What is 17/52 plus 8/21? (Answer: 773/1092)

Exact Answer

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Problem: What is 17/52 plus 8/21?
Formula / Expression: 17/52 + 8/21
Final Answer: 773/1092
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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 17/52 by 21, and multiply the numerator and denominator of 8/21 by 52 so both fractions share the common base 1092.
Working: 17 × 21/52 × 21 = 357/1092 and 8 × 52/21 × 52 = 416/1092

Step 3: Add the Numerators
Now add the numerators (357 + 416 = 773) and keep the common denominator 1092 unchanged.
Working: 357 + 416/1092 = 773/1092

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 773 and 1092 is 1, confirming that 773/1092 cannot be reduced further—it is already in its simplest irreducible form.
Working: 773/1092

Step 5: Decimal & Percentage Representation
Dividing the numerator 773 by denominator 1092 produces a repeating decimal (approximately 0.707875, or 70.7875%).
Working: 773 ÷ 1092 = 0.707875 (70.7875%)

Key Values:
- Simplified Fraction: 773/1092
- Mixed Number Form: 773/1092
- Decimal Value: 0.707875
- Percentage: 70.7875%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-17-52-plus-8-21/
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17/52 + 8/21 = 773/1092

Simplified Fraction

773/1092

Mixed Number

Proper (773/1092)

Decimal Value

0.707875

Percentage

70.7875%

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Step-by-Step Solution: 17/52 + 8/21

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 17/52 by 21, and multiply the numerator and denominator of 8/21 by 52 so both fractions share the common base 1092.

17 × 21/52 × 21 = 357/1092 and 8 × 52/21 × 52 = 416/1092

Step 3

Add the Numerators

Now add the numerators (357 + 416 = 773) and keep the common denominator 1092 unchanged.

357 + 416/1092 = 773/1092

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 773 and 1092 is 1, confirming that 773/1092 cannot be reduced further—it is already in its simplest irreducible form.

773/1092

Step 5

Decimal & Percentage Representation

Dividing the numerator 773 by denominator 1092 produces a repeating decimal (approximately 0.707875, or 70.7875%).

773 ÷ 1092 = 0.707875 (70.7875%)

Visual Representation

The diagram below illustrates 17/52 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`773/1092`
Mixed Number Form	`773/1092`
Decimal Form	`0.707875`
Percentage	`70.7875%`

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Frequently Asked Questions

What is 17/52 plus 8/21 as a fraction?

17/52 + 8/21 in simplest fraction form is 773/1092.

What is 17/52 plus 8/21 as a decimal?

17/52 + 8/21 converted to a decimal is 0.707875.

What is 17/52 plus 8/21 as a percentage?

17/52 + 8/21 expressed as a percentage is 70.7875%.

Does 17/52 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.707875...) because the denominator contains prime factors other than 2 and 5.