What is 4/5 plus 6/7? (Answer: 58/35)

Exact Answer

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Problem: What is 4/5 plus 6/7?
Formula / Expression: 4/5 + 6/7
Final Answer: 1 23/35 (58/35)
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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 4/5 by 7, and multiply the numerator and denominator of 6/7 by 5 so both fractions share the common base 35.
Working: 4 × 7/5 × 7 = 28/35 and 6 × 5/7 × 5 = 30/35

Step 3: Add the Numerators
Now add the numerators (28 + 30 = 58) and keep the common denominator 35 unchanged.
Working: 28 + 30/35 = 58/35

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 58 and 35 is 1, confirming that 58/35 cannot be reduced further—it is already in its simplest irreducible form.
Working: 58/35

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (58) is greater than the denominator (35), divide 58 by 35: it goes in 1 whole time(s) with a remainder of 23, giving the mixed number 1 23/35.
Working: 58/35 = 1 23/35

Step 6: Decimal & Percentage Representation
Dividing the numerator 58 by denominator 35 produces a repeating decimal (approximately 1.657143, or 165.7143%).
Working: 58 ÷ 35 = 1.657143 (165.7143%)

Key Values:
- Simplified Fraction: 58/35
- Mixed Number Form: 1 23/35
- Decimal Value: 1.657143
- Percentage: 165.7143%

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Solved with FractionsCalc:
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4/5 + 6/7 = 58/35

Simplified Fraction

58/35

Mixed Number

1 23/35

Decimal Value

1.657143

Percentage

165.7143%

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Step-by-Step Solution: 4/5 + 6/7

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 4/5 by 7, and multiply the numerator and denominator of 6/7 by 5 so both fractions share the common base 35.

4 × 7/5 × 7 = 28/35 and 6 × 5/7 × 5 = 30/35

Step 3

Add the Numerators

Now add the numerators (28 + 30 = 58) and keep the common denominator 35 unchanged.

28 + 30/35 = 58/35

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 58 and 35 is 1, confirming that 58/35 cannot be reduced further—it is already in its simplest irreducible form.

58/35

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (58) is greater than the denominator (35), divide 58 by 35: it goes in 1 whole time(s) with a remainder of 23, giving the mixed number 1 23/35.

58/35 = 123/35

Step 6

Decimal & Percentage Representation

Dividing the numerator 58 by denominator 35 produces a repeating decimal (approximately 1.657143, or 165.7143%).

58 ÷ 35 = 1.657143 (165.7143%)

Visual Representation

The diagram below illustrates 4/5 plus 6/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`58/35`
Mixed Number Form	`1 23/35`
Decimal Form	`1.657143`
Percentage	`165.7143%`

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Frequently Asked Questions

What is 4/5 plus 6/7 as a fraction?

4/5 + 6/7 in simplest fraction form is 58/35 (or 1 23/35 as a mixed number).

What is 4/5 plus 6/7 as a decimal?

4/5 + 6/7 converted to a decimal is 1.657143.

What is 4/5 plus 6/7 as a percentage?

4/5 + 6/7 expressed as a percentage is 165.7143%.

How do you write 4/5 plus 6/7 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 58/35 can be written as the mixed number 1 23/35.

Does 4/5 plus 6/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.657143...) because the denominator contains prime factors other than 2 and 5.