What is 2/5 plus 5/7? (Answer: 39/35)

Exact Answer

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Problem: What is 2/5 plus 5/7?
Formula / Expression: 2/5 + 5/7
Final Answer: 1 4/35 (39/35)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 5 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 7 = 35.
Working: LCD(5, 7) = 35

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

Step 3: Add the Numerators
Now add the numerators (14 + 25 = 39) and keep the common denominator 35 unchanged.
Working: 14 + 25/35 = 39/35

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 39 and 35 is 1, confirming that 39/35 cannot be reduced further—it is already in its simplest irreducible form.
Working: 39/35

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (39) is greater than the denominator (35), divide 39 by 35: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/35.
Working: 39/35 = 1 4/35

Step 6: Decimal & Percentage Representation
Dividing the numerator 39 by denominator 35 produces a repeating decimal (approximately 1.114286, or 111.4286%).
Working: 39 ÷ 35 = 1.114286 (111.4286%)

Key Values:
- Simplified Fraction: 39/35
- Mixed Number Form: 1 4/35
- Decimal Value: 1.114286
- Percentage: 111.4286%

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Solved with FractionsCalc:
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2/5 + 5/7 = 39/35

Simplified Fraction

39/35

Mixed Number

1 4/35

Decimal Value

1.114286

Percentage

111.4286%

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Step-by-Step Solution: 2/5 + 5/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 5 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 7 = 35.

LCD(5, 7) = 35

Step 2

Convert to Equivalent Fractions with Common Denominator 35

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

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

Step 3

Add the Numerators

Now add the numerators (14 + 25 = 39) and keep the common denominator 35 unchanged.

14 + 25/35 = 39/35

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 39 and 35 is 1, confirming that 39/35 cannot be reduced further—it is already in its simplest irreducible form.

39/35

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (39) is greater than the denominator (35), divide 39 by 35: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/35.

39/35 = 14/35

Step 6

Decimal & Percentage Representation

Dividing the numerator 39 by denominator 35 produces a repeating decimal (approximately 1.114286, or 111.4286%).

39 ÷ 35 = 1.114286 (111.4286%)

Visual Representation

The diagram below illustrates 2/5 plus 5/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`39/35`
Mixed Number Form	`1 4/35`
Decimal Form	`1.114286`
Percentage	`111.4286%`

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Frequently Asked Questions

What is 2/5 plus 5/7 as a fraction?

2/5 + 5/7 in simplest fraction form is 39/35 (or 1 4/35 as a mixed number).

What is 2/5 plus 5/7 as a decimal?

2/5 + 5/7 converted to a decimal is 1.114286.

What is 2/5 plus 5/7 as a percentage?

2/5 + 5/7 expressed as a percentage is 111.4286%.

How do you write 2/5 plus 5/7 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 39/35 can be written as the mixed number 1 4/35.

Does 2/5 plus 5/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.114286...) because the denominator contains prime factors other than 2 and 5.