What is 5/7 plus 4/5? (Answer: 53/35)

Exact Answer

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Problem: What is 5/7 plus 4/5?
Formula / Expression: 5/7 + 4/5
Final Answer: 1 18/35 (53/35)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 35
Multiply the numerator and denominator of 5/7 by 5, and multiply the numerator and denominator of 4/5 by 7 so both fractions share the common base 35.
Working: 5 × 5/7 × 5 = 25/35 and 4 × 7/5 × 7 = 28/35

Step 3: Add the Numerators
Now add the numerators (25 + 28 = 53) and keep the common denominator 35 unchanged.
Working: 25 + 28/35 = 53/35

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 53 and 35 is 1, confirming that 53/35 cannot be reduced further—it is already in its simplest irreducible form.
Working: 53/35

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (53) is greater than the denominator (35), divide 53 by 35: it goes in 1 whole time(s) with a remainder of 18, giving the mixed number 1 18/35.
Working: 53/35 = 1 18/35

Step 6: Decimal & Percentage Representation
Dividing the numerator 53 by denominator 35 produces a repeating decimal (approximately 1.514286, or 151.4286%).
Working: 53 ÷ 35 = 1.514286 (151.4286%)

Key Values:
- Simplified Fraction: 53/35
- Mixed Number Form: 1 18/35
- Decimal Value: 1.514286
- Percentage: 151.4286%

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Solved with FractionsCalc:
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5/7 + 4/5 = 53/35

Simplified Fraction

53/35

Mixed Number

1 18/35

Decimal Value

1.514286

Percentage

151.4286%

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

Step 1

Find the Least Common Denominator (LCD)

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

LCD(7, 5) = 35

Step 2

Convert to Equivalent Fractions with Common Denominator 35

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

5 × 5/7 × 5 = 25/35 and 4 × 7/5 × 7 = 28/35

Step 3

Add the Numerators

Now add the numerators (25 + 28 = 53) and keep the common denominator 35 unchanged.

25 + 28/35 = 53/35

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 53 and 35 is 1, confirming that 53/35 cannot be reduced further—it is already in its simplest irreducible form.

53/35

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (53) is greater than the denominator (35), divide 53 by 35: it goes in 1 whole time(s) with a remainder of 18, giving the mixed number 1 18/35.

53/35 = 118/35

Step 6

Decimal & Percentage Representation

Dividing the numerator 53 by denominator 35 produces a repeating decimal (approximately 1.514286, or 151.4286%).

53 ÷ 35 = 1.514286 (151.4286%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`53/35`
Mixed Number Form	`1 18/35`
Decimal Form	`1.514286`
Percentage	`151.4286%`

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Frequently Asked Questions

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

5/7 + 4/5 in simplest fraction form is 53/35 (or 1 18/35 as a mixed number).

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

5/7 + 4/5 converted to a decimal is 1.514286.

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

5/7 + 4/5 expressed as a percentage is 151.4286%.

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

Because the numerator is greater than the denominator, the improper fraction 53/35 can be written as the mixed number 1 18/35.

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

It results in a repeating decimal (approximately 1.514286...) because the denominator contains prime factors other than 2 and 5.