What is 5/8 plus 5/7? (Answer: 75/56)

Exact Answer

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Problem: What is 5/8 plus 5/7?
Formula / Expression: 5/8 + 5/7
Final Answer: 1 19/56 (75/56)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 56
Multiply the numerator and denominator of 5/8 by 7, and multiply the numerator and denominator of 5/7 by 8 so both fractions share the common base 56.
Working: 5 × 7/8 × 7 = 35/56 and 5 × 8/7 × 8 = 40/56

Step 3: Add the Numerators
Now add the numerators (35 + 40 = 75) and keep the common denominator 56 unchanged.
Working: 35 + 40/56 = 75/56

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 75 and 56 is 1, confirming that 75/56 cannot be reduced further—it is already in its simplest irreducible form.
Working: 75/56

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (75) is greater than the denominator (56), divide 75 by 56: it goes in 1 whole time(s) with a remainder of 19, giving the mixed number 1 19/56.
Working: 75/56 = 1 19/56

Step 6: Decimal & Percentage Representation
Dividing the numerator 75 by denominator 56 produces a repeating decimal (approximately 1.339286, or 133.9286%).
Working: 75 ÷ 56 = 1.339286 (133.9286%)

Key Values:
- Simplified Fraction: 75/56
- Mixed Number Form: 1 19/56
- Decimal Value: 1.339286
- Percentage: 133.9286%

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Solved with FractionsCalc:
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5/8 + 5/7 = 75/56

Simplified Fraction

75/56

Mixed Number

1 19/56

Decimal Value

1.339286

Percentage

133.9286%

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

Step 1

Find the Least Common Denominator (LCD)

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

LCD(8, 7) = 56

Step 2

Convert to Equivalent Fractions with Common Denominator 56

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

5 × 7/8 × 7 = 35/56 and 5 × 8/7 × 8 = 40/56

Step 3

Add the Numerators

Now add the numerators (35 + 40 = 75) and keep the common denominator 56 unchanged.

35 + 40/56 = 75/56

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 75 and 56 is 1, confirming that 75/56 cannot be reduced further—it is already in its simplest irreducible form.

75/56

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (75) is greater than the denominator (56), divide 75 by 56: it goes in 1 whole time(s) with a remainder of 19, giving the mixed number 1 19/56.

75/56 = 119/56

Step 6

Decimal & Percentage Representation

Dividing the numerator 75 by denominator 56 produces a repeating decimal (approximately 1.339286, or 133.9286%).

75 ÷ 56 = 1.339286 (133.9286%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`75/56`
Mixed Number Form	`1 19/56`
Decimal Form	`1.339286`
Percentage	`133.9286%`

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Frequently Asked Questions

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

5/8 + 5/7 in simplest fraction form is 75/56 (or 1 19/56 as a mixed number).

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

5/8 + 5/7 converted to a decimal is 1.339286.

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

5/8 + 5/7 expressed as a percentage is 133.9286%.

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

Because the numerator is greater than the denominator, the improper fraction 75/56 can be written as the mixed number 1 19/56.

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

It results in a repeating decimal (approximately 1.339286...) because the denominator contains prime factors other than 2 and 5.