What is 3/7 plus 5/8? (Answer: 59/56)

Exact Answer

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Problem: What is 3/7 plus 5/8?
Formula / Expression: 3/7 + 5/8
Final Answer: 1 3/56 (59/56)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 8 = 56.
Working: LCD(7, 8) = 56

Step 2: Convert to Equivalent Fractions with Common Denominator 56
Multiply the numerator and denominator of 3/7 by 8, and multiply the numerator and denominator of 5/8 by 7 so both fractions share the common base 56.
Working: 3 × 8/7 × 8 = 24/56 and 5 × 7/8 × 7 = 35/56

Step 3: Add the Numerators
Now add the numerators (24 + 35 = 59) and keep the common denominator 56 unchanged.
Working: 24 + 35/56 = 59/56

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 59 and 56 is 1, confirming that 59/56 cannot be reduced further—it is already in its simplest irreducible form.
Working: 59/56

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (59) is greater than the denominator (56), divide 59 by 56: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/56.
Working: 59/56 = 1 3/56

Step 6: Decimal & Percentage Representation
Dividing the numerator 59 by denominator 56 produces a repeating decimal (approximately 1.053571, or 105.3571%).
Working: 59 ÷ 56 = 1.053571 (105.3571%)

Key Values:
- Simplified Fraction: 59/56
- Mixed Number Form: 1 3/56
- Decimal Value: 1.053571
- Percentage: 105.3571%

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Solved with FractionsCalc:
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3/7 + 5/8 = 59/56

Simplified Fraction

59/56

Mixed Number

1 3/56

Decimal Value

1.053571

Percentage

105.3571%

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Step-by-Step Solution: 3/7 + 5/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 8 = 56.

LCD(7, 8) = 56

Step 2

Convert to Equivalent Fractions with Common Denominator 56

Multiply the numerator and denominator of 3/7 by 8, and multiply the numerator and denominator of 5/8 by 7 so both fractions share the common base 56.

3 × 8/7 × 8 = 24/56 and 5 × 7/8 × 7 = 35/56

Step 3

Add the Numerators

Now add the numerators (24 + 35 = 59) and keep the common denominator 56 unchanged.

24 + 35/56 = 59/56

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 59 and 56 is 1, confirming that 59/56 cannot be reduced further—it is already in its simplest irreducible form.

59/56

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (59) is greater than the denominator (56), divide 59 by 56: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/56.

59/56 = 13/56

Step 6

Decimal & Percentage Representation

Dividing the numerator 59 by denominator 56 produces a repeating decimal (approximately 1.053571, or 105.3571%).

59 ÷ 56 = 1.053571 (105.3571%)

Visual Representation

The diagram below illustrates 3/7 plus 5/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`59/56`
Mixed Number Form	`1 3/56`
Decimal Form	`1.053571`
Percentage	`105.3571%`

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Frequently Asked Questions

What is 3/7 plus 5/8 as a fraction?

3/7 + 5/8 in simplest fraction form is 59/56 (or 1 3/56 as a mixed number).

What is 3/7 plus 5/8 as a decimal?

3/7 + 5/8 converted to a decimal is 1.053571.

What is 3/7 plus 5/8 as a percentage?

3/7 + 5/8 expressed as a percentage is 105.3571%.

How do you write 3/7 plus 5/8 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 59/56 can be written as the mixed number 1 3/56.

Does 3/7 plus 5/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.053571...) because the denominator contains prime factors other than 2 and 5.