What is 1/5 plus 5/7? (Answer: 32/35)

Exact Answer

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Problem: What is 1/5 plus 5/7?
Formula / Expression: 1/5 + 5/7
Final Answer: 32/35
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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 1/5 by 7, and multiply the numerator and denominator of 5/7 by 5 so both fractions share the common base 35.
Working: 1 × 7/5 × 7 = 7/35 and 5 × 5/7 × 5 = 25/35

Step 3: Add the Numerators
Now add the numerators (7 + 25 = 32) and keep the common denominator 35 unchanged.
Working: 7 + 25/35 = 32/35

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 32 and 35 is 1, confirming that 32/35 cannot be reduced further—it is already in its simplest irreducible form.
Working: 32/35

Step 5: Decimal & Percentage Representation
Dividing the numerator 32 by denominator 35 produces a repeating decimal (approximately 0.914286, or 91.4286%).
Working: 32 ÷ 35 = 0.914286 (91.4286%)

Key Values:
- Simplified Fraction: 32/35
- Mixed Number Form: 32/35
- Decimal Value: 0.914286
- Percentage: 91.4286%

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Solved with FractionsCalc:
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1/5 + 5/7 = 32/35

Simplified Fraction

32/35

Mixed Number

Proper (32/35)

Decimal Value

0.914286

Percentage

91.4286%

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Step-by-Step Solution: 1/5 + 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 1/5 by 7, and multiply the numerator and denominator of 5/7 by 5 so both fractions share the common base 35.

1 × 7/5 × 7 = 7/35 and 5 × 5/7 × 5 = 25/35

Step 3

Add the Numerators

Now add the numerators (7 + 25 = 32) and keep the common denominator 35 unchanged.

7 + 25/35 = 32/35

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 32 and 35 is 1, confirming that 32/35 cannot be reduced further—it is already in its simplest irreducible form.

32/35

Step 5

Decimal & Percentage Representation

Dividing the numerator 32 by denominator 35 produces a repeating decimal (approximately 0.914286, or 91.4286%).

32 ÷ 35 = 0.914286 (91.4286%)

Visual Representation

The diagram below illustrates 1/5 plus 5/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`32/35`
Mixed Number Form	`32/35`
Decimal Form	`0.914286`
Percentage	`91.4286%`

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Frequently Asked Questions

What is 1/5 plus 5/7 as a fraction?

1/5 + 5/7 in simplest fraction form is 32/35.

What is 1/5 plus 5/7 as a decimal?

1/5 + 5/7 converted to a decimal is 0.914286.

What is 1/5 plus 5/7 as a percentage?

1/5 + 5/7 expressed as a percentage is 91.4286%.

Does 1/5 plus 5/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.914286...) because the denominator contains prime factors other than 2 and 5.