What is 2/35 plus 2/25? (Answer: 24/175)

Exact Answer

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Problem: What is 2/35 plus 2/25?
Formula / Expression: 2/35 + 2/25
Final Answer: 24/175
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 35 and 25 share a common factor (GCD = 5). Finding their Least Common Multiple gives an LCD of 175 (which is smaller than their product 35 × 25 = 875, keeping the calculation simpler).
Working: LCD(35, 25) = 175

Step 2: Convert to Equivalent Fractions with Common Denominator 175
Multiply the numerator and denominator of 2/35 by 5, and multiply the numerator and denominator of 2/25 by 7 so both fractions share the common base 175.
Working: 2 × 5/35 × 5 = 10/175 and 2 × 7/25 × 7 = 14/175

Step 3: Add the Numerators
Now add the numerators (10 + 14 = 24) and keep the common denominator 175 unchanged.
Working: 10 + 14/175 = 24/175

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 24 and 175 is 1, confirming that 24/175 cannot be reduced further—it is already in its simplest irreducible form.
Working: 24/175

Step 5: Decimal & Percentage Representation
Dividing the numerator 24 by denominator 175 produces a repeating decimal (approximately 0.137143, or 13.7143%).
Working: 24 ÷ 175 = 0.137143 (13.7143%)

Key Values:
- Simplified Fraction: 24/175
- Mixed Number Form: 24/175
- Decimal Value: 0.137143
- Percentage: 13.7143%

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2/35 + 2/25 = 24/175

Simplified Fraction

24/175

Mixed Number

Proper (24/175)

Decimal Value

0.137143

Percentage

13.7143%

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Step-by-Step Solution: 2/35 + 2/25

Step 1

Find the Least Common Denominator (LCD)

The denominators 35 and 25 share a common factor (GCD = 5). Finding their Least Common Multiple gives an LCD of 175 (which is smaller than their product 35 × 25 = 875, keeping the calculation simpler).

LCD(35, 25) = 175

Step 2

Convert to Equivalent Fractions with Common Denominator 175

Multiply the numerator and denominator of 2/35 by 5, and multiply the numerator and denominator of 2/25 by 7 so both fractions share the common base 175.

2 × 5/35 × 5 = 10/175 and 2 × 7/25 × 7 = 14/175

Step 3

Add the Numerators

Now add the numerators (10 + 14 = 24) and keep the common denominator 175 unchanged.

10 + 14/175 = 24/175

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 24 and 175 is 1, confirming that 24/175 cannot be reduced further—it is already in its simplest irreducible form.

24/175

Step 5

Decimal & Percentage Representation

Dividing the numerator 24 by denominator 175 produces a repeating decimal (approximately 0.137143, or 13.7143%).

24 ÷ 175 = 0.137143 (13.7143%)

Visual Representation

The diagram below illustrates 2/35 plus 2/25 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`24/175`
Mixed Number Form	`24/175`
Decimal Form	`0.137143`
Percentage	`13.7143%`

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Frequently Asked Questions

What is 2/35 plus 2/25 as a fraction?

2/35 + 2/25 in simplest fraction form is 24/175.

What is 2/35 plus 2/25 as a decimal?

2/35 + 2/25 converted to a decimal is 0.137143.

What is 2/35 plus 2/25 as a percentage?

2/35 + 2/25 expressed as a percentage is 13.7143%.

Does 2/35 plus 2/25 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.137143...) because the denominator contains prime factors other than 2 and 5.