What is 3/51 plus 7/21? (Answer: 20/51)

Exact Answer

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Problem: What is 3/51 plus 7/21?
Formula / Expression: 3/51 + 7/21
Final Answer: 20/51
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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 3/51 by 7, and multiply the numerator and denominator of 7/21 by 17 so both fractions share the common base 357.
Working: 3 × 7/51 × 7 = 21/357 and 7 × 17/21 × 17 = 119/357

Step 3: Add the Numerators
Now add the numerators (21 + 119 = 140) and keep the common denominator 357 unchanged.
Working: 21 + 119/357 = 140/357

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 140 and 357, which is 7. Divide both the numerator and denominator by 7.
Working: 140 ÷ 7/357 ÷ 7 = 20/51

Step 5: Decimal & Percentage Representation
Dividing the numerator 20 by denominator 51 produces a repeating decimal (approximately 0.392157, or 39.2157%).
Working: 20 ÷ 51 = 0.392157 (39.2157%)

Key Values:
- Simplified Fraction: 20/51
- Mixed Number Form: 20/51
- Decimal Value: 0.392157
- Percentage: 39.2157%

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Solved with FractionsCalc:
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3/51 + 7/21 = 20/51

Simplified Fraction

20/51

Mixed Number

Proper (20/51)

Decimal Value

0.392157

Percentage

39.2157%

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Step-by-Step Solution: 3/51 + 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 3/51 by 7, and multiply the numerator and denominator of 7/21 by 17 so both fractions share the common base 357.

3 × 7/51 × 7 = 21/357 and 7 × 17/21 × 17 = 119/357

Step 3

Add the Numerators

Now add the numerators (21 + 119 = 140) and keep the common denominator 357 unchanged.

21 + 119/357 = 140/357

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 140 and 357, which is 7. Divide both the numerator and denominator by 7.

140 ÷ 7/357 ÷ 7 = 20/51

Step 5

Decimal & Percentage Representation

Dividing the numerator 20 by denominator 51 produces a repeating decimal (approximately 0.392157, or 39.2157%).

20 ÷ 51 = 0.392157 (39.2157%)

Visual Representation

The diagram below illustrates 3/51 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`20/51`
Mixed Number Form	`20/51`
Decimal Form	`0.392157`
Percentage	`39.2157%`

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Frequently Asked Questions

What is 3/51 plus 7/21 as a fraction?

3/51 + 7/21 in simplest fraction form is 20/51.

What is 3/51 plus 7/21 as a decimal?

3/51 + 7/21 converted to a decimal is 0.392157.

What is 3/51 plus 7/21 as a percentage?

3/51 + 7/21 expressed as a percentage is 39.2157%.

Does 3/51 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.392157...) because the denominator contains prime factors other than 2 and 5.