What is 17/45 plus 8/21? (Answer: 239/315)

Exact Answer

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Problem: What is 17/45 plus 8/21?
Formula / Expression: 17/45 + 8/21
Final Answer: 239/315
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 45 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 315 (which is smaller than their product 45 × 21 = 945, keeping the calculation simpler).
Working: LCD(45, 21) = 315

Step 2: Convert to Equivalent Fractions with Common Denominator 315
Multiply the numerator and denominator of 17/45 by 7, and multiply the numerator and denominator of 8/21 by 15 so both fractions share the common base 315.
Working: 17 × 7/45 × 7 = 119/315 and 8 × 15/21 × 15 = 120/315

Step 3: Add the Numerators
Now add the numerators (119 + 120 = 239) and keep the common denominator 315 unchanged.
Working: 119 + 120/315 = 239/315

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 239 and 315 is 1, confirming that 239/315 cannot be reduced further—it is already in its simplest irreducible form.
Working: 239/315

Step 5: Decimal & Percentage Representation
Dividing the numerator 239 by denominator 315 produces a repeating decimal (approximately 0.75873, or 75.873%).
Working: 239 ÷ 315 = 0.75873 (75.873%)

Key Values:
- Simplified Fraction: 239/315
- Mixed Number Form: 239/315
- Decimal Value: 0.75873
- Percentage: 75.873%

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Solved with FractionsCalc:
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17/45 + 8/21 = 239/315

Simplified Fraction

239/315

Mixed Number

Proper (239/315)

Decimal Value

0.75873

Percentage

75.873%

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Step-by-Step Solution: 17/45 + 8/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 45 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 315 (which is smaller than their product 45 × 21 = 945, keeping the calculation simpler).

LCD(45, 21) = 315

Step 2

Convert to Equivalent Fractions with Common Denominator 315

Multiply the numerator and denominator of 17/45 by 7, and multiply the numerator and denominator of 8/21 by 15 so both fractions share the common base 315.

17 × 7/45 × 7 = 119/315 and 8 × 15/21 × 15 = 120/315

Step 3

Add the Numerators

Now add the numerators (119 + 120 = 239) and keep the common denominator 315 unchanged.

119 + 120/315 = 239/315

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 239 and 315 is 1, confirming that 239/315 cannot be reduced further—it is already in its simplest irreducible form.

239/315

Step 5

Decimal & Percentage Representation

Dividing the numerator 239 by denominator 315 produces a repeating decimal (approximately 0.75873, or 75.873%).

239 ÷ 315 = 0.75873 (75.873%)

Visual Representation

The diagram below illustrates 17/45 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`239/315`
Mixed Number Form	`239/315`
Decimal Form	`0.75873`
Percentage	`75.873%`

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Frequently Asked Questions

What is 17/45 plus 8/21 as a fraction?

17/45 + 8/21 in simplest fraction form is 239/315.

What is 17/45 plus 8/21 as a decimal?

17/45 + 8/21 converted to a decimal is 0.75873.

What is 17/45 plus 8/21 as a percentage?

17/45 + 8/21 expressed as a percentage is 75.873%.

Does 17/45 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.75873...) because the denominator contains prime factors other than 2 and 5.