What is 9/21 plus 24/55? (Answer: 333/385)

Exact Answer

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Problem: What is 9/21 plus 24/55?
Formula / Expression: 9/21 + 24/55
Final Answer: 333/385
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 55 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 55 = 1155.
Working: LCD(21, 55) = 1155

Step 2: Convert to Equivalent Fractions with Common Denominator 1155
Multiply the numerator and denominator of 9/21 by 55, and multiply the numerator and denominator of 24/55 by 21 so both fractions share the common base 1155.
Working: 9 × 55/21 × 55 = 495/1155 and 24 × 21/55 × 21 = 504/1155

Step 3: Add the Numerators
Now add the numerators (495 + 504 = 999) and keep the common denominator 1155 unchanged.
Working: 495 + 504/1155 = 999/1155

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 999 and 1155, which is 3. Divide both the numerator and denominator by 3.
Working: 999 ÷ 3/1155 ÷ 3 = 333/385

Step 5: Decimal & Percentage Representation
Dividing the numerator 333 by denominator 385 produces a repeating decimal (approximately 0.864935, or 86.4935%).
Working: 333 ÷ 385 = 0.864935 (86.4935%)

Key Values:
- Simplified Fraction: 333/385
- Mixed Number Form: 333/385
- Decimal Value: 0.864935
- Percentage: 86.4935%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-21-plus-24-55/
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9/21 + 24/55 = 333/385

Simplified Fraction

333/385

Mixed Number

Proper (333/385)

Decimal Value

0.864935

Percentage

86.4935%

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Step-by-Step Solution: 9/21 + 24/55

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 55 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 55 = 1155.

LCD(21, 55) = 1155

Step 2

Convert to Equivalent Fractions with Common Denominator 1155

Multiply the numerator and denominator of 9/21 by 55, and multiply the numerator and denominator of 24/55 by 21 so both fractions share the common base 1155.

9 × 55/21 × 55 = 495/1155 and 24 × 21/55 × 21 = 504/1155

Step 3

Add the Numerators

Now add the numerators (495 + 504 = 999) and keep the common denominator 1155 unchanged.

495 + 504/1155 = 999/1155

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 999 and 1155, which is 3. Divide both the numerator and denominator by 3.

999 ÷ 3/1155 ÷ 3 = 333/385

Step 5

Decimal & Percentage Representation

Dividing the numerator 333 by denominator 385 produces a repeating decimal (approximately 0.864935, or 86.4935%).

333 ÷ 385 = 0.864935 (86.4935%)

Visual Representation

The diagram below illustrates 9/21 plus 24/55 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`333/385`
Mixed Number Form	`333/385`
Decimal Form	`0.864935`
Percentage	`86.4935%`

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Frequently Asked Questions

What is 9/21 plus 24/55 as a fraction?

9/21 + 24/55 in simplest fraction form is 333/385.

What is 9/21 plus 24/55 as a decimal?

9/21 + 24/55 converted to a decimal is 0.864935.

What is 9/21 plus 24/55 as a percentage?

9/21 + 24/55 expressed as a percentage is 86.4935%.

Does 9/21 plus 24/55 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.864935...) because the denominator contains prime factors other than 2 and 5.