What is 5/7 plus 7/8? (Answer: 89/56)

Exact Answer

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Problem: What is 5/7 plus 7/8?
Formula / Expression: 5/7 + 7/8
Final Answer: 1 33/56 (89/56)
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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 5/7 by 8, and multiply the numerator and denominator of 7/8 by 7 so both fractions share the common base 56.
Working: 5 × 8/7 × 8 = 40/56 and 7 × 7/8 × 7 = 49/56

Step 3: Add the Numerators
Now add the numerators (40 + 49 = 89) and keep the common denominator 56 unchanged.
Working: 40 + 49/56 = 89/56

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 89 and 56 is 1, confirming that 89/56 cannot be reduced further—it is already in its simplest irreducible form.
Working: 89/56

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (89) is greater than the denominator (56), divide 89 by 56: it goes in 1 whole time(s) with a remainder of 33, giving the mixed number 1 33/56.
Working: 89/56 = 1 33/56

Step 6: Decimal & Percentage Representation
Dividing the numerator 89 by denominator 56 produces a repeating decimal (approximately 1.589286, or 158.9286%).
Working: 89 ÷ 56 = 1.589286 (158.9286%)

Key Values:
- Simplified Fraction: 89/56
- Mixed Number Form: 1 33/56
- Decimal Value: 1.589286
- Percentage: 158.9286%

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Solved with FractionsCalc:
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5/7 + 7/8 = 89/56

Simplified Fraction

89/56

Mixed Number

1 33/56

Decimal Value

1.589286

Percentage

158.9286%

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

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

5 × 8/7 × 8 = 40/56 and 7 × 7/8 × 7 = 49/56

Step 3

Add the Numerators

Now add the numerators (40 + 49 = 89) and keep the common denominator 56 unchanged.

40 + 49/56 = 89/56

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 89 and 56 is 1, confirming that 89/56 cannot be reduced further—it is already in its simplest irreducible form.

89/56

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (89) is greater than the denominator (56), divide 89 by 56: it goes in 1 whole time(s) with a remainder of 33, giving the mixed number 1 33/56.

89/56 = 133/56

Step 6

Decimal & Percentage Representation

Dividing the numerator 89 by denominator 56 produces a repeating decimal (approximately 1.589286, or 158.9286%).

89 ÷ 56 = 1.589286 (158.9286%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`89/56`
Mixed Number Form	`1 33/56`
Decimal Form	`1.589286`
Percentage	`158.9286%`

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Frequently Asked Questions

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

5/7 + 7/8 in simplest fraction form is 89/56 (or 1 33/56 as a mixed number).

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

5/7 + 7/8 converted to a decimal is 1.589286.

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

5/7 + 7/8 expressed as a percentage is 158.9286%.

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

Because the numerator is greater than the denominator, the improper fraction 89/56 can be written as the mixed number 1 33/56.

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

It results in a repeating decimal (approximately 1.589286...) because the denominator contains prime factors other than 2 and 5.