What is 1/7 plus 5/8? (Answer: 43/56)

Exact Answer

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Problem: What is 1/7 plus 5/8?
Formula / Expression: 1/7 + 5/8
Final Answer: 43/56
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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 1/7 by 8, and multiply the numerator and denominator of 5/8 by 7 so both fractions share the common base 56.
Working: 1 × 8/7 × 8 = 8/56 and 5 × 7/8 × 7 = 35/56

Step 3: Add the Numerators
Now add the numerators (8 + 35 = 43) and keep the common denominator 56 unchanged.
Working: 8 + 35/56 = 43/56

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 43 and 56 is 1, confirming that 43/56 cannot be reduced further—it is already in its simplest irreducible form.
Working: 43/56

Step 5: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 56 produces a repeating decimal (approximately 0.767857, or 76.7857%).
Working: 43 ÷ 56 = 0.767857 (76.7857%)

Key Values:
- Simplified Fraction: 43/56
- Mixed Number Form: 43/56
- Decimal Value: 0.767857
- Percentage: 76.7857%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-7-plus-5-8/
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1/7 + 5/8 = 43/56

Simplified Fraction

43/56

Mixed Number

Proper (43/56)

Decimal Value

0.767857

Percentage

76.7857%

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Step-by-Step Solution: 1/7 + 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 1/7 by 8, and multiply the numerator and denominator of 5/8 by 7 so both fractions share the common base 56.

1 × 8/7 × 8 = 8/56 and 5 × 7/8 × 7 = 35/56

Step 3

Add the Numerators

Now add the numerators (8 + 35 = 43) and keep the common denominator 56 unchanged.

8 + 35/56 = 43/56

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 43 and 56 is 1, confirming that 43/56 cannot be reduced further—it is already in its simplest irreducible form.

43/56

Step 5

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 56 produces a repeating decimal (approximately 0.767857, or 76.7857%).

43 ÷ 56 = 0.767857 (76.7857%)

Visual Representation

The diagram below illustrates 1/7 plus 5/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/56`
Mixed Number Form	`43/56`
Decimal Form	`0.767857`
Percentage	`76.7857%`

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Frequently Asked Questions

What is 1/7 plus 5/8 as a fraction?

1/7 + 5/8 in simplest fraction form is 43/56.

What is 1/7 plus 5/8 as a decimal?

1/7 + 5/8 converted to a decimal is 0.767857.

What is 1/7 plus 5/8 as a percentage?

1/7 + 5/8 expressed as a percentage is 76.7857%.

Does 1/7 plus 5/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.767857...) because the denominator contains prime factors other than 2 and 5.