What is 9/25 plus 4/8? (Answer: 43/50)

Exact Answer

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Problem: What is 9/25 plus 4/8?
Formula / Expression: 9/25 + 4/8
Final Answer: 43/50
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 25 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 8 = 200.
Working: LCD(25, 8) = 200

Step 2: Convert to Equivalent Fractions with Common Denominator 200
Multiply the numerator and denominator of 9/25 by 8, and multiply the numerator and denominator of 4/8 by 25 so both fractions share the common base 200.
Working: 9 × 8/25 × 8 = 72/200 and 4 × 25/8 × 25 = 100/200

Step 3: Add the Numerators
Now add the numerators (72 + 100 = 172) and keep the common denominator 200 unchanged.
Working: 72 + 100/200 = 172/200

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 172 and 200, which is 4. Divide both the numerator and denominator by 4.
Working: 172 ÷ 4/200 ÷ 4 = 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 + 4/8 = 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 + 4/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 25 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 8 = 200.

LCD(25, 8) = 200

Step 2

Convert to Equivalent Fractions with Common Denominator 200

Multiply the numerator and denominator of 9/25 by 8, and multiply the numerator and denominator of 4/8 by 25 so both fractions share the common base 200.

9 × 8/25 × 8 = 72/200 and 4 × 25/8 × 25 = 100/200

Step 3

Add the Numerators

Now add the numerators (72 + 100 = 172) and keep the common denominator 200 unchanged.

72 + 100/200 = 172/200

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 172 and 200, which is 4. Divide both the numerator and denominator by 4.

172 ÷ 4/200 ÷ 4 = 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 4/8 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 4/8 as a fraction?

9/25 + 4/8 in simplest fraction form is 43/50.

What is 9/25 plus 4/8 as a decimal?

9/25 + 4/8 converted to a decimal is 0.86.

What is 9/25 plus 4/8 as a percentage?

9/25 + 4/8 expressed as a percentage is 86%.

Does 9/25 plus 4/8 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.