What is 2/7 plus 3/8? (Answer: 37/56)

Exact Answer

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Problem: What is 2/7 plus 3/8?
Formula / Expression: 2/7 + 3/8
Final Answer: 37/56
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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 3/8 by 7 so both fractions share the common base 56.
Working: 2 × 8/7 × 8 = 16/56 and 3 × 7/8 × 7 = 21/56

Step 3: Add the Numerators
Now add the numerators (16 + 21 = 37) and keep the common denominator 56 unchanged.
Working: 16 + 21/56 = 37/56

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 37 and 56 is 1, confirming that 37/56 cannot be reduced further—it is already in its simplest irreducible form.
Working: 37/56

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 56 produces a repeating decimal (approximately 0.660714, or 66.0714%).
Working: 37 ÷ 56 = 0.660714 (66.0714%)

Key Values:
- Simplified Fraction: 37/56
- Mixed Number Form: 37/56
- Decimal Value: 0.660714
- Percentage: 66.0714%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-7-plus-3-8/
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2/7 + 3/8 = 37/56

Simplified Fraction

37/56

Mixed Number

Proper (37/56)

Decimal Value

0.660714

Percentage

66.0714%

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Step-by-Step Solution: 2/7 + 3/8

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 3/8 by 7 so both fractions share the common base 56.

2 × 8/7 × 8 = 16/56 and 3 × 7/8 × 7 = 21/56

Step 3

Add the Numerators

Now add the numerators (16 + 21 = 37) and keep the common denominator 56 unchanged.

16 + 21/56 = 37/56

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 37 and 56 is 1, confirming that 37/56 cannot be reduced further—it is already in its simplest irreducible form.

37/56

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 56 produces a repeating decimal (approximately 0.660714, or 66.0714%).

37 ÷ 56 = 0.660714 (66.0714%)

Visual Representation

The diagram below illustrates 2/7 plus 3/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/56`
Mixed Number Form	`37/56`
Decimal Form	`0.660714`
Percentage	`66.0714%`

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Frequently Asked Questions

What is 2/7 plus 3/8 as a fraction?

2/7 + 3/8 in simplest fraction form is 37/56.

What is 2/7 plus 3/8 as a decimal?

2/7 + 3/8 converted to a decimal is 0.660714.

What is 2/7 plus 3/8 as a percentage?

2/7 + 3/8 expressed as a percentage is 66.0714%.

Does 2/7 plus 3/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.660714...) because the denominator contains prime factors other than 2 and 5.