What is 15/51 plus 7/21? (Answer: 32/51)

Exact Answer

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Problem: What is 15/51 plus 7/21?
Formula / Expression: 15/51 + 7/21
Final Answer: 32/51
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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 15/51 by 7, and multiply the numerator and denominator of 7/21 by 17 so both fractions share the common base 357.
Working: 15 × 7/51 × 7 = 105/357 and 7 × 17/21 × 17 = 119/357

Step 3: Add the Numerators
Now add the numerators (105 + 119 = 224) and keep the common denominator 357 unchanged.
Working: 105 + 119/357 = 224/357

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 224 and 357, which is 7. Divide both the numerator and denominator by 7.
Working: 224 ÷ 7/357 ÷ 7 = 32/51

Step 5: Decimal & Percentage Representation
Dividing the numerator 32 by denominator 51 produces a repeating decimal (approximately 0.627451, or 62.7451%).
Working: 32 ÷ 51 = 0.627451 (62.7451%)

Key Values:
- Simplified Fraction: 32/51
- Mixed Number Form: 32/51
- Decimal Value: 0.627451
- Percentage: 62.7451%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-15-51-plus-7-21/
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15/51 + 7/21 = 32/51

Simplified Fraction

32/51

Mixed Number

Proper (32/51)

Decimal Value

0.627451

Percentage

62.7451%

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Step-by-Step Solution: 15/51 + 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 15/51 by 7, and multiply the numerator and denominator of 7/21 by 17 so both fractions share the common base 357.

15 × 7/51 × 7 = 105/357 and 7 × 17/21 × 17 = 119/357

Step 3

Add the Numerators

Now add the numerators (105 + 119 = 224) and keep the common denominator 357 unchanged.

105 + 119/357 = 224/357

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 224 and 357, which is 7. Divide both the numerator and denominator by 7.

224 ÷ 7/357 ÷ 7 = 32/51

Step 5

Decimal & Percentage Representation

Dividing the numerator 32 by denominator 51 produces a repeating decimal (approximately 0.627451, or 62.7451%).

32 ÷ 51 = 0.627451 (62.7451%)

Visual Representation

The diagram below illustrates 15/51 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`32/51`
Mixed Number Form	`32/51`
Decimal Form	`0.627451`
Percentage	`62.7451%`

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Frequently Asked Questions

What is 15/51 plus 7/21 as a fraction?

15/51 + 7/21 in simplest fraction form is 32/51.

What is 15/51 plus 7/21 as a decimal?

15/51 + 7/21 converted to a decimal is 0.627451.

What is 15/51 plus 7/21 as a percentage?

15/51 + 7/21 expressed as a percentage is 62.7451%.

Does 15/51 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.627451...) because the denominator contains prime factors other than 2 and 5.