What is 1/51 plus 4/21? (Answer: 25/119)

Exact Answer

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Problem: What is 1/51 plus 4/21?
Formula / Expression: 1/51 + 4/21
Final Answer: 25/119
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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 1/51 by 7, and multiply the numerator and denominator of 4/21 by 17 so both fractions share the common base 357.
Working: 1 × 7/51 × 7 = 7/357 and 4 × 17/21 × 17 = 68/357

Step 3: Add the Numerators
Now add the numerators (7 + 68 = 75) and keep the common denominator 357 unchanged.
Working: 7 + 68/357 = 75/357

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 75 and 357, which is 3. Divide both the numerator and denominator by 3.
Working: 75 ÷ 3/357 ÷ 3 = 25/119

Step 5: Decimal & Percentage Representation
Dividing the numerator 25 by denominator 119 produces a repeating decimal (approximately 0.210084, or 21.0084%).
Working: 25 ÷ 119 = 0.210084 (21.0084%)

Key Values:
- Simplified Fraction: 25/119
- Mixed Number Form: 25/119
- Decimal Value: 0.210084
- Percentage: 21.0084%

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Solved with FractionsCalc:
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1/51 + 4/21 = 25/119

Simplified Fraction

25/119

Mixed Number

Proper (25/119)

Decimal Value

0.210084

Percentage

21.0084%

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Step-by-Step Solution: 1/51 + 4/21

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 1/51 by 7, and multiply the numerator and denominator of 4/21 by 17 so both fractions share the common base 357.

1 × 7/51 × 7 = 7/357 and 4 × 17/21 × 17 = 68/357

Step 3

Add the Numerators

Now add the numerators (7 + 68 = 75) and keep the common denominator 357 unchanged.

7 + 68/357 = 75/357

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 75 and 357, which is 3. Divide both the numerator and denominator by 3.

75 ÷ 3/357 ÷ 3 = 25/119

Step 5

Decimal & Percentage Representation

Dividing the numerator 25 by denominator 119 produces a repeating decimal (approximately 0.210084, or 21.0084%).

25 ÷ 119 = 0.210084 (21.0084%)

Visual Representation

The diagram below illustrates 1/51 plus 4/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`25/119`
Mixed Number Form	`25/119`
Decimal Form	`0.210084`
Percentage	`21.0084%`

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Frequently Asked Questions

What is 1/51 plus 4/21 as a fraction?

1/51 + 4/21 in simplest fraction form is 25/119.

What is 1/51 plus 4/21 as a decimal?

1/51 + 4/21 converted to a decimal is 0.210084.

What is 1/51 plus 4/21 as a percentage?

1/51 + 4/21 expressed as a percentage is 21.0084%.

Does 1/51 plus 4/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.210084...) because the denominator contains prime factors other than 2 and 5.