What is 3/20 plus 4/21? (Answer: 143/420)

Exact Answer

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Problem: What is 3/20 plus 4/21?
Formula / Expression: 3/20 + 4/21
Final Answer: 143/420
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 20 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 20 × 21 = 420.
Working: LCD(20, 21) = 420

Step 2: Convert to Equivalent Fractions with Common Denominator 420
Multiply the numerator and denominator of 3/20 by 21, and multiply the numerator and denominator of 4/21 by 20 so both fractions share the common base 420.
Working: 3 × 21/20 × 21 = 63/420 and 4 × 20/21 × 20 = 80/420

Step 3: Add the Numerators
Now add the numerators (63 + 80 = 143) and keep the common denominator 420 unchanged.
Working: 63 + 80/420 = 143/420

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 143 and 420 is 1, confirming that 143/420 cannot be reduced further—it is already in its simplest irreducible form.
Working: 143/420

Step 5: Decimal & Percentage Representation
Dividing the numerator 143 by denominator 420 produces a repeating decimal (approximately 0.340476, or 34.0476%).
Working: 143 ÷ 420 = 0.340476 (34.0476%)

Key Values:
- Simplified Fraction: 143/420
- Mixed Number Form: 143/420
- Decimal Value: 0.340476
- Percentage: 34.0476%

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3/20 + 4/21 = 143/420

Simplified Fraction

143/420

Mixed Number

Proper (143/420)

Decimal Value

0.340476

Percentage

34.0476%

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Step-by-Step Solution: 3/20 + 4/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 20 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 20 × 21 = 420.

LCD(20, 21) = 420

Step 2

Convert to Equivalent Fractions with Common Denominator 420

Multiply the numerator and denominator of 3/20 by 21, and multiply the numerator and denominator of 4/21 by 20 so both fractions share the common base 420.

3 × 21/20 × 21 = 63/420 and 4 × 20/21 × 20 = 80/420

Step 3

Add the Numerators

Now add the numerators (63 + 80 = 143) and keep the common denominator 420 unchanged.

63 + 80/420 = 143/420

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 143 and 420 is 1, confirming that 143/420 cannot be reduced further—it is already in its simplest irreducible form.

143/420

Step 5

Decimal & Percentage Representation

Dividing the numerator 143 by denominator 420 produces a repeating decimal (approximately 0.340476, or 34.0476%).

143 ÷ 420 = 0.340476 (34.0476%)

Visual Representation

The diagram below illustrates 3/20 plus 4/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`143/420`
Mixed Number Form	`143/420`
Decimal Form	`0.340476`
Percentage	`34.0476%`

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Frequently Asked Questions

What is 3/20 plus 4/21 as a fraction?

3/20 + 4/21 in simplest fraction form is 143/420.

What is 3/20 plus 4/21 as a decimal?

3/20 + 4/21 converted to a decimal is 0.340476.

What is 3/20 plus 4/21 as a percentage?

3/20 + 4/21 expressed as a percentage is 34.0476%.

Does 3/20 plus 4/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.340476...) because the denominator contains prime factors other than 2 and 5.