What is 4/25 plus 3/9? (Answer: 37/75)

Exact Answer

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Problem: What is 4/25 plus 3/9?
Formula / Expression: 4/25 + 3/9
Final Answer: 37/75
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 25 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 9 = 225.
Working: LCD(25, 9) = 225

Step 2: Convert to Equivalent Fractions with Common Denominator 225
Multiply the numerator and denominator of 4/25 by 9, and multiply the numerator and denominator of 3/9 by 25 so both fractions share the common base 225.
Working: 4 × 9/25 × 9 = 36/225 and 3 × 25/9 × 25 = 75/225

Step 3: Add the Numerators
Now add the numerators (36 + 75 = 111) and keep the common denominator 225 unchanged.
Working: 36 + 75/225 = 111/225

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 111 and 225, which is 3. Divide both the numerator and denominator by 3.
Working: 111 ÷ 3/225 ÷ 3 = 37/75

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 75 produces a repeating decimal (approximately 0.493333, or 49.3333%).
Working: 37 ÷ 75 = 0.493333 (49.3333%)

Key Values:
- Simplified Fraction: 37/75
- Mixed Number Form: 37/75
- Decimal Value: 0.493333
- Percentage: 49.3333%

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Solved with FractionsCalc:
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4/25 + 3/9 = 37/75

Simplified Fraction

37/75

Mixed Number

Proper (37/75)

Decimal Value

0.493333

Percentage

49.3333%

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Step-by-Step Solution: 4/25 + 3/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 25 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 9 = 225.

LCD(25, 9) = 225

Step 2

Convert to Equivalent Fractions with Common Denominator 225

Multiply the numerator and denominator of 4/25 by 9, and multiply the numerator and denominator of 3/9 by 25 so both fractions share the common base 225.

4 × 9/25 × 9 = 36/225 and 3 × 25/9 × 25 = 75/225

Step 3

Add the Numerators

Now add the numerators (36 + 75 = 111) and keep the common denominator 225 unchanged.

36 + 75/225 = 111/225

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 111 and 225, which is 3. Divide both the numerator and denominator by 3.

111 ÷ 3/225 ÷ 3 = 37/75

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 75 produces a repeating decimal (approximately 0.493333, or 49.3333%).

37 ÷ 75 = 0.493333 (49.3333%)

Visual Representation

The diagram below illustrates 4/25 plus 3/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/75`
Mixed Number Form	`37/75`
Decimal Form	`0.493333`
Percentage	`49.3333%`

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Frequently Asked Questions

What is 4/25 plus 3/9 as a fraction?

4/25 + 3/9 in simplest fraction form is 37/75.

What is 4/25 plus 3/9 as a decimal?

4/25 + 3/9 converted to a decimal is 0.493333.

What is 4/25 plus 3/9 as a percentage?

4/25 + 3/9 expressed as a percentage is 49.3333%.

Does 4/25 plus 3/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.493333...) because the denominator contains prime factors other than 2 and 5.