What is 13/57 plus 8/21? (Answer: 81/133)

Exact Answer

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Problem: What is 13/57 plus 8/21?
Formula / Expression: 13/57 + 8/21
Final Answer: 81/133
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 57 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 399 (which is smaller than their product 57 × 21 = 1197, keeping the calculation simpler).
Working: LCD(57, 21) = 399

Step 2: Convert to Equivalent Fractions with Common Denominator 399
Multiply the numerator and denominator of 13/57 by 7, and multiply the numerator and denominator of 8/21 by 19 so both fractions share the common base 399.
Working: 13 × 7/57 × 7 = 91/399 and 8 × 19/21 × 19 = 152/399

Step 3: Add the Numerators
Now add the numerators (91 + 152 = 243) and keep the common denominator 399 unchanged.
Working: 91 + 152/399 = 243/399

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 243 and 399, which is 3. Divide both the numerator and denominator by 3.
Working: 243 ÷ 3/399 ÷ 3 = 81/133

Step 5: Decimal & Percentage Representation
Dividing the numerator 81 by denominator 133 produces a repeating decimal (approximately 0.609023, or 60.9023%).
Working: 81 ÷ 133 = 0.609023 (60.9023%)

Key Values:
- Simplified Fraction: 81/133
- Mixed Number Form: 81/133
- Decimal Value: 0.609023
- Percentage: 60.9023%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-57-plus-8-21/
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13/57 + 8/21 = 81/133

Simplified Fraction

81/133

Mixed Number

Proper (81/133)

Decimal Value

0.609023

Percentage

60.9023%

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Step-by-Step Solution: 13/57 + 8/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 57 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 399 (which is smaller than their product 57 × 21 = 1197, keeping the calculation simpler).

LCD(57, 21) = 399

Step 2

Convert to Equivalent Fractions with Common Denominator 399

Multiply the numerator and denominator of 13/57 by 7, and multiply the numerator and denominator of 8/21 by 19 so both fractions share the common base 399.

13 × 7/57 × 7 = 91/399 and 8 × 19/21 × 19 = 152/399

Step 3

Add the Numerators

Now add the numerators (91 + 152 = 243) and keep the common denominator 399 unchanged.

91 + 152/399 = 243/399

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 243 and 399, which is 3. Divide both the numerator and denominator by 3.

243 ÷ 3/399 ÷ 3 = 81/133

Step 5

Decimal & Percentage Representation

Dividing the numerator 81 by denominator 133 produces a repeating decimal (approximately 0.609023, or 60.9023%).

81 ÷ 133 = 0.609023 (60.9023%)

Visual Representation

The diagram below illustrates 13/57 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`81/133`
Mixed Number Form	`81/133`
Decimal Form	`0.609023`
Percentage	`60.9023%`

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Frequently Asked Questions

What is 13/57 plus 8/21 as a fraction?

13/57 + 8/21 in simplest fraction form is 81/133.

What is 13/57 plus 8/21 as a decimal?

13/57 + 8/21 converted to a decimal is 0.609023.

What is 13/57 plus 8/21 as a percentage?

13/57 + 8/21 expressed as a percentage is 60.9023%.

Does 13/57 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.609023...) because the denominator contains prime factors other than 2 and 5.