What is 2/45 plus 2/10? (Answer: 11/45)

Exact Answer

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Problem: What is 2/45 plus 2/10?
Formula / Expression: 2/45 + 2/10
Final Answer: 11/45
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 45 and 10 share a common factor (GCD = 5). Finding their Least Common Multiple gives an LCD of 90 (which is smaller than their product 45 × 10 = 450, keeping the calculation simpler).
Working: LCD(45, 10) = 90

Step 2: Convert to Equivalent Fractions with Common Denominator 90
Multiply the numerator and denominator of 2/45 by 2, and multiply the numerator and denominator of 2/10 by 9 so both fractions share the common base 90.
Working: 2 × 2/45 × 2 = 4/90 and 2 × 9/10 × 9 = 18/90

Step 3: Add the Numerators
Now add the numerators (4 + 18 = 22) and keep the common denominator 90 unchanged.
Working: 4 + 18/90 = 22/90

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 22 and 90, which is 2. Divide both the numerator and denominator by 2.
Working: 22 ÷ 2/90 ÷ 2 = 11/45

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 45 produces a repeating decimal (approximately 0.244444, or 24.4444%).
Working: 11 ÷ 45 = 0.244444 (24.4444%)

Key Values:
- Simplified Fraction: 11/45
- Mixed Number Form: 11/45
- Decimal Value: 0.244444
- Percentage: 24.4444%

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Solved with FractionsCalc:
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2/45 + 2/10 = 11/45

Simplified Fraction

11/45

Mixed Number

Proper (11/45)

Decimal Value

0.244444

Percentage

24.4444%

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Step-by-Step Solution: 2/45 + 2/10

Step 1

Find the Least Common Denominator (LCD)

The denominators 45 and 10 share a common factor (GCD = 5). Finding their Least Common Multiple gives an LCD of 90 (which is smaller than their product 45 × 10 = 450, keeping the calculation simpler).

LCD(45, 10) = 90

Step 2

Convert to Equivalent Fractions with Common Denominator 90

Multiply the numerator and denominator of 2/45 by 2, and multiply the numerator and denominator of 2/10 by 9 so both fractions share the common base 90.

2 × 2/45 × 2 = 4/90 and 2 × 9/10 × 9 = 18/90

Step 3

Add the Numerators

Now add the numerators (4 + 18 = 22) and keep the common denominator 90 unchanged.

4 + 18/90 = 22/90

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 22 and 90, which is 2. Divide both the numerator and denominator by 2.

22 ÷ 2/90 ÷ 2 = 11/45

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 45 produces a repeating decimal (approximately 0.244444, or 24.4444%).

11 ÷ 45 = 0.244444 (24.4444%)

Visual Representation

The diagram below illustrates 2/45 plus 2/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/45`
Mixed Number Form	`11/45`
Decimal Form	`0.244444`
Percentage	`24.4444%`

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Frequently Asked Questions

What is 2/45 plus 2/10 as a fraction?

2/45 + 2/10 in simplest fraction form is 11/45.

What is 2/45 plus 2/10 as a decimal?

2/45 + 2/10 converted to a decimal is 0.244444.

What is 2/45 plus 2/10 as a percentage?

2/45 + 2/10 expressed as a percentage is 24.4444%.

Does 2/45 plus 2/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.244444...) because the denominator contains prime factors other than 2 and 5.