What is 4/51 plus 4/21? (Answer: 32/119)

Exact Answer

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Problem: What is 4/51 plus 4/21?
Formula / Expression: 4/51 + 4/21
Final Answer: 32/119
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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 4/51 by 7, and multiply the numerator and denominator of 4/21 by 17 so both fractions share the common base 357.
Working: 4 × 7/51 × 7 = 28/357 and 4 × 17/21 × 17 = 68/357

Step 3: Add the Numerators
Now add the numerators (28 + 68 = 96) and keep the common denominator 357 unchanged.
Working: 28 + 68/357 = 96/357

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 96 and 357, which is 3. Divide both the numerator and denominator by 3.
Working: 96 ÷ 3/357 ÷ 3 = 32/119

Step 5: Decimal & Percentage Representation
Dividing the numerator 32 by denominator 119 produces a repeating decimal (approximately 0.268908, or 26.8908%).
Working: 32 ÷ 119 = 0.268908 (26.8908%)

Key Values:
- Simplified Fraction: 32/119
- Mixed Number Form: 32/119
- Decimal Value: 0.268908
- Percentage: 26.8908%

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Solved with FractionsCalc:
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4/51 + 4/21 = 32/119

Simplified Fraction

32/119

Mixed Number

Proper (32/119)

Decimal Value

0.268908

Percentage

26.8908%

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Step-by-Step Solution: 4/51 + 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 4/51 by 7, and multiply the numerator and denominator of 4/21 by 17 so both fractions share the common base 357.

4 × 7/51 × 7 = 28/357 and 4 × 17/21 × 17 = 68/357

Step 3

Add the Numerators

Now add the numerators (28 + 68 = 96) and keep the common denominator 357 unchanged.

28 + 68/357 = 96/357

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 96 and 357, which is 3. Divide both the numerator and denominator by 3.

96 ÷ 3/357 ÷ 3 = 32/119

Step 5

Decimal & Percentage Representation

Dividing the numerator 32 by denominator 119 produces a repeating decimal (approximately 0.268908, or 26.8908%).

32 ÷ 119 = 0.268908 (26.8908%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`32/119`
Mixed Number Form	`32/119`
Decimal Form	`0.268908`
Percentage	`26.8908%`

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Frequently Asked Questions

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

4/51 + 4/21 in simplest fraction form is 32/119.

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

4/51 + 4/21 converted to a decimal is 0.268908.

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

4/51 + 4/21 expressed as a percentage is 26.8908%.

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

It results in a repeating decimal (approximately 0.268908...) because the denominator contains prime factors other than 2 and 5.