What is 15/58 plus 8/21? (Answer: 779/1218)

Exact Answer

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Problem: What is 15/58 plus 8/21?
Formula / Expression: 15/58 + 8/21
Final Answer: 779/1218
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 58 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 58 × 21 = 1218.
Working: LCD(58, 21) = 1218

Step 2: Convert to Equivalent Fractions with Common Denominator 1218
Multiply the numerator and denominator of 15/58 by 21, and multiply the numerator and denominator of 8/21 by 58 so both fractions share the common base 1218.
Working: 15 × 21/58 × 21 = 315/1218 and 8 × 58/21 × 58 = 464/1218

Step 3: Add the Numerators
Now add the numerators (315 + 464 = 779) and keep the common denominator 1218 unchanged.
Working: 315 + 464/1218 = 779/1218

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 779 and 1218 is 1, confirming that 779/1218 cannot be reduced further—it is already in its simplest irreducible form.
Working: 779/1218

Step 5: Decimal & Percentage Representation
Dividing the numerator 779 by denominator 1218 produces a repeating decimal (approximately 0.639573, or 63.9573%).
Working: 779 ÷ 1218 = 0.639573 (63.9573%)

Key Values:
- Simplified Fraction: 779/1218
- Mixed Number Form: 779/1218
- Decimal Value: 0.639573
- Percentage: 63.9573%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-15-58-plus-8-21/
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15/58 + 8/21 = 779/1218

Simplified Fraction

779/1218

Mixed Number

Proper (779/1218)

Decimal Value

0.639573

Percentage

63.9573%

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Step-by-Step Solution: 15/58 + 8/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 58 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 58 × 21 = 1218.

LCD(58, 21) = 1218

Step 2

Convert to Equivalent Fractions with Common Denominator 1218

Multiply the numerator and denominator of 15/58 by 21, and multiply the numerator and denominator of 8/21 by 58 so both fractions share the common base 1218.

15 × 21/58 × 21 = 315/1218 and 8 × 58/21 × 58 = 464/1218

Step 3

Add the Numerators

Now add the numerators (315 + 464 = 779) and keep the common denominator 1218 unchanged.

315 + 464/1218 = 779/1218

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 779 and 1218 is 1, confirming that 779/1218 cannot be reduced further—it is already in its simplest irreducible form.

779/1218

Step 5

Decimal & Percentage Representation

Dividing the numerator 779 by denominator 1218 produces a repeating decimal (approximately 0.639573, or 63.9573%).

779 ÷ 1218 = 0.639573 (63.9573%)

Visual Representation

The diagram below illustrates 15/58 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`779/1218`
Mixed Number Form	`779/1218`
Decimal Form	`0.639573`
Percentage	`63.9573%`

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Frequently Asked Questions

What is 15/58 plus 8/21 as a fraction?

15/58 + 8/21 in simplest fraction form is 779/1218.

What is 15/58 plus 8/21 as a decimal?

15/58 + 8/21 converted to a decimal is 0.639573.

What is 15/58 plus 8/21 as a percentage?

15/58 + 8/21 expressed as a percentage is 63.9573%.

Does 15/58 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.639573...) because the denominator contains prime factors other than 2 and 5.