What is 2/57 plus 4/21? (Answer: 30/133)

Exact Answer

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Problem: What is 2/57 plus 4/21?
Formula / Expression: 2/57 + 4/21
Final Answer: 30/133
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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 2/57 by 7, and multiply the numerator and denominator of 4/21 by 19 so both fractions share the common base 399.
Working: 2 × 7/57 × 7 = 14/399 and 4 × 19/21 × 19 = 76/399

Step 3: Add the Numerators
Now add the numerators (14 + 76 = 90) and keep the common denominator 399 unchanged.
Working: 14 + 76/399 = 90/399

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 90 and 399, which is 3. Divide both the numerator and denominator by 3.
Working: 90 ÷ 3/399 ÷ 3 = 30/133

Step 5: Decimal & Percentage Representation
Dividing the numerator 30 by denominator 133 produces a repeating decimal (approximately 0.225564, or 22.5564%).
Working: 30 ÷ 133 = 0.225564 (22.5564%)

Key Values:
- Simplified Fraction: 30/133
- Mixed Number Form: 30/133
- Decimal Value: 0.225564
- Percentage: 22.5564%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-57-plus-4-21/
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2/57 + 4/21 = 30/133

Simplified Fraction

30/133

Mixed Number

Proper (30/133)

Decimal Value

0.225564

Percentage

22.5564%

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Step-by-Step Solution: 2/57 + 4/21

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 2/57 by 7, and multiply the numerator and denominator of 4/21 by 19 so both fractions share the common base 399.

2 × 7/57 × 7 = 14/399 and 4 × 19/21 × 19 = 76/399

Step 3

Add the Numerators

Now add the numerators (14 + 76 = 90) and keep the common denominator 399 unchanged.

14 + 76/399 = 90/399

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 90 and 399, which is 3. Divide both the numerator and denominator by 3.

90 ÷ 3/399 ÷ 3 = 30/133

Step 5

Decimal & Percentage Representation

Dividing the numerator 30 by denominator 133 produces a repeating decimal (approximately 0.225564, or 22.5564%).

30 ÷ 133 = 0.225564 (22.5564%)

Visual Representation

The diagram below illustrates 2/57 plus 4/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`30/133`
Mixed Number Form	`30/133`
Decimal Form	`0.225564`
Percentage	`22.5564%`

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Frequently Asked Questions

What is 2/57 plus 4/21 as a fraction?

2/57 + 4/21 in simplest fraction form is 30/133.

What is 2/57 plus 4/21 as a decimal?

2/57 + 4/21 converted to a decimal is 0.225564.

What is 2/57 plus 4/21 as a percentage?

2/57 + 4/21 expressed as a percentage is 22.5564%.

Does 2/57 plus 4/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.225564...) because the denominator contains prime factors other than 2 and 5.