decimal Value

0.165006

Percentage

16.5006%

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Step-by-Step Solution: 3/43 + 2/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 43 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 43 × 21 = 903.

LCD(43, 21) = 903

Step 2

Convert to Equivalent Fractions with Common Denominator 903

Multiply the numerator and denominator of 3/43 by 21, and multiply the numerator and denominator of 2/21 by 43 so both fractions share the common base 903.

3 × 21/43 × 21 = 63/903 and 2 × 43/21 × 43 = 86/903

Step 3

Add the Numerators

Now add the numerators (63 + 86 = 149) and keep the common denominator 903 unchanged.

63 + 86/903 = 149/903

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 149 and 903 is 1, confirming that 149/903 cannot be reduced further—it is already in its simplest irreducible form.

149/903

Step 5

Decimal & Percentage Representation

Dividing the numerator 149 by denominator 903 produces a repeating decimal (approximately 0.165006, or 16.5006%).

149 ÷ 903 = 0.165006 (16.5006%)

Visual Representation

The diagram below illustrates 3/43 plus 2/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`149/903`
Mixed Number Form	`149/903`
Decimal Form	`0.165006`
Percentage	`16.5006%`

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Frequently Asked Questions

What is 3/43 plus 2/21 as a fraction?

3/43 + 2/21 in simplest fraction form is 149/903.

What is 3/43 plus 2/21 as a decimal?

3/43 + 2/21 converted to a decimal is 0.165006.

What is 3/43 plus 2/21 as a percentage?

3/43 + 2/21 expressed as a percentage is 16.5006%.

Does 3/43 plus 2/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.165006...) because the denominator contains prime factors other than 2 and 5.