What is 7/51 plus 8/21? (Answer: 185/357)

Exact Answer

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Problem: What is 7/51 plus 8/21?
Formula / Expression: 7/51 + 8/21
Final Answer: 185/357
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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 7/51 by 7, and multiply the numerator and denominator of 8/21 by 17 so both fractions share the common base 357.
Working: 7 × 7/51 × 7 = 49/357 and 8 × 17/21 × 17 = 136/357

Step 3: Add the Numerators
Now add the numerators (49 + 136 = 185) and keep the common denominator 357 unchanged.
Working: 49 + 136/357 = 185/357

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 185 and 357 is 1, confirming that 185/357 cannot be reduced further—it is already in its simplest irreducible form.
Working: 185/357

Step 5: Decimal & Percentage Representation
Dividing the numerator 185 by denominator 357 produces a repeating decimal (approximately 0.518207, or 51.8207%).
Working: 185 ÷ 357 = 0.518207 (51.8207%)

Key Values:
- Simplified Fraction: 185/357
- Mixed Number Form: 185/357
- Decimal Value: 0.518207
- Percentage: 51.8207%

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Solved with FractionsCalc:
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7/51 + 8/21 = 185/357

Simplified Fraction

185/357

Mixed Number

Proper (185/357)

Decimal Value

0.518207

Percentage

51.8207%

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

7 × 7/51 × 7 = 49/357 and 8 × 17/21 × 17 = 136/357

Step 3

Add the Numerators

Now add the numerators (49 + 136 = 185) and keep the common denominator 357 unchanged.

49 + 136/357 = 185/357

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 185 and 357 is 1, confirming that 185/357 cannot be reduced further—it is already in its simplest irreducible form.

185/357

Step 5

Decimal & Percentage Representation

Dividing the numerator 185 by denominator 357 produces a repeating decimal (approximately 0.518207, or 51.8207%).

185 ÷ 357 = 0.518207 (51.8207%)

Visual Representation

The diagram below illustrates 7/51 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`185/357`
Mixed Number Form	`185/357`
Decimal Form	`0.518207`
Percentage	`51.8207%`

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Frequently Asked Questions

What is 7/51 plus 8/21 as a fraction?

7/51 + 8/21 in simplest fraction form is 185/357.

What is 7/51 plus 8/21 as a decimal?

7/51 + 8/21 converted to a decimal is 0.518207.

What is 7/51 plus 8/21 as a percentage?

7/51 + 8/21 expressed as a percentage is 51.8207%.

Does 7/51 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.518207...) because the denominator contains prime factors other than 2 and 5.