What is 13/50 plus 10/21? (Answer: 773/1050)

Exact Answer

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Problem: What is 13/50 plus 10/21?
Formula / Expression: 13/50 + 10/21
Final Answer: 773/1050
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 50 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 50 × 21 = 1050.
Working: LCD(50, 21) = 1050

Step 2: Convert to Equivalent Fractions with Common Denominator 1050
Multiply the numerator and denominator of 13/50 by 21, and multiply the numerator and denominator of 10/21 by 50 so both fractions share the common base 1050.
Working: 13 × 21/50 × 21 = 273/1050 and 10 × 50/21 × 50 = 500/1050

Step 3: Add the Numerators
Now add the numerators (273 + 500 = 773) and keep the common denominator 1050 unchanged.
Working: 273 + 500/1050 = 773/1050

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 773 and 1050 is 1, confirming that 773/1050 cannot be reduced further—it is already in its simplest irreducible form.
Working: 773/1050

Step 5: Decimal & Percentage Representation
Dividing the numerator 773 by denominator 1050 produces a repeating decimal (approximately 0.73619, or 73.619%).
Working: 773 ÷ 1050 = 0.73619 (73.619%)

Key Values:
- Simplified Fraction: 773/1050
- Mixed Number Form: 773/1050
- Decimal Value: 0.73619
- Percentage: 73.619%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-50-plus-10-21/
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13/50 + 10/21 = 773/1050

Simplified Fraction

773/1050

Mixed Number

Proper (773/1050)

Decimal Value

0.73619

Percentage

73.619%

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Step-by-Step Solution: 13/50 + 10/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 50 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 50 × 21 = 1050.

LCD(50, 21) = 1050

Step 2

Convert to Equivalent Fractions with Common Denominator 1050

Multiply the numerator and denominator of 13/50 by 21, and multiply the numerator and denominator of 10/21 by 50 so both fractions share the common base 1050.

13 × 21/50 × 21 = 273/1050 and 10 × 50/21 × 50 = 500/1050

Step 3

Add the Numerators

Now add the numerators (273 + 500 = 773) and keep the common denominator 1050 unchanged.

273 + 500/1050 = 773/1050

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 773 and 1050 is 1, confirming that 773/1050 cannot be reduced further—it is already in its simplest irreducible form.

773/1050

Step 5

Decimal & Percentage Representation

Dividing the numerator 773 by denominator 1050 produces a repeating decimal (approximately 0.73619, or 73.619%).

773 ÷ 1050 = 0.73619 (73.619%)

Visual Representation

The diagram below illustrates 13/50 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`773/1050`
Mixed Number Form	`773/1050`
Decimal Form	`0.73619`
Percentage	`73.619%`

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Frequently Asked Questions

What is 13/50 plus 10/21 as a fraction?

13/50 + 10/21 in simplest fraction form is 773/1050.

What is 13/50 plus 10/21 as a decimal?

13/50 + 10/21 converted to a decimal is 0.73619.

What is 13/50 plus 10/21 as a percentage?

13/50 + 10/21 expressed as a percentage is 73.619%.

Does 13/50 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.73619...) because the denominator contains prime factors other than 2 and 5.