What is 14/51 plus 8/21? (Answer: 78/119)

Exact Answer

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Problem: What is 14/51 plus 8/21?
Formula / Expression: 14/51 + 8/21
Final Answer: 78/119
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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 14/51 by 7, and multiply the numerator and denominator of 8/21 by 17 so both fractions share the common base 357.
Working: 14 × 7/51 × 7 = 98/357 and 8 × 17/21 × 17 = 136/357

Step 3: Add the Numerators
Now add the numerators (98 + 136 = 234) and keep the common denominator 357 unchanged.
Working: 98 + 136/357 = 234/357

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 234 and 357, which is 3. Divide both the numerator and denominator by 3.
Working: 234 ÷ 3/357 ÷ 3 = 78/119

Step 5: Decimal & Percentage Representation
Dividing the numerator 78 by denominator 119 produces a repeating decimal (approximately 0.655462, or 65.5462%).
Working: 78 ÷ 119 = 0.655462 (65.5462%)

Key Values:
- Simplified Fraction: 78/119
- Mixed Number Form: 78/119
- Decimal Value: 0.655462
- Percentage: 65.5462%

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Solved with FractionsCalc:
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14/51 + 8/21 = 78/119

Simplified Fraction

78/119

Mixed Number

Proper (78/119)

Decimal Value

0.655462

Percentage

65.5462%

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Step-by-Step Solution: 14/51 + 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 14/51 by 7, and multiply the numerator and denominator of 8/21 by 17 so both fractions share the common base 357.

14 × 7/51 × 7 = 98/357 and 8 × 17/21 × 17 = 136/357

Step 3

Add the Numerators

Now add the numerators (98 + 136 = 234) and keep the common denominator 357 unchanged.

98 + 136/357 = 234/357

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 234 and 357, which is 3. Divide both the numerator and denominator by 3.

234 ÷ 3/357 ÷ 3 = 78/119

Step 5

Decimal & Percentage Representation

Dividing the numerator 78 by denominator 119 produces a repeating decimal (approximately 0.655462, or 65.5462%).

78 ÷ 119 = 0.655462 (65.5462%)

Visual Representation

The diagram below illustrates 14/51 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`78/119`
Mixed Number Form	`78/119`
Decimal Form	`0.655462`
Percentage	`65.5462%`

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Frequently Asked Questions

What is 14/51 plus 8/21 as a fraction?

14/51 + 8/21 in simplest fraction form is 78/119.

What is 14/51 plus 8/21 as a decimal?

14/51 + 8/21 converted to a decimal is 0.655462.

What is 14/51 plus 8/21 as a percentage?

14/51 + 8/21 expressed as a percentage is 65.5462%.

Does 14/51 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.655462...) because the denominator contains prime factors other than 2 and 5.