What is 13/37 plus 11/21? (Answer: 680/777)

Exact Answer

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Problem: What is 13/37 plus 11/21?
Formula / Expression: 13/37 + 11/21
Final Answer: 680/777
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 37 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 37 × 21 = 777.
Working: LCD(37, 21) = 777

Step 2: Convert to Equivalent Fractions with Common Denominator 777
Multiply the numerator and denominator of 13/37 by 21, and multiply the numerator and denominator of 11/21 by 37 so both fractions share the common base 777.
Working: 13 × 21/37 × 21 = 273/777 and 11 × 37/21 × 37 = 407/777

Step 3: Add the Numerators
Now add the numerators (273 + 407 = 680) and keep the common denominator 777 unchanged.
Working: 273 + 407/777 = 680/777

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 680 and 777 is 1, confirming that 680/777 cannot be reduced further—it is already in its simplest irreducible form.
Working: 680/777

Step 5: Decimal & Percentage Representation
Dividing the numerator 680 by denominator 777 produces a repeating decimal (approximately 0.875161, or 87.5161%).
Working: 680 ÷ 777 = 0.875161 (87.5161%)

Key Values:
- Simplified Fraction: 680/777
- Mixed Number Form: 680/777
- Decimal Value: 0.875161
- Percentage: 87.5161%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-37-plus-11-21/
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13/37 + 11/21 = 680/777

Simplified Fraction

680/777

Mixed Number

Proper (680/777)

Decimal Value

0.875161

Percentage

87.5161%

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Step-by-Step Solution: 13/37 + 11/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 37 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 37 × 21 = 777.

LCD(37, 21) = 777

Step 2

Convert to Equivalent Fractions with Common Denominator 777

Multiply the numerator and denominator of 13/37 by 21, and multiply the numerator and denominator of 11/21 by 37 so both fractions share the common base 777.

13 × 21/37 × 21 = 273/777 and 11 × 37/21 × 37 = 407/777

Step 3

Add the Numerators

Now add the numerators (273 + 407 = 680) and keep the common denominator 777 unchanged.

273 + 407/777 = 680/777

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 680 and 777 is 1, confirming that 680/777 cannot be reduced further—it is already in its simplest irreducible form.

680/777

Step 5

Decimal & Percentage Representation

Dividing the numerator 680 by denominator 777 produces a repeating decimal (approximately 0.875161, or 87.5161%).

680 ÷ 777 = 0.875161 (87.5161%)

Visual Representation

The diagram below illustrates 13/37 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`680/777`
Mixed Number Form	`680/777`
Decimal Form	`0.875161`
Percentage	`87.5161%`

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Frequently Asked Questions

What is 13/37 plus 11/21 as a fraction?

13/37 + 11/21 in simplest fraction form is 680/777.

What is 13/37 plus 11/21 as a decimal?

13/37 + 11/21 converted to a decimal is 0.875161.

What is 13/37 plus 11/21 as a percentage?

13/37 + 11/21 expressed as a percentage is 87.5161%.

Does 13/37 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.875161...) because the denominator contains prime factors other than 2 and 5.