What is 2/7 plus 7/8? (Answer: 65/56)

Exact Answer

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Problem: What is 2/7 plus 7/8?
Formula / Expression: 2/7 + 7/8
Final Answer: 1 9/56 (65/56)
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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 2/7 by 8, and multiply the numerator and denominator of 7/8 by 7 so both fractions share the common base 56.
Working: 2 × 8/7 × 8 = 16/56 and 7 × 7/8 × 7 = 49/56

Step 3: Add the Numerators
Now add the numerators (16 + 49 = 65) and keep the common denominator 56 unchanged.
Working: 16 + 49/56 = 65/56

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 65 and 56 is 1, confirming that 65/56 cannot be reduced further—it is already in its simplest irreducible form.
Working: 65/56

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (65) is greater than the denominator (56), divide 65 by 56: it goes in 1 whole time(s) with a remainder of 9, giving the mixed number 1 9/56.
Working: 65/56 = 1 9/56

Step 6: Decimal & Percentage Representation
Dividing the numerator 65 by denominator 56 produces a repeating decimal (approximately 1.160714, or 116.0714%).
Working: 65 ÷ 56 = 1.160714 (116.0714%)

Key Values:
- Simplified Fraction: 65/56
- Mixed Number Form: 1 9/56
- Decimal Value: 1.160714
- Percentage: 116.0714%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-7-plus-7-8/
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2/7 + 7/8 = 65/56

Simplified Fraction

65/56

Mixed Number

1 9/56

Decimal Value

1.160714

Percentage

116.0714%

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Step-by-Step Solution: 2/7 + 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 2/7 by 8, and multiply the numerator and denominator of 7/8 by 7 so both fractions share the common base 56.

2 × 8/7 × 8 = 16/56 and 7 × 7/8 × 7 = 49/56

Step 3

Add the Numerators

Now add the numerators (16 + 49 = 65) and keep the common denominator 56 unchanged.

16 + 49/56 = 65/56

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 65 and 56 is 1, confirming that 65/56 cannot be reduced further—it is already in its simplest irreducible form.

65/56

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (65) is greater than the denominator (56), divide 65 by 56: it goes in 1 whole time(s) with a remainder of 9, giving the mixed number 1 9/56.

65/56 = 19/56

Step 6

Decimal & Percentage Representation

Dividing the numerator 65 by denominator 56 produces a repeating decimal (approximately 1.160714, or 116.0714%).

65 ÷ 56 = 1.160714 (116.0714%)

Visual Representation

The diagram below illustrates 2/7 plus 7/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`65/56`
Mixed Number Form	`1 9/56`
Decimal Form	`1.160714`
Percentage	`116.0714%`

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Frequently Asked Questions

What is 2/7 plus 7/8 as a fraction?

2/7 + 7/8 in simplest fraction form is 65/56 (or 1 9/56 as a mixed number).

What is 2/7 plus 7/8 as a decimal?

2/7 + 7/8 converted to a decimal is 1.160714.

What is 2/7 plus 7/8 as a percentage?

2/7 + 7/8 expressed as a percentage is 116.0714%.

How do you write 2/7 plus 7/8 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 65/56 can be written as the mixed number 1 9/56.

Does 2/7 plus 7/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.160714...) because the denominator contains prime factors other than 2 and 5.