What is 17/45 plus 10/21? (Answer: 269/315)

Exact Answer

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Problem: What is 17/45 plus 10/21?
Formula / Expression: 17/45 + 10/21
Final Answer: 269/315
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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 10/21 by 15 so both fractions share the common base 315.
Working: 17 × 7/45 × 7 = 119/315 and 10 × 15/21 × 15 = 150/315

Step 3: Add the Numerators
Now add the numerators (119 + 150 = 269) and keep the common denominator 315 unchanged.
Working: 119 + 150/315 = 269/315

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 269 and 315 is 1, confirming that 269/315 cannot be reduced further—it is already in its simplest irreducible form.
Working: 269/315

Step 5: Decimal & Percentage Representation
Dividing the numerator 269 by denominator 315 produces a repeating decimal (approximately 0.853968, or 85.3968%).
Working: 269 ÷ 315 = 0.853968 (85.3968%)

Key Values:
- Simplified Fraction: 269/315
- Mixed Number Form: 269/315
- Decimal Value: 0.853968
- Percentage: 85.3968%

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17/45 + 10/21 = 269/315

Simplified Fraction

269/315

Mixed Number

Proper (269/315)

Decimal Value

0.853968

Percentage

85.3968%

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Step-by-Step Solution: 17/45 + 10/21

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 10/21 by 15 so both fractions share the common base 315.

17 × 7/45 × 7 = 119/315 and 10 × 15/21 × 15 = 150/315

Step 3

Add the Numerators

Now add the numerators (119 + 150 = 269) and keep the common denominator 315 unchanged.

119 + 150/315 = 269/315

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 269 and 315 is 1, confirming that 269/315 cannot be reduced further—it is already in its simplest irreducible form.

269/315

Step 5

Decimal & Percentage Representation

Dividing the numerator 269 by denominator 315 produces a repeating decimal (approximately 0.853968, or 85.3968%).

269 ÷ 315 = 0.853968 (85.3968%)

Visual Representation

The diagram below illustrates 17/45 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`269/315`
Mixed Number Form	`269/315`
Decimal Form	`0.853968`
Percentage	`85.3968%`

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Frequently Asked Questions

What is 17/45 plus 10/21 as a fraction?

17/45 + 10/21 in simplest fraction form is 269/315.

What is 17/45 plus 10/21 as a decimal?

17/45 + 10/21 converted to a decimal is 0.853968.

What is 17/45 plus 10/21 as a percentage?

17/45 + 10/21 expressed as a percentage is 85.3968%.

Does 17/45 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.853968...) because the denominator contains prime factors other than 2 and 5.