What is 9/51 plus 15/21? (Answer: 106/119)

Exact Answer

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Problem: What is 9/51 plus 15/21?
Formula / Expression: 9/51 + 15/21
Final Answer: 106/119
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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 9/51 by 7, and multiply the numerator and denominator of 15/21 by 17 so both fractions share the common base 357.
Working: 9 × 7/51 × 7 = 63/357 and 15 × 17/21 × 17 = 255/357

Step 3: Add the Numerators
Now add the numerators (63 + 255 = 318) and keep the common denominator 357 unchanged.
Working: 63 + 255/357 = 318/357

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 318 and 357, which is 3. Divide both the numerator and denominator by 3.
Working: 318 ÷ 3/357 ÷ 3 = 106/119

Step 5: Decimal & Percentage Representation
Dividing the numerator 106 by denominator 119 produces a repeating decimal (approximately 0.890756, or 89.0756%).
Working: 106 ÷ 119 = 0.890756 (89.0756%)

Key Values:
- Simplified Fraction: 106/119
- Mixed Number Form: 106/119
- Decimal Value: 0.890756
- Percentage: 89.0756%

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Solved with FractionsCalc:
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9/51 + 15/21 = 106/119

Simplified Fraction

106/119

Mixed Number

Proper (106/119)

Decimal Value

0.890756

Percentage

89.0756%

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

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

9 × 7/51 × 7 = 63/357 and 15 × 17/21 × 17 = 255/357

Step 3

Add the Numerators

Now add the numerators (63 + 255 = 318) and keep the common denominator 357 unchanged.

63 + 255/357 = 318/357

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 318 and 357, which is 3. Divide both the numerator and denominator by 3.

318 ÷ 3/357 ÷ 3 = 106/119

Step 5

Decimal & Percentage Representation

Dividing the numerator 106 by denominator 119 produces a repeating decimal (approximately 0.890756, or 89.0756%).

106 ÷ 119 = 0.890756 (89.0756%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`106/119`
Mixed Number Form	`106/119`
Decimal Form	`0.890756`
Percentage	`89.0756%`

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Frequently Asked Questions

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

9/51 + 15/21 in simplest fraction form is 106/119.

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

9/51 + 15/21 converted to a decimal is 0.890756.

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

9/51 + 15/21 expressed as a percentage is 89.0756%.

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

It results in a repeating decimal (approximately 0.890756...) because the denominator contains prime factors other than 2 and 5.