What is 6/51 plus 7/21? (Answer: 23/51)

Exact Answer

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Problem: What is 6/51 plus 7/21?
Formula / Expression: 6/51 + 7/21
Final Answer: 23/51
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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 6/51 by 7, and multiply the numerator and denominator of 7/21 by 17 so both fractions share the common base 357.
Working: 6 × 7/51 × 7 = 42/357 and 7 × 17/21 × 17 = 119/357

Step 3: Add the Numerators
Now add the numerators (42 + 119 = 161) and keep the common denominator 357 unchanged.
Working: 42 + 119/357 = 161/357

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 161 and 357, which is 7. Divide both the numerator and denominator by 7.
Working: 161 ÷ 7/357 ÷ 7 = 23/51

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 51 produces a repeating decimal (approximately 0.45098, or 45.098%).
Working: 23 ÷ 51 = 0.45098 (45.098%)

Key Values:
- Simplified Fraction: 23/51
- Mixed Number Form: 23/51
- Decimal Value: 0.45098
- Percentage: 45.098%

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Solved with FractionsCalc:
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6/51 + 7/21 = 23/51

Simplified Fraction

23/51

Mixed Number

Proper (23/51)

Decimal Value

0.45098

Percentage

45.098%

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Step-by-Step Solution: 6/51 + 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 6/51 by 7, and multiply the numerator and denominator of 7/21 by 17 so both fractions share the common base 357.

6 × 7/51 × 7 = 42/357 and 7 × 17/21 × 17 = 119/357

Step 3

Add the Numerators

Now add the numerators (42 + 119 = 161) and keep the common denominator 357 unchanged.

42 + 119/357 = 161/357

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 161 and 357, which is 7. Divide both the numerator and denominator by 7.

161 ÷ 7/357 ÷ 7 = 23/51

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 51 produces a repeating decimal (approximately 0.45098, or 45.098%).

23 ÷ 51 = 0.45098 (45.098%)

Visual Representation

The diagram below illustrates 6/51 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/51`
Mixed Number Form	`23/51`
Decimal Form	`0.45098`
Percentage	`45.098%`

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Frequently Asked Questions

What is 6/51 plus 7/21 as a fraction?

6/51 + 7/21 in simplest fraction form is 23/51.

What is 6/51 plus 7/21 as a decimal?

6/51 + 7/21 converted to a decimal is 0.45098.

What is 6/51 plus 7/21 as a percentage?

6/51 + 7/21 expressed as a percentage is 45.098%.

Does 6/51 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.45098...) because the denominator contains prime factors other than 2 and 5.