What is 11/51 plus 5/21? (Answer: 54/119)

Exact Answer

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Problem: What is 11/51 plus 5/21?
Formula / Expression: 11/51 + 5/21
Final Answer: 54/119
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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 11/51 by 7, and multiply the numerator and denominator of 5/21 by 17 so both fractions share the common base 357.
Working: 11 × 7/51 × 7 = 77/357 and 5 × 17/21 × 17 = 85/357

Step 3: Add the Numerators
Now add the numerators (77 + 85 = 162) and keep the common denominator 357 unchanged.
Working: 77 + 85/357 = 162/357

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 162 and 357, which is 3. Divide both the numerator and denominator by 3.
Working: 162 ÷ 3/357 ÷ 3 = 54/119

Step 5: Decimal & Percentage Representation
Dividing the numerator 54 by denominator 119 produces a repeating decimal (approximately 0.453782, or 45.3782%).
Working: 54 ÷ 119 = 0.453782 (45.3782%)

Key Values:
- Simplified Fraction: 54/119
- Mixed Number Form: 54/119
- Decimal Value: 0.453782
- Percentage: 45.3782%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-11-51-plus-5-21/
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11/51 + 5/21 = 54/119

Simplified Fraction

54/119

Mixed Number

Proper (54/119)

Decimal Value

0.453782

Percentage

45.3782%

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Step-by-Step Solution: 11/51 + 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 11/51 by 7, and multiply the numerator and denominator of 5/21 by 17 so both fractions share the common base 357.

11 × 7/51 × 7 = 77/357 and 5 × 17/21 × 17 = 85/357

Step 3

Add the Numerators

Now add the numerators (77 + 85 = 162) and keep the common denominator 357 unchanged.

77 + 85/357 = 162/357

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 162 and 357, which is 3. Divide both the numerator and denominator by 3.

162 ÷ 3/357 ÷ 3 = 54/119

Step 5

Decimal & Percentage Representation

Dividing the numerator 54 by denominator 119 produces a repeating decimal (approximately 0.453782, or 45.3782%).

54 ÷ 119 = 0.453782 (45.3782%)

Visual Representation

The diagram below illustrates 11/51 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`54/119`
Mixed Number Form	`54/119`
Decimal Form	`0.453782`
Percentage	`45.3782%`

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Frequently Asked Questions

What is 11/51 plus 5/21 as a fraction?

11/51 + 5/21 in simplest fraction form is 54/119.

What is 11/51 plus 5/21 as a decimal?

11/51 + 5/21 converted to a decimal is 0.453782.

What is 11/51 plus 5/21 as a percentage?

11/51 + 5/21 expressed as a percentage is 45.3782%.

Does 11/51 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.453782...) because the denominator contains prime factors other than 2 and 5.