What is 9/25 plus 2/4? (Answer: 43/50)

Exact Answer

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Problem: What is 9/25 plus 2/4?
Formula / Expression: 9/25 + 2/4
Final Answer: 43/50
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 25 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 4 = 100.
Working: LCD(25, 4) = 100

Step 2: Convert to Equivalent Fractions with Common Denominator 100
Multiply the numerator and denominator of 9/25 by 4, and multiply the numerator and denominator of 2/4 by 25 so both fractions share the common base 100.
Working: 9 × 4/25 × 4 = 36/100 and 2 × 25/4 × 25 = 50/100

Step 3: Add the Numerators
Now add the numerators (36 + 50 = 86) and keep the common denominator 100 unchanged.
Working: 36 + 50/100 = 86/100

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 86 and 100, which is 2. Divide both the numerator and denominator by 2.
Working: 86 ÷ 2/100 ÷ 2 = 43/50

Step 5: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 50 yields an exact terminating decimal of 0.86 (or 86%).
Working: 43 ÷ 50 = 0.86 (86%)

Key Values:
- Simplified Fraction: 43/50
- Mixed Number Form: 43/50
- Decimal Value: 0.86
- Percentage: 86%

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Solved with FractionsCalc:
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9/25 + 2/4 = 43/50

Simplified Fraction

43/50

Mixed Number

Proper (43/50)

Decimal Value

0.86

Percentage

86%

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Step-by-Step Solution: 9/25 + 2/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 25 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 4 = 100.

LCD(25, 4) = 100

Step 2

Convert to Equivalent Fractions with Common Denominator 100

Multiply the numerator and denominator of 9/25 by 4, and multiply the numerator and denominator of 2/4 by 25 so both fractions share the common base 100.

9 × 4/25 × 4 = 36/100 and 2 × 25/4 × 25 = 50/100

Step 3

Add the Numerators

Now add the numerators (36 + 50 = 86) and keep the common denominator 100 unchanged.

36 + 50/100 = 86/100

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 86 and 100, which is 2. Divide both the numerator and denominator by 2.

86 ÷ 2/100 ÷ 2 = 43/50

Step 5

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 50 yields an exact terminating decimal of 0.86 (or 86%).

43 ÷ 50 = 0.86 (86%)

Visual Representation

The diagram below illustrates 9/25 plus 2/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/50`
Mixed Number Form	`43/50`
Decimal Form	`0.86`
Percentage	`86%`

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Frequently Asked Questions

What is 9/25 plus 2/4 as a fraction?

9/25 + 2/4 in simplest fraction form is 43/50.

What is 9/25 plus 2/4 as a decimal?

9/25 + 2/4 converted to a decimal is 0.86.

What is 9/25 plus 2/4 as a percentage?

9/25 + 2/4 expressed as a percentage is 86%.

Does 9/25 plus 2/4 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.86) because the denominator in simplest terms contains only prime factors 2 and/or 5.