What is 4/53 plus 2/9? (Answer: 142/477)

Exact Answer

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Problem: What is 4/53 plus 2/9?
Formula / Expression: 4/53 + 2/9
Final Answer: 142/477
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 53 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 53 × 9 = 477.
Working: LCD(53, 9) = 477

Step 2: Convert to Equivalent Fractions with Common Denominator 477
Multiply the numerator and denominator of 4/53 by 9, and multiply the numerator and denominator of 2/9 by 53 so both fractions share the common base 477.
Working: 4 × 9/53 × 9 = 36/477 and 2 × 53/9 × 53 = 106/477

Step 3: Add the Numerators
Now add the numerators (36 + 106 = 142) and keep the common denominator 477 unchanged.
Working: 36 + 106/477 = 142/477

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 142 and 477 is 1, confirming that 142/477 cannot be reduced further—it is already in its simplest irreducible form.
Working: 142/477

Step 5: Decimal & Percentage Representation
Dividing the numerator 142 by denominator 477 produces a repeating decimal (approximately 0.297694, or 29.7694%).
Working: 142 ÷ 477 = 0.297694 (29.7694%)

Key Values:
- Simplified Fraction: 142/477
- Mixed Number Form: 142/477
- Decimal Value: 0.297694
- Percentage: 29.7694%

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Solved with FractionsCalc:
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4/53 + 2/9 = 142/477

Simplified Fraction

142/477

Mixed Number

Proper (142/477)

Decimal Value

0.297694

Percentage

29.7694%

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Step-by-Step Solution: 4/53 + 2/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 53 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 53 × 9 = 477.

LCD(53, 9) = 477

Step 2

Convert to Equivalent Fractions with Common Denominator 477

Multiply the numerator and denominator of 4/53 by 9, and multiply the numerator and denominator of 2/9 by 53 so both fractions share the common base 477.

4 × 9/53 × 9 = 36/477 and 2 × 53/9 × 53 = 106/477

Step 3

Add the Numerators

Now add the numerators (36 + 106 = 142) and keep the common denominator 477 unchanged.

36 + 106/477 = 142/477

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 142 and 477 is 1, confirming that 142/477 cannot be reduced further—it is already in its simplest irreducible form.

142/477

Step 5

Decimal & Percentage Representation

Dividing the numerator 142 by denominator 477 produces a repeating decimal (approximately 0.297694, or 29.7694%).

142 ÷ 477 = 0.297694 (29.7694%)

Visual Representation

The diagram below illustrates 4/53 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`142/477`
Mixed Number Form	`142/477`
Decimal Form	`0.297694`
Percentage	`29.7694%`

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Frequently Asked Questions

What is 4/53 plus 2/9 as a fraction?

4/53 + 2/9 in simplest fraction form is 142/477.

What is 4/53 plus 2/9 as a decimal?

4/53 + 2/9 converted to a decimal is 0.297694.

What is 4/53 plus 2/9 as a percentage?

4/53 + 2/9 expressed as a percentage is 29.7694%.

Does 4/53 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.297694...) because the denominator contains prime factors other than 2 and 5.