What is 9/20 plus 10/21? (Answer: 389/420)

Exact Answer

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Problem: What is 9/20 plus 10/21?
Formula / Expression: 9/20 + 10/21
Final Answer: 389/420
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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 9/20 by 21, and multiply the numerator and denominator of 10/21 by 20 so both fractions share the common base 420.
Working: 9 × 21/20 × 21 = 189/420 and 10 × 20/21 × 20 = 200/420

Step 3: Add the Numerators
Now add the numerators (189 + 200 = 389) and keep the common denominator 420 unchanged.
Working: 189 + 200/420 = 389/420

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 389 and 420 is 1, confirming that 389/420 cannot be reduced further—it is already in its simplest irreducible form.
Working: 389/420

Step 5: Decimal & Percentage Representation
Dividing the numerator 389 by denominator 420 produces a repeating decimal (approximately 0.92619, or 92.619%).
Working: 389 ÷ 420 = 0.92619 (92.619%)

Key Values:
- Simplified Fraction: 389/420
- Mixed Number Form: 389/420
- Decimal Value: 0.92619
- Percentage: 92.619%

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Solved with FractionsCalc:
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9/20 + 10/21 = 389/420

Simplified Fraction

389/420

Mixed Number

Proper (389/420)

Decimal Value

0.92619

Percentage

92.619%

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Step-by-Step Solution: 9/20 + 10/21

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 9/20 by 21, and multiply the numerator and denominator of 10/21 by 20 so both fractions share the common base 420.

9 × 21/20 × 21 = 189/420 and 10 × 20/21 × 20 = 200/420

Step 3

Add the Numerators

Now add the numerators (189 + 200 = 389) and keep the common denominator 420 unchanged.

189 + 200/420 = 389/420

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 389 and 420 is 1, confirming that 389/420 cannot be reduced further—it is already in its simplest irreducible form.

389/420

Step 5

Decimal & Percentage Representation

Dividing the numerator 389 by denominator 420 produces a repeating decimal (approximately 0.92619, or 92.619%).

389 ÷ 420 = 0.92619 (92.619%)

Visual Representation

The diagram below illustrates 9/20 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`389/420`
Mixed Number Form	`389/420`
Decimal Form	`0.92619`
Percentage	`92.619%`

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Frequently Asked Questions

What is 9/20 plus 10/21 as a fraction?

9/20 + 10/21 in simplest fraction form is 389/420.

What is 9/20 plus 10/21 as a decimal?

9/20 + 10/21 converted to a decimal is 0.92619.

What is 9/20 plus 10/21 as a percentage?

9/20 + 10/21 expressed as a percentage is 92.619%.

Does 9/20 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.92619...) because the denominator contains prime factors other than 2 and 5.