What is 3/38 plus 9/21? (Answer: 135/266)

Exact Answer

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Problem: What is 3/38 plus 9/21?
Formula / Expression: 3/38 + 9/21
Final Answer: 135/266
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 38 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 38 × 21 = 798.
Working: LCD(38, 21) = 798

Step 2: Convert to Equivalent Fractions with Common Denominator 798
Multiply the numerator and denominator of 3/38 by 21, and multiply the numerator and denominator of 9/21 by 38 so both fractions share the common base 798.
Working: 3 × 21/38 × 21 = 63/798 and 9 × 38/21 × 38 = 342/798

Step 3: Add the Numerators
Now add the numerators (63 + 342 = 405) and keep the common denominator 798 unchanged.
Working: 63 + 342/798 = 405/798

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 405 and 798, which is 3. Divide both the numerator and denominator by 3.
Working: 405 ÷ 3/798 ÷ 3 = 135/266

Step 5: Decimal & Percentage Representation
Dividing the numerator 135 by denominator 266 produces a repeating decimal (approximately 0.507519, or 50.7519%).
Working: 135 ÷ 266 = 0.507519 (50.7519%)

Key Values:
- Simplified Fraction: 135/266
- Mixed Number Form: 135/266
- Decimal Value: 0.507519
- Percentage: 50.7519%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-38-plus-9-21/
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3/38 + 9/21 = 135/266

Simplified Fraction

135/266

Mixed Number

Proper (135/266)

Decimal Value

0.507519

Percentage

50.7519%

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Step-by-Step Solution: 3/38 + 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 38 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 38 × 21 = 798.

LCD(38, 21) = 798

Step 2

Convert to Equivalent Fractions with Common Denominator 798

Multiply the numerator and denominator of 3/38 by 21, and multiply the numerator and denominator of 9/21 by 38 so both fractions share the common base 798.

3 × 21/38 × 21 = 63/798 and 9 × 38/21 × 38 = 342/798

Step 3

Add the Numerators

Now add the numerators (63 + 342 = 405) and keep the common denominator 798 unchanged.

63 + 342/798 = 405/798

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 405 and 798, which is 3. Divide both the numerator and denominator by 3.

405 ÷ 3/798 ÷ 3 = 135/266

Step 5

Decimal & Percentage Representation

Dividing the numerator 135 by denominator 266 produces a repeating decimal (approximately 0.507519, or 50.7519%).

135 ÷ 266 = 0.507519 (50.7519%)

Visual Representation

The diagram below illustrates 3/38 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`135/266`
Mixed Number Form	`135/266`
Decimal Form	`0.507519`
Percentage	`50.7519%`

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Frequently Asked Questions

What is 3/38 plus 9/21 as a fraction?

3/38 + 9/21 in simplest fraction form is 135/266.

What is 3/38 plus 9/21 as a decimal?

3/38 + 9/21 converted to a decimal is 0.507519.

What is 3/38 plus 9/21 as a percentage?

3/38 + 9/21 expressed as a percentage is 50.7519%.

Does 3/38 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.507519...) because the denominator contains prime factors other than 2 and 5.