What is 5/51 plus 5/21? (Answer: 40/119)

Exact Answer

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Problem: What is 5/51 plus 5/21?
Formula / Expression: 5/51 + 5/21
Final Answer: 40/119
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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 5/51 by 7, and multiply the numerator and denominator of 5/21 by 17 so both fractions share the common base 357.
Working: 5 × 7/51 × 7 = 35/357 and 5 × 17/21 × 17 = 85/357

Step 3: Add the Numerators
Now add the numerators (35 + 85 = 120) and keep the common denominator 357 unchanged.
Working: 35 + 85/357 = 120/357

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 120 and 357, which is 3. Divide both the numerator and denominator by 3.
Working: 120 ÷ 3/357 ÷ 3 = 40/119

Step 5: Decimal & Percentage Representation
Dividing the numerator 40 by denominator 119 produces a repeating decimal (approximately 0.336134, or 33.6134%).
Working: 40 ÷ 119 = 0.336134 (33.6134%)

Key Values:
- Simplified Fraction: 40/119
- Mixed Number Form: 40/119
- Decimal Value: 0.336134
- Percentage: 33.6134%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-51-plus-5-21/
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5/51 + 5/21 = 40/119

Simplified Fraction

40/119

Mixed Number

Proper (40/119)

Decimal Value

0.336134

Percentage

33.6134%

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Step-by-Step Solution: 5/51 + 5/21

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 5/51 by 7, and multiply the numerator and denominator of 5/21 by 17 so both fractions share the common base 357.

5 × 7/51 × 7 = 35/357 and 5 × 17/21 × 17 = 85/357

Step 3

Add the Numerators

Now add the numerators (35 + 85 = 120) and keep the common denominator 357 unchanged.

35 + 85/357 = 120/357

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 120 and 357, which is 3. Divide both the numerator and denominator by 3.

120 ÷ 3/357 ÷ 3 = 40/119

Step 5

Decimal & Percentage Representation

Dividing the numerator 40 by denominator 119 produces a repeating decimal (approximately 0.336134, or 33.6134%).

40 ÷ 119 = 0.336134 (33.6134%)

Visual Representation

The diagram below illustrates 5/51 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`40/119`
Mixed Number Form	`40/119`
Decimal Form	`0.336134`
Percentage	`33.6134%`

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Frequently Asked Questions

What is 5/51 plus 5/21 as a fraction?

5/51 + 5/21 in simplest fraction form is 40/119.

What is 5/51 plus 5/21 as a decimal?

5/51 + 5/21 converted to a decimal is 0.336134.

What is 5/51 plus 5/21 as a percentage?

5/51 + 5/21 expressed as a percentage is 33.6134%.

Does 5/51 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.336134...) because the denominator contains prime factors other than 2 and 5.