What is 13/57 plus 5/21? (Answer: 62/133)

Exact Answer

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Problem: What is 13/57 plus 5/21?
Formula / Expression: 13/57 + 5/21
Final Answer: 62/133
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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 5/21 by 19 so both fractions share the common base 399.
Working: 13 × 7/57 × 7 = 91/399 and 5 × 19/21 × 19 = 95/399

Step 3: Add the Numerators
Now add the numerators (91 + 95 = 186) and keep the common denominator 399 unchanged.
Working: 91 + 95/399 = 186/399

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 186 and 399, which is 3. Divide both the numerator and denominator by 3.
Working: 186 ÷ 3/399 ÷ 3 = 62/133

Step 5: Decimal & Percentage Representation
Dividing the numerator 62 by denominator 133 produces a repeating decimal (approximately 0.466165, or 46.6165%).
Working: 62 ÷ 133 = 0.466165 (46.6165%)

Key Values:
- Simplified Fraction: 62/133
- Mixed Number Form: 62/133
- Decimal Value: 0.466165
- Percentage: 46.6165%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-57-plus-5-21/
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13/57 + 5/21 = 62/133

Simplified Fraction

62/133

Mixed Number

Proper (62/133)

Decimal Value

0.466165

Percentage

46.6165%

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Step-by-Step Solution: 13/57 + 5/21

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 5/21 by 19 so both fractions share the common base 399.

13 × 7/57 × 7 = 91/399 and 5 × 19/21 × 19 = 95/399

Step 3

Add the Numerators

Now add the numerators (91 + 95 = 186) and keep the common denominator 399 unchanged.

91 + 95/399 = 186/399

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 186 and 399, which is 3. Divide both the numerator and denominator by 3.

186 ÷ 3/399 ÷ 3 = 62/133

Step 5

Decimal & Percentage Representation

Dividing the numerator 62 by denominator 133 produces a repeating decimal (approximately 0.466165, or 46.6165%).

62 ÷ 133 = 0.466165 (46.6165%)

Visual Representation

The diagram below illustrates 13/57 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`62/133`
Mixed Number Form	`62/133`
Decimal Form	`0.466165`
Percentage	`46.6165%`

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Frequently Asked Questions

What is 13/57 plus 5/21 as a fraction?

13/57 + 5/21 in simplest fraction form is 62/133.

What is 13/57 plus 5/21 as a decimal?

13/57 + 5/21 converted to a decimal is 0.466165.

What is 13/57 plus 5/21 as a percentage?

13/57 + 5/21 expressed as a percentage is 46.6165%.

Does 13/57 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.466165...) because the denominator contains prime factors other than 2 and 5.