What is 7/25 plus 2/4? (Answer: 39/50)

Exact Answer

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Problem: What is 7/25 plus 2/4?
Formula / Expression: 7/25 + 2/4
Final Answer: 39/50
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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 7/25 by 4, and multiply the numerator and denominator of 2/4 by 25 so both fractions share the common base 100.
Working: 7 × 4/25 × 4 = 28/100 and 2 × 25/4 × 25 = 50/100

Step 3: Add the Numerators
Now add the numerators (28 + 50 = 78) and keep the common denominator 100 unchanged.
Working: 28 + 50/100 = 78/100

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 78 and 100, which is 2. Divide both the numerator and denominator by 2.
Working: 78 ÷ 2/100 ÷ 2 = 39/50

Step 5: Decimal & Percentage Representation
Dividing the numerator 39 by denominator 50 yields an exact terminating decimal of 0.78 (or 78%).
Working: 39 ÷ 50 = 0.78 (78%)

Key Values:
- Simplified Fraction: 39/50
- Mixed Number Form: 39/50
- Decimal Value: 0.78
- Percentage: 78%

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Solved with FractionsCalc:
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7/25 + 2/4 = 39/50

Simplified Fraction

39/50

Mixed Number

Proper (39/50)

Decimal Value

0.78

Percentage

78%

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Step-by-Step Solution: 7/25 + 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 7/25 by 4, and multiply the numerator and denominator of 2/4 by 25 so both fractions share the common base 100.

7 × 4/25 × 4 = 28/100 and 2 × 25/4 × 25 = 50/100

Step 3

Add the Numerators

Now add the numerators (28 + 50 = 78) and keep the common denominator 100 unchanged.

28 + 50/100 = 78/100

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 78 and 100, which is 2. Divide both the numerator and denominator by 2.

78 ÷ 2/100 ÷ 2 = 39/50

Step 5

Decimal & Percentage Representation

Dividing the numerator 39 by denominator 50 yields an exact terminating decimal of 0.78 (or 78%).

39 ÷ 50 = 0.78 (78%)

Visual Representation

The diagram below illustrates 7/25 plus 2/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`39/50`
Mixed Number Form	`39/50`
Decimal Form	`0.78`
Percentage	`78%`

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Frequently Asked Questions

What is 7/25 plus 2/4 as a fraction?

7/25 + 2/4 in simplest fraction form is 39/50.

What is 7/25 plus 2/4 as a decimal?

7/25 + 2/4 converted to a decimal is 0.78.

What is 7/25 plus 2/4 as a percentage?

7/25 + 2/4 expressed as a percentage is 78%.

Does 7/25 plus 2/4 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.78) because the denominator in simplest terms contains only prime factors 2 and/or 5.