What is 3/21 plus 5/31? (Answer: 66/217)

Exact Answer

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Problem: What is 3/21 plus 5/31?
Formula / Expression: 3/21 + 5/31
Final Answer: 66/217
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 31 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 31 = 651.
Working: LCD(21, 31) = 651

Step 2: Convert to Equivalent Fractions with Common Denominator 651
Multiply the numerator and denominator of 3/21 by 31, and multiply the numerator and denominator of 5/31 by 21 so both fractions share the common base 651.
Working: 3 × 31/21 × 31 = 93/651 and 5 × 21/31 × 21 = 105/651

Step 3: Add the Numerators
Now add the numerators (93 + 105 = 198) and keep the common denominator 651 unchanged.
Working: 93 + 105/651 = 198/651

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 198 and 651, which is 3. Divide both the numerator and denominator by 3.
Working: 198 ÷ 3/651 ÷ 3 = 66/217

Step 5: Decimal & Percentage Representation
Dividing the numerator 66 by denominator 217 produces a repeating decimal (approximately 0.304147, or 30.4147%).
Working: 66 ÷ 217 = 0.304147 (30.4147%)

Key Values:
- Simplified Fraction: 66/217
- Mixed Number Form: 66/217
- Decimal Value: 0.304147
- Percentage: 30.4147%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-21-plus-5-31/
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3/21 + 5/31 = 66/217

Simplified Fraction

66/217

Mixed Number

Proper (66/217)

Decimal Value

0.304147

Percentage

30.4147%

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Step-by-Step Solution: 3/21 + 5/31

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 31 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 31 = 651.

LCD(21, 31) = 651

Step 2

Convert to Equivalent Fractions with Common Denominator 651

Multiply the numerator and denominator of 3/21 by 31, and multiply the numerator and denominator of 5/31 by 21 so both fractions share the common base 651.

3 × 31/21 × 31 = 93/651 and 5 × 21/31 × 21 = 105/651

Step 3

Add the Numerators

Now add the numerators (93 + 105 = 198) and keep the common denominator 651 unchanged.

93 + 105/651 = 198/651

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 198 and 651, which is 3. Divide both the numerator and denominator by 3.

198 ÷ 3/651 ÷ 3 = 66/217

Step 5

Decimal & Percentage Representation

Dividing the numerator 66 by denominator 217 produces a repeating decimal (approximately 0.304147, or 30.4147%).

66 ÷ 217 = 0.304147 (30.4147%)

Visual Representation

The diagram below illustrates 3/21 plus 5/31 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`66/217`
Mixed Number Form	`66/217`
Decimal Form	`0.304147`
Percentage	`30.4147%`

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Frequently Asked Questions

What is 3/21 plus 5/31 as a fraction?

3/21 + 5/31 in simplest fraction form is 66/217.

What is 3/21 plus 5/31 as a decimal?

3/21 + 5/31 converted to a decimal is 0.304147.

What is 3/21 plus 5/31 as a percentage?

3/21 + 5/31 expressed as a percentage is 30.4147%.

Does 3/21 plus 5/31 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.304147...) because the denominator contains prime factors other than 2 and 5.