What is 8/21 plus 20/51? (Answer: 92/119)

Exact Answer

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Problem: What is 8/21 plus 20/51?
Formula / Expression: 8/21 + 20/51
Final Answer: 92/119
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 357
Multiply the numerator and denominator of 8/21 by 17, and multiply the numerator and denominator of 20/51 by 7 so both fractions share the common base 357.
Working: 8 × 17/21 × 17 = 136/357 and 20 × 7/51 × 7 = 140/357

Step 3: Add the Numerators
Now add the numerators (136 + 140 = 276) and keep the common denominator 357 unchanged.
Working: 136 + 140/357 = 276/357

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 276 and 357, which is 3. Divide both the numerator and denominator by 3.
Working: 276 ÷ 3/357 ÷ 3 = 92/119

Step 5: Decimal & Percentage Representation
Dividing the numerator 92 by denominator 119 produces a repeating decimal (approximately 0.773109, or 77.3109%).
Working: 92 ÷ 119 = 0.773109 (77.3109%)

Key Values:
- Simplified Fraction: 92/119
- Mixed Number Form: 92/119
- Decimal Value: 0.773109
- Percentage: 77.3109%

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Solved with FractionsCalc:
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8/21 + 20/51 = 92/119

Simplified Fraction

92/119

Mixed Number

Proper (92/119)

Decimal Value

0.773109

Percentage

77.3109%

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Step-by-Step Solution: 8/21 + 20/51

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 51) = 357

Step 2

Convert to Equivalent Fractions with Common Denominator 357

Multiply the numerator and denominator of 8/21 by 17, and multiply the numerator and denominator of 20/51 by 7 so both fractions share the common base 357.

8 × 17/21 × 17 = 136/357 and 20 × 7/51 × 7 = 140/357

Step 3

Add the Numerators

Now add the numerators (136 + 140 = 276) and keep the common denominator 357 unchanged.

136 + 140/357 = 276/357

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 276 and 357, which is 3. Divide both the numerator and denominator by 3.

276 ÷ 3/357 ÷ 3 = 92/119

Step 5

Decimal & Percentage Representation

Dividing the numerator 92 by denominator 119 produces a repeating decimal (approximately 0.773109, or 77.3109%).

92 ÷ 119 = 0.773109 (77.3109%)

Visual Representation

The diagram below illustrates 8/21 plus 20/51 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`92/119`
Mixed Number Form	`92/119`
Decimal Form	`0.773109`
Percentage	`77.3109%`

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Frequently Asked Questions

What is 8/21 plus 20/51 as a fraction?

8/21 + 20/51 in simplest fraction form is 92/119.

What is 8/21 plus 20/51 as a decimal?

8/21 + 20/51 converted to a decimal is 0.773109.

What is 8/21 plus 20/51 as a percentage?

8/21 + 20/51 expressed as a percentage is 77.3109%.

Does 8/21 plus 20/51 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.773109...) because the denominator contains prime factors other than 2 and 5.