What is 5/51 plus 8/21? (Answer: 57/119)

Exact Answer

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Problem: What is 5/51 plus 8/21?
Formula / Expression: 5/51 + 8/21
Final Answer: 57/119
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 51 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 357 (which is smaller than their product 51 × 21 = 1071, keeping the calculation simpler).
Working: LCD(51, 21) = 357

Step 2: Convert to Equivalent Fractions with Common Denominator 357
Multiply the numerator and denominator of 5/51 by 7, and multiply the numerator and denominator of 8/21 by 17 so both fractions share the common base 357.
Working: 5 × 7/51 × 7 = 35/357 and 8 × 17/21 × 17 = 136/357

Step 3: Add the Numerators
Now add the numerators (35 + 136 = 171) and keep the common denominator 357 unchanged.
Working: 35 + 136/357 = 171/357

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 171 and 357, which is 3. Divide both the numerator and denominator by 3.
Working: 171 ÷ 3/357 ÷ 3 = 57/119

Step 5: Decimal & Percentage Representation
Dividing the numerator 57 by denominator 119 produces a repeating decimal (approximately 0.478992, or 47.8992%).
Working: 57 ÷ 119 = 0.478992 (47.8992%)

Key Values:
- Simplified Fraction: 57/119
- Mixed Number Form: 57/119
- Decimal Value: 0.478992
- Percentage: 47.8992%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-51-plus-8-21/
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5/51 + 8/21 = 57/119

Simplified Fraction

57/119

Mixed Number

Proper (57/119)

Decimal Value

0.478992

Percentage

47.8992%

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Step-by-Step Solution: 5/51 + 8/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 51 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 357 (which is smaller than their product 51 × 21 = 1071, keeping the calculation simpler).

LCD(51, 21) = 357

Step 2

Convert to Equivalent Fractions with Common Denominator 357

Multiply the numerator and denominator of 5/51 by 7, and multiply the numerator and denominator of 8/21 by 17 so both fractions share the common base 357.

5 × 7/51 × 7 = 35/357 and 8 × 17/21 × 17 = 136/357

Step 3

Add the Numerators

Now add the numerators (35 + 136 = 171) and keep the common denominator 357 unchanged.

35 + 136/357 = 171/357

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 171 and 357, which is 3. Divide both the numerator and denominator by 3.

171 ÷ 3/357 ÷ 3 = 57/119

Step 5

Decimal & Percentage Representation

Dividing the numerator 57 by denominator 119 produces a repeating decimal (approximately 0.478992, or 47.8992%).

57 ÷ 119 = 0.478992 (47.8992%)

Visual Representation

The diagram below illustrates 5/51 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`57/119`
Mixed Number Form	`57/119`
Decimal Form	`0.478992`
Percentage	`47.8992%`

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Frequently Asked Questions

What is 5/51 plus 8/21 as a fraction?

5/51 + 8/21 in simplest fraction form is 57/119.

What is 5/51 plus 8/21 as a decimal?

5/51 + 8/21 converted to a decimal is 0.478992.

What is 5/51 plus 8/21 as a percentage?

5/51 + 8/21 expressed as a percentage is 47.8992%.

Does 5/51 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.478992...) because the denominator contains prime factors other than 2 and 5.