What is 9/25 plus 2/5? (Answer: 19/25)

Exact Answer

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Problem: What is 9/25 plus 2/5?
Formula / Expression: 9/25 + 2/5
Final Answer: 19/25
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 25 is an exact multiple of 5 (5 × 5 = 25). The Least Common Denominator (LCD) is simply 25, meaning we only need to scale one fraction.
Working: LCD(25, 5) = 25

Step 2: Convert to Equivalent Fractions with Common Denominator 25
Multiply the numerator and denominator of 9/25 by 1, and multiply the numerator and denominator of 2/5 by 5 so both fractions share the common base 25.
Working: 9 × 1/25 × 1 = 9/25 and 2 × 5/5 × 5 = 10/25

Step 3: Add the Numerators
Now add the numerators (9 + 10 = 19) and keep the common denominator 25 unchanged.
Working: 9 + 10/25 = 19/25

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 19 and 25 is 1, confirming that 19/25 cannot be reduced further—it is already in its simplest irreducible form.
Working: 19/25

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 25 yields an exact terminating decimal of 0.76 (or 76%).
Working: 19 ÷ 25 = 0.76 (76%)

Key Values:
- Simplified Fraction: 19/25
- Mixed Number Form: 19/25
- Decimal Value: 0.76
- Percentage: 76%

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Solved with FractionsCalc:
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9/25 + 2/5 = 19/25

Simplified Fraction

19/25

Mixed Number

Proper (19/25)

Decimal Value

0.76

Percentage

76%

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Step-by-Step Solution: 9/25 + 2/5

Step 1

Find the Least Common Denominator (LCD)

Notice that 25 is an exact multiple of 5 (5 × 5 = 25). The Least Common Denominator (LCD) is simply 25, meaning we only need to scale one fraction.

LCD(25, 5) = 25

Step 2

Convert to Equivalent Fractions with Common Denominator 25

Multiply the numerator and denominator of 9/25 by 1, and multiply the numerator and denominator of 2/5 by 5 so both fractions share the common base 25.

9 × 1/25 × 1 = 9/25 and 2 × 5/5 × 5 = 10/25

Step 3

Add the Numerators

Now add the numerators (9 + 10 = 19) and keep the common denominator 25 unchanged.

9 + 10/25 = 19/25

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 19 and 25 is 1, confirming that 19/25 cannot be reduced further—it is already in its simplest irreducible form.

19/25

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 25 yields an exact terminating decimal of 0.76 (or 76%).

19 ÷ 25 = 0.76 (76%)

Visual Representation

The diagram below illustrates 9/25 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/25`
Mixed Number Form	`19/25`
Decimal Form	`0.76`
Percentage	`76%`

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Frequently Asked Questions

What is 9/25 plus 2/5 as a fraction?

9/25 + 2/5 in simplest fraction form is 19/25.

What is 9/25 plus 2/5 as a decimal?

9/25 + 2/5 converted to a decimal is 0.76.

What is 9/25 plus 2/5 as a percentage?

9/25 + 2/5 expressed as a percentage is 76%.

Does 9/25 plus 2/5 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.76) because the denominator in simplest terms contains only prime factors 2 and/or 5.