What is 3/5 plus 5/7? (Answer: 46/35)

Exact Answer

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Problem: What is 3/5 plus 5/7?
Formula / Expression: 3/5 + 5/7
Final Answer: 1 11/35 (46/35)
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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 3/5 by 7, and multiply the numerator and denominator of 5/7 by 5 so both fractions share the common base 35.
Working: 3 × 7/5 × 7 = 21/35 and 5 × 5/7 × 5 = 25/35

Step 3: Add the Numerators
Now add the numerators (21 + 25 = 46) and keep the common denominator 35 unchanged.
Working: 21 + 25/35 = 46/35

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 46 and 35 is 1, confirming that 46/35 cannot be reduced further—it is already in its simplest irreducible form.
Working: 46/35

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (46) is greater than the denominator (35), divide 46 by 35: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/35.
Working: 46/35 = 1 11/35

Step 6: Decimal & Percentage Representation
Dividing the numerator 46 by denominator 35 produces a repeating decimal (approximately 1.314286, or 131.4286%).
Working: 46 ÷ 35 = 1.314286 (131.4286%)

Key Values:
- Simplified Fraction: 46/35
- Mixed Number Form: 1 11/35
- Decimal Value: 1.314286
- Percentage: 131.4286%

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3/5 + 5/7 = 46/35

Simplified Fraction

46/35

Mixed Number

1 11/35

Decimal Value

1.314286

Percentage

131.4286%

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Step-by-Step Solution: 3/5 + 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 3/5 by 7, and multiply the numerator and denominator of 5/7 by 5 so both fractions share the common base 35.

3 × 7/5 × 7 = 21/35 and 5 × 5/7 × 5 = 25/35

Step 3

Add the Numerators

Now add the numerators (21 + 25 = 46) and keep the common denominator 35 unchanged.

21 + 25/35 = 46/35

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 46 and 35 is 1, confirming that 46/35 cannot be reduced further—it is already in its simplest irreducible form.

46/35

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (46) is greater than the denominator (35), divide 46 by 35: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/35.

46/35 = 111/35

Step 6

Decimal & Percentage Representation

Dividing the numerator 46 by denominator 35 produces a repeating decimal (approximately 1.314286, or 131.4286%).

46 ÷ 35 = 1.314286 (131.4286%)

Visual Representation

The diagram below illustrates 3/5 plus 5/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`46/35`
Mixed Number Form	`1 11/35`
Decimal Form	`1.314286`
Percentage	`131.4286%`

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Frequently Asked Questions

What is 3/5 plus 5/7 as a fraction?

3/5 + 5/7 in simplest fraction form is 46/35 (or 1 11/35 as a mixed number).

What is 3/5 plus 5/7 as a decimal?

3/5 + 5/7 converted to a decimal is 1.314286.

What is 3/5 plus 5/7 as a percentage?

3/5 + 5/7 expressed as a percentage is 131.4286%.

How do you write 3/5 plus 5/7 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 46/35 can be written as the mixed number 1 11/35.

Does 3/5 plus 5/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.314286...) because the denominator contains prime factors other than 2 and 5.