What is 1/8 plus 3/7? (Answer: 31/56)

Exact Answer

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Problem: What is 1/8 plus 3/7?
Formula / Expression: 1/8 + 3/7
Final Answer: 31/56
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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 1/8 by 7, and multiply the numerator and denominator of 3/7 by 8 so both fractions share the common base 56.
Working: 1 × 7/8 × 7 = 7/56 and 3 × 8/7 × 8 = 24/56

Step 3: Add the Numerators
Now add the numerators (7 + 24 = 31) and keep the common denominator 56 unchanged.
Working: 7 + 24/56 = 31/56

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 31 and 56 is 1, confirming that 31/56 cannot be reduced further—it is already in its simplest irreducible form.
Working: 31/56

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 56 produces a repeating decimal (approximately 0.553571, or 55.3571%).
Working: 31 ÷ 56 = 0.553571 (55.3571%)

Key Values:
- Simplified Fraction: 31/56
- Mixed Number Form: 31/56
- Decimal Value: 0.553571
- Percentage: 55.3571%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-8-plus-3-7/
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1/8 + 3/7 = 31/56

Simplified Fraction

31/56

Mixed Number

Proper (31/56)

Decimal Value

0.553571

Percentage

55.3571%

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Step-by-Step Solution: 1/8 + 3/7

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 1/8 by 7, and multiply the numerator and denominator of 3/7 by 8 so both fractions share the common base 56.

1 × 7/8 × 7 = 7/56 and 3 × 8/7 × 8 = 24/56

Step 3

Add the Numerators

Now add the numerators (7 + 24 = 31) and keep the common denominator 56 unchanged.

7 + 24/56 = 31/56

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 31 and 56 is 1, confirming that 31/56 cannot be reduced further—it is already in its simplest irreducible form.

31/56

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 56 produces a repeating decimal (approximately 0.553571, or 55.3571%).

31 ÷ 56 = 0.553571 (55.3571%)

Visual Representation

The diagram below illustrates 1/8 plus 3/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/56`
Mixed Number Form	`31/56`
Decimal Form	`0.553571`
Percentage	`55.3571%`

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Frequently Asked Questions

What is 1/8 plus 3/7 as a fraction?

1/8 + 3/7 in simplest fraction form is 31/56.

What is 1/8 plus 3/7 as a decimal?

1/8 + 3/7 converted to a decimal is 0.553571.

What is 1/8 plus 3/7 as a percentage?

1/8 + 3/7 expressed as a percentage is 55.3571%.

Does 1/8 plus 3/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.553571...) because the denominator contains prime factors other than 2 and 5.