What is 2/10 plus 9/25? (Answer: 14/25)

Exact Answer

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Problem: What is 2/10 plus 9/25?
Formula / Expression: 2/10 + 9/25
Final Answer: 14/25
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 10 and 25 share a common factor (GCD = 5). Finding their Least Common Multiple gives an LCD of 50 (which is smaller than their product 10 × 25 = 250, keeping the calculation simpler).
Working: LCD(10, 25) = 50

Step 2: Convert to Equivalent Fractions with Common Denominator 50
Multiply the numerator and denominator of 2/10 by 5, and multiply the numerator and denominator of 9/25 by 2 so both fractions share the common base 50.
Working: 2 × 5/10 × 5 = 10/50 and 9 × 2/25 × 2 = 18/50

Step 3: Add the Numerators
Now add the numerators (10 + 18 = 28) and keep the common denominator 50 unchanged.
Working: 10 + 18/50 = 28/50

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 28 and 50, which is 2. Divide both the numerator and denominator by 2.
Working: 28 ÷ 2/50 ÷ 2 = 14/25

Step 5: Decimal & Percentage Representation
Dividing the numerator 14 by denominator 25 yields an exact terminating decimal of 0.56 (or 56%).
Working: 14 ÷ 25 = 0.56 (56%)

Key Values:
- Simplified Fraction: 14/25
- Mixed Number Form: 14/25
- Decimal Value: 0.56
- Percentage: 56%

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Solved with FractionsCalc:
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2/10 + 9/25 = 14/25

Simplified Fraction

14/25

Mixed Number

Proper (14/25)

Decimal Value

0.56

Percentage

56%

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Step-by-Step Solution: 2/10 + 9/25

Step 1

Find the Least Common Denominator (LCD)

The denominators 10 and 25 share a common factor (GCD = 5). Finding their Least Common Multiple gives an LCD of 50 (which is smaller than their product 10 × 25 = 250, keeping the calculation simpler).

LCD(10, 25) = 50

Step 2

Convert to Equivalent Fractions with Common Denominator 50

Multiply the numerator and denominator of 2/10 by 5, and multiply the numerator and denominator of 9/25 by 2 so both fractions share the common base 50.

2 × 5/10 × 5 = 10/50 and 9 × 2/25 × 2 = 18/50

Step 3

Add the Numerators

Now add the numerators (10 + 18 = 28) and keep the common denominator 50 unchanged.

10 + 18/50 = 28/50

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 28 and 50, which is 2. Divide both the numerator and denominator by 2.

28 ÷ 2/50 ÷ 2 = 14/25

Step 5

Decimal & Percentage Representation

Dividing the numerator 14 by denominator 25 yields an exact terminating decimal of 0.56 (or 56%).

14 ÷ 25 = 0.56 (56%)

Visual Representation

The diagram below illustrates 2/10 plus 9/25 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`14/25`
Mixed Number Form	`14/25`
Decimal Form	`0.56`
Percentage	`56%`

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Frequently Asked Questions

What is 2/10 plus 9/25 as a fraction?

2/10 + 9/25 in simplest fraction form is 14/25.

What is 2/10 plus 9/25 as a decimal?

2/10 + 9/25 converted to a decimal is 0.56.

What is 2/10 plus 9/25 as a percentage?

2/10 + 9/25 expressed as a percentage is 56%.

Does 2/10 plus 9/25 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.56) because the denominator in simplest terms contains only prime factors 2 and/or 5.