What is 13/37 plus 10/21? (Answer: 643/777)

Exact Answer

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Problem: What is 13/37 plus 10/21?
Formula / Expression: 13/37 + 10/21
Final Answer: 643/777
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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 10/21 by 37 so both fractions share the common base 777.
Working: 13 × 21/37 × 21 = 273/777 and 10 × 37/21 × 37 = 370/777

Step 3: Add the Numerators
Now add the numerators (273 + 370 = 643) and keep the common denominator 777 unchanged.
Working: 273 + 370/777 = 643/777

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 643 and 777 is 1, confirming that 643/777 cannot be reduced further—it is already in its simplest irreducible form.
Working: 643/777

Step 5: Decimal & Percentage Representation
Dividing the numerator 643 by denominator 777 produces a repeating decimal (approximately 0.827542, or 82.7542%).
Working: 643 ÷ 777 = 0.827542 (82.7542%)

Key Values:
- Simplified Fraction: 643/777
- Mixed Number Form: 643/777
- Decimal Value: 0.827542
- Percentage: 82.7542%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-37-plus-10-21/
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13/37 + 10/21 = 643/777

Simplified Fraction

643/777

Mixed Number

Proper (643/777)

Decimal Value

0.827542

Percentage

82.7542%

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Step-by-Step Solution: 13/37 + 10/21

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 10/21 by 37 so both fractions share the common base 777.

13 × 21/37 × 21 = 273/777 and 10 × 37/21 × 37 = 370/777

Step 3

Add the Numerators

Now add the numerators (273 + 370 = 643) and keep the common denominator 777 unchanged.

273 + 370/777 = 643/777

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 643 and 777 is 1, confirming that 643/777 cannot be reduced further—it is already in its simplest irreducible form.

643/777

Step 5

Decimal & Percentage Representation

Dividing the numerator 643 by denominator 777 produces a repeating decimal (approximately 0.827542, or 82.7542%).

643 ÷ 777 = 0.827542 (82.7542%)

Visual Representation

The diagram below illustrates 13/37 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`643/777`
Mixed Number Form	`643/777`
Decimal Form	`0.827542`
Percentage	`82.7542%`

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Frequently Asked Questions

What is 13/37 plus 10/21 as a fraction?

13/37 + 10/21 in simplest fraction form is 643/777.

What is 13/37 plus 10/21 as a decimal?

13/37 + 10/21 converted to a decimal is 0.827542.

What is 13/37 plus 10/21 as a percentage?

13/37 + 10/21 expressed as a percentage is 82.7542%.

Does 13/37 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.827542...) because the denominator contains prime factors other than 2 and 5.