What is 2/25 plus 2/10? (Answer: 7/25)

Exact Answer

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Problem: What is 2/25 plus 2/10?
Formula / Expression: 2/25 + 2/10
Final Answer: 7/25
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 50
Multiply the numerator and denominator of 2/25 by 2, and multiply the numerator and denominator of 2/10 by 5 so both fractions share the common base 50.
Working: 2 × 2/25 × 2 = 4/50 and 2 × 5/10 × 5 = 10/50

Step 3: Add the Numerators
Now add the numerators (4 + 10 = 14) and keep the common denominator 50 unchanged.
Working: 4 + 10/50 = 14/50

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 14 and 50, which is 2. Divide both the numerator and denominator by 2.
Working: 14 ÷ 2/50 ÷ 2 = 7/25

Step 5: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 25 yields an exact terminating decimal of 0.28 (or 28%).
Working: 7 ÷ 25 = 0.28 (28%)

Key Values:
- Simplified Fraction: 7/25
- Mixed Number Form: 7/25
- Decimal Value: 0.28
- Percentage: 28%

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Solved with FractionsCalc:
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2/25 + 2/10 = 7/25

Simplified Fraction

7/25

Mixed Number

Proper (7/25)

Decimal Value

0.28

Percentage

28%

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

Step 1

Find the Least Common Denominator (LCD)

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

LCD(25, 10) = 50

Step 2

Convert to Equivalent Fractions with Common Denominator 50

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

2 × 2/25 × 2 = 4/50 and 2 × 5/10 × 5 = 10/50

Step 3

Add the Numerators

Now add the numerators (4 + 10 = 14) and keep the common denominator 50 unchanged.

4 + 10/50 = 14/50

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 14 and 50, which is 2. Divide both the numerator and denominator by 2.

14 ÷ 2/50 ÷ 2 = 7/25

Step 5

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 25 yields an exact terminating decimal of 0.28 (or 28%).

7 ÷ 25 = 0.28 (28%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/25`
Mixed Number Form	`7/25`
Decimal Form	`0.28`
Percentage	`28%`

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Frequently Asked Questions

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

2/25 + 2/10 in simplest fraction form is 7/25.

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

2/25 + 2/10 converted to a decimal is 0.28.

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

2/25 + 2/10 expressed as a percentage is 28%.

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

It results in an exact terminating decimal (0.28) because the denominator in simplest terms contains only prime factors 2 and/or 5.