What is 13/40 plus 8/21? (Answer: 593/840)

Exact Answer

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Problem: What is 13/40 plus 8/21?
Formula / Expression: 13/40 + 8/21
Final Answer: 593/840
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 40 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 21 = 840.
Working: LCD(40, 21) = 840

Step 2: Convert to Equivalent Fractions with Common Denominator 840
Multiply the numerator and denominator of 13/40 by 21, and multiply the numerator and denominator of 8/21 by 40 so both fractions share the common base 840.
Working: 13 × 21/40 × 21 = 273/840 and 8 × 40/21 × 40 = 320/840

Step 3: Add the Numerators
Now add the numerators (273 + 320 = 593) and keep the common denominator 840 unchanged.
Working: 273 + 320/840 = 593/840

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 593 and 840 is 1, confirming that 593/840 cannot be reduced further—it is already in its simplest irreducible form.
Working: 593/840

Step 5: Decimal & Percentage Representation
Dividing the numerator 593 by denominator 840 produces a repeating decimal (approximately 0.705952, or 70.5952%).
Working: 593 ÷ 840 = 0.705952 (70.5952%)

Key Values:
- Simplified Fraction: 593/840
- Mixed Number Form: 593/840
- Decimal Value: 0.705952
- Percentage: 70.5952%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-40-plus-8-21/
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13/40 + 8/21 = 593/840

Simplified Fraction

593/840

Mixed Number

Proper (593/840)

Decimal Value

0.705952

Percentage

70.5952%

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Step-by-Step Solution: 13/40 + 8/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 40 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 21 = 840.

LCD(40, 21) = 840

Step 2

Convert to Equivalent Fractions with Common Denominator 840

Multiply the numerator and denominator of 13/40 by 21, and multiply the numerator and denominator of 8/21 by 40 so both fractions share the common base 840.

13 × 21/40 × 21 = 273/840 and 8 × 40/21 × 40 = 320/840

Step 3

Add the Numerators

Now add the numerators (273 + 320 = 593) and keep the common denominator 840 unchanged.

273 + 320/840 = 593/840

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 593 and 840 is 1, confirming that 593/840 cannot be reduced further—it is already in its simplest irreducible form.

593/840

Step 5

Decimal & Percentage Representation

Dividing the numerator 593 by denominator 840 produces a repeating decimal (approximately 0.705952, or 70.5952%).

593 ÷ 840 = 0.705952 (70.5952%)

Visual Representation

The diagram below illustrates 13/40 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`593/840`
Mixed Number Form	`593/840`
Decimal Form	`0.705952`
Percentage	`70.5952%`

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Frequently Asked Questions

What is 13/40 plus 8/21 as a fraction?

13/40 + 8/21 in simplest fraction form is 593/840.

What is 13/40 plus 8/21 as a decimal?

13/40 + 8/21 converted to a decimal is 0.705952.

What is 13/40 plus 8/21 as a percentage?

13/40 + 8/21 expressed as a percentage is 70.5952%.

Does 13/40 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.705952...) because the denominator contains prime factors other than 2 and 5.