What is 6/21 plus 15/51? (Answer: 69/119)

Exact Answer

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Problem: What is 6/21 plus 15/51?
Formula / Expression: 6/21 + 15/51
Final Answer: 69/119
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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 6/21 by 17, and multiply the numerator and denominator of 15/51 by 7 so both fractions share the common base 357.
Working: 6 × 17/21 × 17 = 102/357 and 15 × 7/51 × 7 = 105/357

Step 3: Add the Numerators
Now add the numerators (102 + 105 = 207) and keep the common denominator 357 unchanged.
Working: 102 + 105/357 = 207/357

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 207 and 357, which is 3. Divide both the numerator and denominator by 3.
Working: 207 ÷ 3/357 ÷ 3 = 69/119

Step 5: Decimal & Percentage Representation
Dividing the numerator 69 by denominator 119 produces a repeating decimal (approximately 0.579832, or 57.9832%).
Working: 69 ÷ 119 = 0.579832 (57.9832%)

Key Values:
- Simplified Fraction: 69/119
- Mixed Number Form: 69/119
- Decimal Value: 0.579832
- Percentage: 57.9832%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-6-21-plus-15-51/
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6/21 + 15/51 = 69/119

Simplified Fraction

69/119

Mixed Number

Proper (69/119)

Decimal Value

0.579832

Percentage

57.9832%

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Step-by-Step Solution: 6/21 + 15/51

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 6/21 by 17, and multiply the numerator and denominator of 15/51 by 7 so both fractions share the common base 357.

6 × 17/21 × 17 = 102/357 and 15 × 7/51 × 7 = 105/357

Step 3

Add the Numerators

Now add the numerators (102 + 105 = 207) and keep the common denominator 357 unchanged.

102 + 105/357 = 207/357

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 207 and 357, which is 3. Divide both the numerator and denominator by 3.

207 ÷ 3/357 ÷ 3 = 69/119

Step 5

Decimal & Percentage Representation

Dividing the numerator 69 by denominator 119 produces a repeating decimal (approximately 0.579832, or 57.9832%).

69 ÷ 119 = 0.579832 (57.9832%)

Visual Representation

The diagram below illustrates 6/21 plus 15/51 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`69/119`
Mixed Number Form	`69/119`
Decimal Form	`0.579832`
Percentage	`57.9832%`

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Frequently Asked Questions

What is 6/21 plus 15/51 as a fraction?

6/21 + 15/51 in simplest fraction form is 69/119.

What is 6/21 plus 15/51 as a decimal?

6/21 + 15/51 converted to a decimal is 0.579832.

What is 6/21 plus 15/51 as a percentage?

6/21 + 15/51 expressed as a percentage is 57.9832%.

Does 6/21 plus 15/51 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.579832...) because the denominator contains prime factors other than 2 and 5.