What is 5/26 plus 15/21? (Answer: 165/182)

Exact Answer

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Problem: What is 5/26 plus 15/21?
Formula / Expression: 5/26 + 15/21
Final Answer: 165/182
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 546
Multiply the numerator and denominator of 5/26 by 21, and multiply the numerator and denominator of 15/21 by 26 so both fractions share the common base 546.
Working: 5 × 21/26 × 21 = 105/546 and 15 × 26/21 × 26 = 390/546

Step 3: Add the Numerators
Now add the numerators (105 + 390 = 495) and keep the common denominator 546 unchanged.
Working: 105 + 390/546 = 495/546

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 495 and 546, which is 3. Divide both the numerator and denominator by 3.
Working: 495 ÷ 3/546 ÷ 3 = 165/182

Step 5: Decimal & Percentage Representation
Dividing the numerator 165 by denominator 182 produces a repeating decimal (approximately 0.906593, or 90.6593%).
Working: 165 ÷ 182 = 0.906593 (90.6593%)

Key Values:
- Simplified Fraction: 165/182
- Mixed Number Form: 165/182
- Decimal Value: 0.906593
- Percentage: 90.6593%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-26-plus-15-21/
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5/26 + 15/21 = 165/182

Simplified Fraction

165/182

Mixed Number

Proper (165/182)

Decimal Value

0.906593

Percentage

90.6593%

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Step-by-Step Solution: 5/26 + 15/21

Step 1

Find the Least Common Denominator (LCD)

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

LCD(26, 21) = 546

Step 2

Convert to Equivalent Fractions with Common Denominator 546

Multiply the numerator and denominator of 5/26 by 21, and multiply the numerator and denominator of 15/21 by 26 so both fractions share the common base 546.

5 × 21/26 × 21 = 105/546 and 15 × 26/21 × 26 = 390/546

Step 3

Add the Numerators

Now add the numerators (105 + 390 = 495) and keep the common denominator 546 unchanged.

105 + 390/546 = 495/546

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 495 and 546, which is 3. Divide both the numerator and denominator by 3.

495 ÷ 3/546 ÷ 3 = 165/182

Step 5

Decimal & Percentage Representation

Dividing the numerator 165 by denominator 182 produces a repeating decimal (approximately 0.906593, or 90.6593%).

165 ÷ 182 = 0.906593 (90.6593%)

Visual Representation

The diagram below illustrates 5/26 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`165/182`
Mixed Number Form	`165/182`
Decimal Form	`0.906593`
Percentage	`90.6593%`

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Frequently Asked Questions

What is 5/26 plus 15/21 as a fraction?

5/26 + 15/21 in simplest fraction form is 165/182.

What is 5/26 plus 15/21 as a decimal?

5/26 + 15/21 converted to a decimal is 0.906593.

What is 5/26 plus 15/21 as a percentage?

5/26 + 15/21 expressed as a percentage is 90.6593%.

Does 5/26 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.906593...) because the denominator contains prime factors other than 2 and 5.