What is 2/21 plus 5/51? (Answer: 23/119)

Exact Answer

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Problem: What is 2/21 plus 5/51?
Formula / Expression: 2/21 + 5/51
Final Answer: 23/119
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 51 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 357 (which is smaller than their product 21 × 51 = 1071, keeping the calculation simpler).
Working: LCD(21, 51) = 357

Step 2: Convert to Equivalent Fractions with Common Denominator 357
Multiply the numerator and denominator of 2/21 by 17, and multiply the numerator and denominator of 5/51 by 7 so both fractions share the common base 357.
Working: 2 × 17/21 × 17 = 34/357 and 5 × 7/51 × 7 = 35/357

Step 3: Add the Numerators
Now add the numerators (34 + 35 = 69) and keep the common denominator 357 unchanged.
Working: 34 + 35/357 = 69/357

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 69 and 357, which is 3. Divide both the numerator and denominator by 3.
Working: 69 ÷ 3/357 ÷ 3 = 23/119

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 119 produces a repeating decimal (approximately 0.193277, or 19.3277%).
Working: 23 ÷ 119 = 0.193277 (19.3277%)

Key Values:
- Simplified Fraction: 23/119
- Mixed Number Form: 23/119
- Decimal Value: 0.193277
- Percentage: 19.3277%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-21-plus-5-51/
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2/21 + 5/51 = 23/119

Simplified Fraction

23/119

Mixed Number

Proper (23/119)

Decimal Value

0.193277

Percentage

19.3277%

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Step-by-Step Solution: 2/21 + 5/51

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 51 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 357 (which is smaller than their product 21 × 51 = 1071, keeping the calculation simpler).

LCD(21, 51) = 357

Step 2

Convert to Equivalent Fractions with Common Denominator 357

Multiply the numerator and denominator of 2/21 by 17, and multiply the numerator and denominator of 5/51 by 7 so both fractions share the common base 357.

2 × 17/21 × 17 = 34/357 and 5 × 7/51 × 7 = 35/357

Step 3

Add the Numerators

Now add the numerators (34 + 35 = 69) and keep the common denominator 357 unchanged.

34 + 35/357 = 69/357

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 69 and 357, which is 3. Divide both the numerator and denominator by 3.

69 ÷ 3/357 ÷ 3 = 23/119

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 119 produces a repeating decimal (approximately 0.193277, or 19.3277%).

23 ÷ 119 = 0.193277 (19.3277%)

Visual Representation

The diagram below illustrates 2/21 plus 5/51 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/119`
Mixed Number Form	`23/119`
Decimal Form	`0.193277`
Percentage	`19.3277%`

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Frequently Asked Questions

What is 2/21 plus 5/51 as a fraction?

2/21 + 5/51 in simplest fraction form is 23/119.

What is 2/21 plus 5/51 as a decimal?

2/21 + 5/51 converted to a decimal is 0.193277.

What is 2/21 plus 5/51 as a percentage?

2/21 + 5/51 expressed as a percentage is 19.3277%.

Does 2/21 plus 5/51 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.193277...) because the denominator contains prime factors other than 2 and 5.