What is 11/21 plus 14/26? (Answer: 290/273)

Exact Answer

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Problem: What is 11/21 plus 14/26?
Formula / Expression: 11/21 + 14/26
Final Answer: 1 17/273 (290/273)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 26 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 26 = 546.
Working: LCD(21, 26) = 546

Step 2: Convert to Equivalent Fractions with Common Denominator 546
Multiply the numerator and denominator of 11/21 by 26, and multiply the numerator and denominator of 14/26 by 21 so both fractions share the common base 546.
Working: 11 × 26/21 × 26 = 286/546 and 14 × 21/26 × 21 = 294/546

Step 3: Add the Numerators
Now add the numerators (286 + 294 = 580) and keep the common denominator 546 unchanged.
Working: 286 + 294/546 = 580/546

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 580 and 546, which is 2. Divide both the numerator and denominator by 2.
Working: 580 ÷ 2/546 ÷ 2 = 290/273

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (290) is greater than the denominator (273), divide 290 by 273: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/273.
Working: 290/273 = 1 17/273

Step 6: Decimal & Percentage Representation
Dividing the numerator 290 by denominator 273 produces a repeating decimal (approximately 1.062271, or 106.2271%).
Working: 290 ÷ 273 = 1.062271 (106.2271%)

Key Values:
- Simplified Fraction: 290/273
- Mixed Number Form: 1 17/273
- Decimal Value: 1.062271
- Percentage: 106.2271%

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Solved with FractionsCalc:
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11/21 + 14/26 = 290/273

Simplified Fraction

290/273

Mixed Number

1 17/273

Decimal Value

1.062271

Percentage

106.2271%

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Step-by-Step Solution: 11/21 + 14/26

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 26 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 26 = 546.

LCD(21, 26) = 546

Step 2

Convert to Equivalent Fractions with Common Denominator 546

Multiply the numerator and denominator of 11/21 by 26, and multiply the numerator and denominator of 14/26 by 21 so both fractions share the common base 546.

11 × 26/21 × 26 = 286/546 and 14 × 21/26 × 21 = 294/546

Step 3

Add the Numerators

Now add the numerators (286 + 294 = 580) and keep the common denominator 546 unchanged.

286 + 294/546 = 580/546

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 580 and 546, which is 2. Divide both the numerator and denominator by 2.

580 ÷ 2/546 ÷ 2 = 290/273

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (290) is greater than the denominator (273), divide 290 by 273: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/273.

290/273 = 117/273

Step 6

Decimal & Percentage Representation

Dividing the numerator 290 by denominator 273 produces a repeating decimal (approximately 1.062271, or 106.2271%).

290 ÷ 273 = 1.062271 (106.2271%)

Visual Representation

The diagram below illustrates 11/21 plus 14/26 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`290/273`
Mixed Number Form	`1 17/273`
Decimal Form	`1.062271`
Percentage	`106.2271%`

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Frequently Asked Questions

What is 11/21 plus 14/26 as a fraction?

11/21 + 14/26 in simplest fraction form is 290/273 (or 1 17/273 as a mixed number).

What is 11/21 plus 14/26 as a decimal?

11/21 + 14/26 converted to a decimal is 1.062271.

What is 11/21 plus 14/26 as a percentage?

11/21 + 14/26 expressed as a percentage is 106.2271%.

How do you write 11/21 plus 14/26 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 290/273 can be written as the mixed number 1 17/273.

Does 11/21 plus 14/26 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.062271...) because the denominator contains prime factors other than 2 and 5.