What is 7/21 plus 17/51? (Answer: 2/3)

Exact Answer

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Problem: What is 7/21 plus 17/51?
Formula / Expression: 7/21 + 17/51
Final Answer: 2/3
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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 7/21 by 17, and multiply the numerator and denominator of 17/51 by 7 so both fractions share the common base 357.
Working: 7 × 17/21 × 17 = 119/357 and 17 × 7/51 × 7 = 119/357

Step 3: Add the Numerators
Now add the numerators (119 + 119 = 238) and keep the common denominator 357 unchanged.
Working: 119 + 119/357 = 238/357

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 238 and 357, which is 119. Divide both the numerator and denominator by 119.
Working: 238 ÷ 119/357 ÷ 119 = 2/3

Step 5: Decimal & Percentage Representation
Dividing the numerator 2 by denominator 3 produces a repeating decimal (approximately 0.666667, or 66.6667%).
Working: 2 ÷ 3 = 0.666667 (66.6667%)

Key Values:
- Simplified Fraction: 2/3
- Mixed Number Form: 2/3
- Decimal Value: 0.666667
- Percentage: 66.6667%

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Solved with FractionsCalc:
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7/21 + 17/51 = 2/3

Simplified Fraction

2/3

Mixed Number

Proper (2/3)

Decimal Value

0.666667

Percentage

66.6667%

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Step-by-Step Solution: 7/21 + 17/51

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

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

Step 3

Add the Numerators

Now add the numerators (119 + 119 = 238) and keep the common denominator 357 unchanged.

119 + 119/357 = 238/357

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 238 and 357, which is 119. Divide both the numerator and denominator by 119.

238 ÷ 119/357 ÷ 119 = 2/3

Step 5

Decimal & Percentage Representation

Dividing the numerator 2 by denominator 3 produces a repeating decimal (approximately 0.666667, or 66.6667%).

2 ÷ 3 = 0.666667 (66.6667%)

Visual Representation

The diagram below illustrates 7/21 plus 17/51 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`2/3`
Mixed Number Form	`2/3`
Decimal Form	`0.666667`
Percentage	`66.6667%`

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Frequently Asked Questions

What is 7/21 plus 17/51 as a fraction?

7/21 + 17/51 in simplest fraction form is 2/3.

What is 7/21 plus 17/51 as a decimal?

7/21 + 17/51 converted to a decimal is 0.666667.

What is 7/21 plus 17/51 as a percentage?

7/21 + 17/51 expressed as a percentage is 66.6667%.

Does 7/21 plus 17/51 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.666667...) because the denominator contains prime factors other than 2 and 5.