What is 15/51 plus 9/21? (Answer: 86/119)

Exact Answer

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Problem: What is 15/51 plus 9/21?
Formula / Expression: 15/51 + 9/21
Final Answer: 86/119
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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 15/51 by 7, and multiply the numerator and denominator of 9/21 by 17 so both fractions share the common base 357.
Working: 15 × 7/51 × 7 = 105/357 and 9 × 17/21 × 17 = 153/357

Step 3: Add the Numerators
Now add the numerators (105 + 153 = 258) and keep the common denominator 357 unchanged.
Working: 105 + 153/357 = 258/357

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 258 and 357, which is 3. Divide both the numerator and denominator by 3.
Working: 258 ÷ 3/357 ÷ 3 = 86/119

Step 5: Decimal & Percentage Representation
Dividing the numerator 86 by denominator 119 produces a repeating decimal (approximately 0.722689, or 72.2689%).
Working: 86 ÷ 119 = 0.722689 (72.2689%)

Key Values:
- Simplified Fraction: 86/119
- Mixed Number Form: 86/119
- Decimal Value: 0.722689
- Percentage: 72.2689%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-15-51-plus-9-21/
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15/51 + 9/21 = 86/119

Simplified Fraction

86/119

Mixed Number

Proper (86/119)

Decimal Value

0.722689

Percentage

72.2689%

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Step-by-Step Solution: 15/51 + 9/21

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 15/51 by 7, and multiply the numerator and denominator of 9/21 by 17 so both fractions share the common base 357.

15 × 7/51 × 7 = 105/357 and 9 × 17/21 × 17 = 153/357

Step 3

Add the Numerators

Now add the numerators (105 + 153 = 258) and keep the common denominator 357 unchanged.

105 + 153/357 = 258/357

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 258 and 357, which is 3. Divide both the numerator and denominator by 3.

258 ÷ 3/357 ÷ 3 = 86/119

Step 5

Decimal & Percentage Representation

Dividing the numerator 86 by denominator 119 produces a repeating decimal (approximately 0.722689, or 72.2689%).

86 ÷ 119 = 0.722689 (72.2689%)

Visual Representation

The diagram below illustrates 15/51 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`86/119`
Mixed Number Form	`86/119`
Decimal Form	`0.722689`
Percentage	`72.2689%`

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Frequently Asked Questions

What is 15/51 plus 9/21 as a fraction?

15/51 + 9/21 in simplest fraction form is 86/119.

What is 15/51 plus 9/21 as a decimal?

15/51 + 9/21 converted to a decimal is 0.722689.

What is 15/51 plus 9/21 as a percentage?

15/51 + 9/21 expressed as a percentage is 72.2689%.

Does 15/51 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.722689...) because the denominator contains prime factors other than 2 and 5.