What is 3/11 plus 9/21? (Answer: 54/77)

Exact Answer

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Problem: What is 3/11 plus 9/21?
Formula / Expression: 3/11 + 9/21
Final Answer: 54/77
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 11 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 11 × 21 = 231.
Working: LCD(11, 21) = 231

Step 2: Convert to Equivalent Fractions with Common Denominator 231
Multiply the numerator and denominator of 3/11 by 21, and multiply the numerator and denominator of 9/21 by 11 so both fractions share the common base 231.
Working: 3 × 21/11 × 21 = 63/231 and 9 × 11/21 × 11 = 99/231

Step 3: Add the Numerators
Now add the numerators (63 + 99 = 162) and keep the common denominator 231 unchanged.
Working: 63 + 99/231 = 162/231

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 162 and 231, which is 3. Divide both the numerator and denominator by 3.
Working: 162 ÷ 3/231 ÷ 3 = 54/77

Step 5: Decimal & Percentage Representation
Dividing the numerator 54 by denominator 77 produces a repeating decimal (approximately 0.701299, or 70.1299%).
Working: 54 ÷ 77 = 0.701299 (70.1299%)

Key Values:
- Simplified Fraction: 54/77
- Mixed Number Form: 54/77
- Decimal Value: 0.701299
- Percentage: 70.1299%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-11-plus-9-21/
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3/11 + 9/21 = 54/77

Simplified Fraction

54/77

Mixed Number

Proper (54/77)

Decimal Value

0.701299

Percentage

70.1299%

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Step-by-Step Solution: 3/11 + 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 11 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 11 × 21 = 231.

LCD(11, 21) = 231

Step 2

Convert to Equivalent Fractions with Common Denominator 231

Multiply the numerator and denominator of 3/11 by 21, and multiply the numerator and denominator of 9/21 by 11 so both fractions share the common base 231.

3 × 21/11 × 21 = 63/231 and 9 × 11/21 × 11 = 99/231

Step 3

Add the Numerators

Now add the numerators (63 + 99 = 162) and keep the common denominator 231 unchanged.

63 + 99/231 = 162/231

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 162 and 231, which is 3. Divide both the numerator and denominator by 3.

162 ÷ 3/231 ÷ 3 = 54/77

Step 5

Decimal & Percentage Representation

Dividing the numerator 54 by denominator 77 produces a repeating decimal (approximately 0.701299, or 70.1299%).

54 ÷ 77 = 0.701299 (70.1299%)

Visual Representation

The diagram below illustrates 3/11 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`54/77`
Mixed Number Form	`54/77`
Decimal Form	`0.701299`
Percentage	`70.1299%`

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Frequently Asked Questions

What is 3/11 plus 9/21 as a fraction?

3/11 + 9/21 in simplest fraction form is 54/77.

What is 3/11 plus 9/21 as a decimal?

3/11 + 9/21 converted to a decimal is 0.701299.

What is 3/11 plus 9/21 as a percentage?

3/11 + 9/21 expressed as a percentage is 70.1299%.

Does 3/11 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.701299...) because the denominator contains prime factors other than 2 and 5.