What is 13/57 plus 7/21? (Answer: 32/57)

Exact Answer

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Problem: What is 13/57 plus 7/21?
Formula / Expression: 13/57 + 7/21
Final Answer: 32/57
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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 7/21 by 19 so both fractions share the common base 399.
Working: 13 × 7/57 × 7 = 91/399 and 7 × 19/21 × 19 = 133/399

Step 3: Add the Numerators
Now add the numerators (91 + 133 = 224) and keep the common denominator 399 unchanged.
Working: 91 + 133/399 = 224/399

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 224 and 399, which is 7. Divide both the numerator and denominator by 7.
Working: 224 ÷ 7/399 ÷ 7 = 32/57

Step 5: Decimal & Percentage Representation
Dividing the numerator 32 by denominator 57 produces a repeating decimal (approximately 0.561404, or 56.1404%).
Working: 32 ÷ 57 = 0.561404 (56.1404%)

Key Values:
- Simplified Fraction: 32/57
- Mixed Number Form: 32/57
- Decimal Value: 0.561404
- Percentage: 56.1404%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-57-plus-7-21/
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13/57 + 7/21 = 32/57

Simplified Fraction

32/57

Mixed Number

Proper (32/57)

Decimal Value

0.561404

Percentage

56.1404%

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Step-by-Step Solution: 13/57 + 7/21

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 7/21 by 19 so both fractions share the common base 399.

13 × 7/57 × 7 = 91/399 and 7 × 19/21 × 19 = 133/399

Step 3

Add the Numerators

Now add the numerators (91 + 133 = 224) and keep the common denominator 399 unchanged.

91 + 133/399 = 224/399

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 224 and 399, which is 7. Divide both the numerator and denominator by 7.

224 ÷ 7/399 ÷ 7 = 32/57

Step 5

Decimal & Percentage Representation

Dividing the numerator 32 by denominator 57 produces a repeating decimal (approximately 0.561404, or 56.1404%).

32 ÷ 57 = 0.561404 (56.1404%)

Visual Representation

The diagram below illustrates 13/57 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`32/57`
Mixed Number Form	`32/57`
Decimal Form	`0.561404`
Percentage	`56.1404%`

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Frequently Asked Questions

What is 13/57 plus 7/21 as a fraction?

13/57 + 7/21 in simplest fraction form is 32/57.

What is 13/57 plus 7/21 as a decimal?

13/57 + 7/21 converted to a decimal is 0.561404.

What is 13/57 plus 7/21 as a percentage?

13/57 + 7/21 expressed as a percentage is 56.1404%.

Does 13/57 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.561404...) because the denominator contains prime factors other than 2 and 5.