What is 12/51 plus 7/21? (Answer: 29/51)

Exact Answer

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Problem: What is 12/51 plus 7/21?
Formula / Expression: 12/51 + 7/21
Final Answer: 29/51
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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 12/51 by 7, and multiply the numerator and denominator of 7/21 by 17 so both fractions share the common base 357.
Working: 12 × 7/51 × 7 = 84/357 and 7 × 17/21 × 17 = 119/357

Step 3: Add the Numerators
Now add the numerators (84 + 119 = 203) and keep the common denominator 357 unchanged.
Working: 84 + 119/357 = 203/357

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 203 and 357, which is 7. Divide both the numerator and denominator by 7.
Working: 203 ÷ 7/357 ÷ 7 = 29/51

Step 5: Decimal & Percentage Representation
Dividing the numerator 29 by denominator 51 produces a repeating decimal (approximately 0.568627, or 56.8627%).
Working: 29 ÷ 51 = 0.568627 (56.8627%)

Key Values:
- Simplified Fraction: 29/51
- Mixed Number Form: 29/51
- Decimal Value: 0.568627
- Percentage: 56.8627%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-12-51-plus-7-21/
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12/51 + 7/21 = 29/51

Simplified Fraction

29/51

Mixed Number

Proper (29/51)

Decimal Value

0.568627

Percentage

56.8627%

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Step-by-Step Solution: 12/51 + 7/21

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 12/51 by 7, and multiply the numerator and denominator of 7/21 by 17 so both fractions share the common base 357.

12 × 7/51 × 7 = 84/357 and 7 × 17/21 × 17 = 119/357

Step 3

Add the Numerators

Now add the numerators (84 + 119 = 203) and keep the common denominator 357 unchanged.

84 + 119/357 = 203/357

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 203 and 357, which is 7. Divide both the numerator and denominator by 7.

203 ÷ 7/357 ÷ 7 = 29/51

Step 5

Decimal & Percentage Representation

Dividing the numerator 29 by denominator 51 produces a repeating decimal (approximately 0.568627, or 56.8627%).

29 ÷ 51 = 0.568627 (56.8627%)

Visual Representation

The diagram below illustrates 12/51 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`29/51`
Mixed Number Form	`29/51`
Decimal Form	`0.568627`
Percentage	`56.8627%`

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Frequently Asked Questions

What is 12/51 plus 7/21 as a fraction?

12/51 + 7/21 in simplest fraction form is 29/51.

What is 12/51 plus 7/21 as a decimal?

12/51 + 7/21 converted to a decimal is 0.568627.

What is 12/51 plus 7/21 as a percentage?

12/51 + 7/21 expressed as a percentage is 56.8627%.

Does 12/51 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.568627...) because the denominator contains prime factors other than 2 and 5.