What is 10/21 plus 24/50? (Answer: 502/525)

Exact Answer

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Problem: What is 10/21 plus 24/50?
Formula / Expression: 10/21 + 24/50
Final Answer: 502/525
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 1050
Multiply the numerator and denominator of 10/21 by 50, and multiply the numerator and denominator of 24/50 by 21 so both fractions share the common base 1050.
Working: 10 × 50/21 × 50 = 500/1050 and 24 × 21/50 × 21 = 504/1050

Step 3: Add the Numerators
Now add the numerators (500 + 504 = 1004) and keep the common denominator 1050 unchanged.
Working: 500 + 504/1050 = 1004/1050

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 1004 and 1050, which is 2. Divide both the numerator and denominator by 2.
Working: 1004 ÷ 2/1050 ÷ 2 = 502/525

Step 5: Decimal & Percentage Representation
Dividing the numerator 502 by denominator 525 produces a repeating decimal (approximately 0.95619, or 95.619%).
Working: 502 ÷ 525 = 0.95619 (95.619%)

Key Values:
- Simplified Fraction: 502/525
- Mixed Number Form: 502/525
- Decimal Value: 0.95619
- Percentage: 95.619%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-21-plus-24-50/
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10/21 + 24/50 = 502/525

Simplified Fraction

502/525

Mixed Number

Proper (502/525)

Decimal Value

0.95619

Percentage

95.619%

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Step-by-Step Solution: 10/21 + 24/50

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 50) = 1050

Step 2

Convert to Equivalent Fractions with Common Denominator 1050

Multiply the numerator and denominator of 10/21 by 50, and multiply the numerator and denominator of 24/50 by 21 so both fractions share the common base 1050.

10 × 50/21 × 50 = 500/1050 and 24 × 21/50 × 21 = 504/1050

Step 3

Add the Numerators

Now add the numerators (500 + 504 = 1004) and keep the common denominator 1050 unchanged.

500 + 504/1050 = 1004/1050

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 1004 and 1050, which is 2. Divide both the numerator and denominator by 2.

1004 ÷ 2/1050 ÷ 2 = 502/525

Step 5

Decimal & Percentage Representation

Dividing the numerator 502 by denominator 525 produces a repeating decimal (approximately 0.95619, or 95.619%).

502 ÷ 525 = 0.95619 (95.619%)

Visual Representation

The diagram below illustrates 10/21 plus 24/50 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`502/525`
Mixed Number Form	`502/525`
Decimal Form	`0.95619`
Percentage	`95.619%`

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Frequently Asked Questions

What is 10/21 plus 24/50 as a fraction?

10/21 + 24/50 in simplest fraction form is 502/525.

What is 10/21 plus 24/50 as a decimal?

10/21 + 24/50 converted to a decimal is 0.95619.

What is 10/21 plus 24/50 as a percentage?

10/21 + 24/50 expressed as a percentage is 95.619%.

Does 10/21 plus 24/50 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.95619...) because the denominator contains prime factors other than 2 and 5.