What is 4/45 plus 2/9? (Answer: 14/45)

Exact Answer

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Problem: What is 4/45 plus 2/9?
Formula / Expression: 4/45 + 2/9
Final Answer: 14/45
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 45 is an exact multiple of 9 (9 × 5 = 45). The Least Common Denominator (LCD) is simply 45, meaning we only need to scale one fraction.
Working: LCD(45, 9) = 45

Step 2: Convert to Equivalent Fractions with Common Denominator 45
Multiply the numerator and denominator of 4/45 by 1, and multiply the numerator and denominator of 2/9 by 5 so both fractions share the common base 45.
Working: 4 × 1/45 × 1 = 4/45 and 2 × 5/9 × 5 = 10/45

Step 3: Add the Numerators
Now add the numerators (4 + 10 = 14) and keep the common denominator 45 unchanged.
Working: 4 + 10/45 = 14/45

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 14 and 45 is 1, confirming that 14/45 cannot be reduced further—it is already in its simplest irreducible form.
Working: 14/45

Step 5: Decimal & Percentage Representation
Dividing the numerator 14 by denominator 45 produces a repeating decimal (approximately 0.311111, or 31.1111%).
Working: 14 ÷ 45 = 0.311111 (31.1111%)

Key Values:
- Simplified Fraction: 14/45
- Mixed Number Form: 14/45
- Decimal Value: 0.311111
- Percentage: 31.1111%

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Solved with FractionsCalc:
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4/45 + 2/9 = 14/45

Simplified Fraction

14/45

Mixed Number

Proper (14/45)

Decimal Value

0.311111

Percentage

31.1111%

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Step-by-Step Solution: 4/45 + 2/9

Step 1

Find the Least Common Denominator (LCD)

Notice that 45 is an exact multiple of 9 (9 × 5 = 45). The Least Common Denominator (LCD) is simply 45, meaning we only need to scale one fraction.

LCD(45, 9) = 45

Step 2

Convert to Equivalent Fractions with Common Denominator 45

Multiply the numerator and denominator of 4/45 by 1, and multiply the numerator and denominator of 2/9 by 5 so both fractions share the common base 45.

4 × 1/45 × 1 = 4/45 and 2 × 5/9 × 5 = 10/45

Step 3

Add the Numerators

Now add the numerators (4 + 10 = 14) and keep the common denominator 45 unchanged.

4 + 10/45 = 14/45

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 14 and 45 is 1, confirming that 14/45 cannot be reduced further—it is already in its simplest irreducible form.

14/45

Step 5

Decimal & Percentage Representation

Dividing the numerator 14 by denominator 45 produces a repeating decimal (approximately 0.311111, or 31.1111%).

14 ÷ 45 = 0.311111 (31.1111%)

Visual Representation

The diagram below illustrates 4/45 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`14/45`
Mixed Number Form	`14/45`
Decimal Form	`0.311111`
Percentage	`31.1111%`

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Frequently Asked Questions

What is 4/45 plus 2/9 as a fraction?

4/45 + 2/9 in simplest fraction form is 14/45.

What is 4/45 plus 2/9 as a decimal?

4/45 + 2/9 converted to a decimal is 0.311111.

What is 4/45 plus 2/9 as a percentage?

4/45 + 2/9 expressed as a percentage is 31.1111%.

Does 4/45 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.311111...) because the denominator contains prime factors other than 2 and 5.