What is 17/40 plus 7/13? (Answer: 501/520)

Exact Answer

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Problem: What is 17/40 plus 7/13?
Formula / Expression: 17/40 + 7/13
Final Answer: 501/520
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 40 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 13 = 520.
Working: LCD(40, 13) = 520

Step 2: Convert to Equivalent Fractions with Common Denominator 520
Multiply the numerator and denominator of 17/40 by 13, and multiply the numerator and denominator of 7/13 by 40 so both fractions share the common base 520.
Working: 17 × 13/40 × 13 = 221/520 and 7 × 40/13 × 40 = 280/520

Step 3: Add the Numerators
Now add the numerators (221 + 280 = 501) and keep the common denominator 520 unchanged.
Working: 221 + 280/520 = 501/520

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 501 and 520 is 1, confirming that 501/520 cannot be reduced further—it is already in its simplest irreducible form.
Working: 501/520

Step 5: Decimal & Percentage Representation
Dividing the numerator 501 by denominator 520 produces a repeating decimal (approximately 0.963462, or 96.3462%).
Working: 501 ÷ 520 = 0.963462 (96.3462%)

Key Values:
- Simplified Fraction: 501/520
- Mixed Number Form: 501/520
- Decimal Value: 0.963462
- Percentage: 96.3462%

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Solved with FractionsCalc:
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17/40 + 7/13 = 501/520

Simplified Fraction

501/520

Mixed Number

Proper (501/520)

Decimal Value

0.963462

Percentage

96.3462%

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Step-by-Step Solution: 17/40 + 7/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 40 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 13 = 520.

LCD(40, 13) = 520

Step 2

Convert to Equivalent Fractions with Common Denominator 520

Multiply the numerator and denominator of 17/40 by 13, and multiply the numerator and denominator of 7/13 by 40 so both fractions share the common base 520.

17 × 13/40 × 13 = 221/520 and 7 × 40/13 × 40 = 280/520

Step 3

Add the Numerators

Now add the numerators (221 + 280 = 501) and keep the common denominator 520 unchanged.

221 + 280/520 = 501/520

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 501 and 520 is 1, confirming that 501/520 cannot be reduced further—it is already in its simplest irreducible form.

501/520

Step 5

Decimal & Percentage Representation

Dividing the numerator 501 by denominator 520 produces a repeating decimal (approximately 0.963462, or 96.3462%).

501 ÷ 520 = 0.963462 (96.3462%)

Visual Representation

The diagram below illustrates 17/40 plus 7/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`501/520`
Mixed Number Form	`501/520`
Decimal Form	`0.963462`
Percentage	`96.3462%`

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Frequently Asked Questions

What is 17/40 plus 7/13 as a fraction?

17/40 + 7/13 in simplest fraction form is 501/520.

What is 17/40 plus 7/13 as a decimal?

17/40 + 7/13 converted to a decimal is 0.963462.

What is 17/40 plus 7/13 as a percentage?

17/40 + 7/13 expressed as a percentage is 96.3462%.

Does 17/40 plus 7/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.963462...) because the denominator contains prime factors other than 2 and 5.