What is 13/43 plus 7/21? (Answer: 82/129)

Exact Answer

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Problem: What is 13/43 plus 7/21?
Formula / Expression: 13/43 + 7/21
Final Answer: 82/129
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 43 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 43 × 21 = 903.
Working: LCD(43, 21) = 903

Step 2: Convert to Equivalent Fractions with Common Denominator 903
Multiply the numerator and denominator of 13/43 by 21, and multiply the numerator and denominator of 7/21 by 43 so both fractions share the common base 903.
Working: 13 × 21/43 × 21 = 273/903 and 7 × 43/21 × 43 = 301/903

Step 3: Add the Numerators
Now add the numerators (273 + 301 = 574) and keep the common denominator 903 unchanged.
Working: 273 + 301/903 = 574/903

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 574 and 903, which is 7. Divide both the numerator and denominator by 7.
Working: 574 ÷ 7/903 ÷ 7 = 82/129

Step 5: Decimal & Percentage Representation
Dividing the numerator 82 by denominator 129 produces a repeating decimal (approximately 0.635659, or 63.5659%).
Working: 82 ÷ 129 = 0.635659 (63.5659%)

Key Values:
- Simplified Fraction: 82/129
- Mixed Number Form: 82/129
- Decimal Value: 0.635659
- Percentage: 63.5659%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-43-plus-7-21/
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13/43 + 7/21 = 82/129

Simplified Fraction

82/129

Mixed Number

Proper (82/129)

Decimal Value

0.635659

Percentage

63.5659%

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Step-by-Step Solution: 13/43 + 7/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 43 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 43 × 21 = 903.

LCD(43, 21) = 903

Step 2

Convert to Equivalent Fractions with Common Denominator 903

Multiply the numerator and denominator of 13/43 by 21, and multiply the numerator and denominator of 7/21 by 43 so both fractions share the common base 903.

13 × 21/43 × 21 = 273/903 and 7 × 43/21 × 43 = 301/903

Step 3

Add the Numerators

Now add the numerators (273 + 301 = 574) and keep the common denominator 903 unchanged.

273 + 301/903 = 574/903

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 574 and 903, which is 7. Divide both the numerator and denominator by 7.

574 ÷ 7/903 ÷ 7 = 82/129

Step 5

Decimal & Percentage Representation

Dividing the numerator 82 by denominator 129 produces a repeating decimal (approximately 0.635659, or 63.5659%).

82 ÷ 129 = 0.635659 (63.5659%)

Visual Representation

The diagram below illustrates 13/43 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`82/129`
Mixed Number Form	`82/129`
Decimal Form	`0.635659`
Percentage	`63.5659%`

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Frequently Asked Questions

What is 13/43 plus 7/21 as a fraction?

13/43 + 7/21 in simplest fraction form is 82/129.

What is 13/43 plus 7/21 as a decimal?

13/43 + 7/21 converted to a decimal is 0.635659.

What is 13/43 plus 7/21 as a percentage?

13/43 + 7/21 expressed as a percentage is 63.5659%.

Does 13/43 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.635659...) because the denominator contains prime factors other than 2 and 5.