What is 9/20 plus 12/21? (Answer: 143/140)

Exact Answer

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Problem: What is 9/20 plus 12/21?
Formula / Expression: 9/20 + 12/21
Final Answer: 1 3/140 (143/140)
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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 12/21 by 20 so both fractions share the common base 420.
Working: 9 × 21/20 × 21 = 189/420 and 12 × 20/21 × 20 = 240/420

Step 3: Add the Numerators
Now add the numerators (189 + 240 = 429) and keep the common denominator 420 unchanged.
Working: 189 + 240/420 = 429/420

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 429 and 420, which is 3. Divide both the numerator and denominator by 3.
Working: 429 ÷ 3/420 ÷ 3 = 143/140

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (143) is greater than the denominator (140), divide 143 by 140: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/140.
Working: 143/140 = 1 3/140

Step 6: Decimal & Percentage Representation
Dividing the numerator 143 by denominator 140 produces a repeating decimal (approximately 1.021429, or 102.1429%).
Working: 143 ÷ 140 = 1.021429 (102.1429%)

Key Values:
- Simplified Fraction: 143/140
- Mixed Number Form: 1 3/140
- Decimal Value: 1.021429
- Percentage: 102.1429%

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Solved with FractionsCalc:
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9/20 + 12/21 = 143/140

Simplified Fraction

143/140

Mixed Number

1 3/140

Decimal Value

1.021429

Percentage

102.1429%

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Step-by-Step Solution: 9/20 + 12/21

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 12/21 by 20 so both fractions share the common base 420.

9 × 21/20 × 21 = 189/420 and 12 × 20/21 × 20 = 240/420

Step 3

Add the Numerators

Now add the numerators (189 + 240 = 429) and keep the common denominator 420 unchanged.

189 + 240/420 = 429/420

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 429 and 420, which is 3. Divide both the numerator and denominator by 3.

429 ÷ 3/420 ÷ 3 = 143/140

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (143) is greater than the denominator (140), divide 143 by 140: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/140.

143/140 = 13/140

Step 6

Decimal & Percentage Representation

Dividing the numerator 143 by denominator 140 produces a repeating decimal (approximately 1.021429, or 102.1429%).

143 ÷ 140 = 1.021429 (102.1429%)

Visual Representation

The diagram below illustrates 9/20 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`143/140`
Mixed Number Form	`1 3/140`
Decimal Form	`1.021429`
Percentage	`102.1429%`

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Frequently Asked Questions

What is 9/20 plus 12/21 as a fraction?

9/20 + 12/21 in simplest fraction form is 143/140 (or 1 3/140 as a mixed number).

What is 9/20 plus 12/21 as a decimal?

9/20 + 12/21 converted to a decimal is 1.021429.

What is 9/20 plus 12/21 as a percentage?

9/20 + 12/21 expressed as a percentage is 102.1429%.

How do you write 9/20 plus 12/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 143/140 can be written as the mixed number 1 3/140.

Does 9/20 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.021429...) because the denominator contains prime factors other than 2 and 5.