What is 9/52 plus 10/21? (Answer: 709/1092)

Exact Answer

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Problem: What is 9/52 plus 10/21?
Formula / Expression: 9/52 + 10/21
Final Answer: 709/1092
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 52 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 52 × 21 = 1092.
Working: LCD(52, 21) = 1092

Step 2: Convert to Equivalent Fractions with Common Denominator 1092
Multiply the numerator and denominator of 9/52 by 21, and multiply the numerator and denominator of 10/21 by 52 so both fractions share the common base 1092.
Working: 9 × 21/52 × 21 = 189/1092 and 10 × 52/21 × 52 = 520/1092

Step 3: Add the Numerators
Now add the numerators (189 + 520 = 709) and keep the common denominator 1092 unchanged.
Working: 189 + 520/1092 = 709/1092

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 709 and 1092 is 1, confirming that 709/1092 cannot be reduced further—it is already in its simplest irreducible form.
Working: 709/1092

Step 5: Decimal & Percentage Representation
Dividing the numerator 709 by denominator 1092 produces a repeating decimal (approximately 0.649267, or 64.9267%).
Working: 709 ÷ 1092 = 0.649267 (64.9267%)

Key Values:
- Simplified Fraction: 709/1092
- Mixed Number Form: 709/1092
- Decimal Value: 0.649267
- Percentage: 64.9267%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-52-plus-10-21/
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9/52 + 10/21 = 709/1092

Simplified Fraction

709/1092

Mixed Number

Proper (709/1092)

Decimal Value

0.649267

Percentage

64.9267%

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Step-by-Step Solution: 9/52 + 10/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 52 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 52 × 21 = 1092.

LCD(52, 21) = 1092

Step 2

Convert to Equivalent Fractions with Common Denominator 1092

Multiply the numerator and denominator of 9/52 by 21, and multiply the numerator and denominator of 10/21 by 52 so both fractions share the common base 1092.

9 × 21/52 × 21 = 189/1092 and 10 × 52/21 × 52 = 520/1092

Step 3

Add the Numerators

Now add the numerators (189 + 520 = 709) and keep the common denominator 1092 unchanged.

189 + 520/1092 = 709/1092

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 709 and 1092 is 1, confirming that 709/1092 cannot be reduced further—it is already in its simplest irreducible form.

709/1092

Step 5

Decimal & Percentage Representation

Dividing the numerator 709 by denominator 1092 produces a repeating decimal (approximately 0.649267, or 64.9267%).

709 ÷ 1092 = 0.649267 (64.9267%)

Visual Representation

The diagram below illustrates 9/52 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`709/1092`
Mixed Number Form	`709/1092`
Decimal Form	`0.649267`
Percentage	`64.9267%`

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Frequently Asked Questions

What is 9/52 plus 10/21 as a fraction?

9/52 + 10/21 in simplest fraction form is 709/1092.

What is 9/52 plus 10/21 as a decimal?

9/52 + 10/21 converted to a decimal is 0.649267.

What is 9/52 plus 10/21 as a percentage?

9/52 + 10/21 expressed as a percentage is 64.9267%.

Does 9/52 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.649267...) because the denominator contains prime factors other than 2 and 5.