What is 4/7 plus 4/5? (Answer: 48/35)

Exact Answer

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Problem: What is 4/7 plus 4/5?
Formula / Expression: 4/7 + 4/5
Final Answer: 1 13/35 (48/35)
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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 4/7 by 5, and multiply the numerator and denominator of 4/5 by 7 so both fractions share the common base 35.
Working: 4 × 5/7 × 5 = 20/35 and 4 × 7/5 × 7 = 28/35

Step 3: Add the Numerators
Now add the numerators (20 + 28 = 48) and keep the common denominator 35 unchanged.
Working: 20 + 28/35 = 48/35

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 48 and 35 is 1, confirming that 48/35 cannot be reduced further—it is already in its simplest irreducible form.
Working: 48/35

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (48) is greater than the denominator (35), divide 48 by 35: it goes in 1 whole time(s) with a remainder of 13, giving the mixed number 1 13/35.
Working: 48/35 = 1 13/35

Step 6: Decimal & Percentage Representation
Dividing the numerator 48 by denominator 35 produces a repeating decimal (approximately 1.371429, or 137.1429%).
Working: 48 ÷ 35 = 1.371429 (137.1429%)

Key Values:
- Simplified Fraction: 48/35
- Mixed Number Form: 1 13/35
- Decimal Value: 1.371429
- Percentage: 137.1429%

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Solved with FractionsCalc:
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4/7 + 4/5 = 48/35

Simplified Fraction

48/35

Mixed Number

1 13/35

Decimal Value

1.371429

Percentage

137.1429%

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Step-by-Step Solution: 4/7 + 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 4/7 by 5, and multiply the numerator and denominator of 4/5 by 7 so both fractions share the common base 35.

4 × 5/7 × 5 = 20/35 and 4 × 7/5 × 7 = 28/35

Step 3

Add the Numerators

Now add the numerators (20 + 28 = 48) and keep the common denominator 35 unchanged.

20 + 28/35 = 48/35

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 48 and 35 is 1, confirming that 48/35 cannot be reduced further—it is already in its simplest irreducible form.

48/35

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (48) is greater than the denominator (35), divide 48 by 35: it goes in 1 whole time(s) with a remainder of 13, giving the mixed number 1 13/35.

48/35 = 113/35

Step 6

Decimal & Percentage Representation

Dividing the numerator 48 by denominator 35 produces a repeating decimal (approximately 1.371429, or 137.1429%).

48 ÷ 35 = 1.371429 (137.1429%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`48/35`
Mixed Number Form	`1 13/35`
Decimal Form	`1.371429`
Percentage	`137.1429%`

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Frequently Asked Questions

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

4/7 + 4/5 in simplest fraction form is 48/35 (or 1 13/35 as a mixed number).

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

4/7 + 4/5 converted to a decimal is 1.371429.

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

4/7 + 4/5 expressed as a percentage is 137.1429%.

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

Because the numerator is greater than the denominator, the improper fraction 48/35 can be written as the mixed number 1 13/35.

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

It results in a repeating decimal (approximately 1.371429...) because the denominator contains prime factors other than 2 and 5.