What is 1/57 plus 2/21? (Answer: 15/133)

Exact Answer

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Problem: What is 1/57 plus 2/21?
Formula / Expression: 1/57 + 2/21
Final Answer: 15/133
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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 1/57 by 7, and multiply the numerator and denominator of 2/21 by 19 so both fractions share the common base 399.
Working: 1 × 7/57 × 7 = 7/399 and 2 × 19/21 × 19 = 38/399

Step 3: Add the Numerators
Now add the numerators (7 + 38 = 45) and keep the common denominator 399 unchanged.
Working: 7 + 38/399 = 45/399

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 45 and 399, which is 3. Divide both the numerator and denominator by 3.
Working: 45 ÷ 3/399 ÷ 3 = 15/133

Step 5: Decimal & Percentage Representation
Dividing the numerator 15 by denominator 133 produces a repeating decimal (approximately 0.112782, or 11.2782%).
Working: 15 ÷ 133 = 0.112782 (11.2782%)

Key Values:
- Simplified Fraction: 15/133
- Mixed Number Form: 15/133
- Decimal Value: 0.112782
- Percentage: 11.2782%

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Solved with FractionsCalc:
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1/57 + 2/21 = 15/133

Simplified Fraction

15/133

Mixed Number

Proper (15/133)

Decimal Value

0.112782

Percentage

11.2782%

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Step-by-Step Solution: 1/57 + 2/21

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 1/57 by 7, and multiply the numerator and denominator of 2/21 by 19 so both fractions share the common base 399.

1 × 7/57 × 7 = 7/399 and 2 × 19/21 × 19 = 38/399

Step 3

Add the Numerators

Now add the numerators (7 + 38 = 45) and keep the common denominator 399 unchanged.

7 + 38/399 = 45/399

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 45 and 399, which is 3. Divide both the numerator and denominator by 3.

45 ÷ 3/399 ÷ 3 = 15/133

Step 5

Decimal & Percentage Representation

Dividing the numerator 15 by denominator 133 produces a repeating decimal (approximately 0.112782, or 11.2782%).

15 ÷ 133 = 0.112782 (11.2782%)

Visual Representation

The diagram below illustrates 1/57 plus 2/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`15/133`
Mixed Number Form	`15/133`
Decimal Form	`0.112782`
Percentage	`11.2782%`

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Frequently Asked Questions

What is 1/57 plus 2/21 as a fraction?

1/57 + 2/21 in simplest fraction form is 15/133.

What is 1/57 plus 2/21 as a decimal?

1/57 + 2/21 converted to a decimal is 0.112782.

What is 1/57 plus 2/21 as a percentage?

1/57 + 2/21 expressed as a percentage is 11.2782%.

Does 1/57 plus 2/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.112782...) because the denominator contains prime factors other than 2 and 5.