What is 2/3 plus 7/8? (Answer: 37/24)

Exact Answer

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Problem: What is 2/3 plus 7/8?
Formula / Expression: 2/3 + 7/8
Final Answer: 1 13/24 (37/24)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 3 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 3 × 8 = 24.
Working: LCD(3, 8) = 24

Step 2: Convert to Equivalent Fractions with Common Denominator 24
Multiply the numerator and denominator of 2/3 by 8, and multiply the numerator and denominator of 7/8 by 3 so both fractions share the common base 24.
Working: 2 × 8/3 × 8 = 16/24 and 7 × 3/8 × 3 = 21/24

Step 3: Add the Numerators
Now add the numerators (16 + 21 = 37) and keep the common denominator 24 unchanged.
Working: 16 + 21/24 = 37/24

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 37 and 24 is 1, confirming that 37/24 cannot be reduced further—it is already in its simplest irreducible form.
Working: 37/24

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (37) is greater than the denominator (24), divide 37 by 24: it goes in 1 whole time(s) with a remainder of 13, giving the mixed number 1 13/24.
Working: 37/24 = 1 13/24

Step 6: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 24 produces a repeating decimal (approximately 1.541667, or 154.1667%).
Working: 37 ÷ 24 = 1.541667 (154.1667%)

Key Values:
- Simplified Fraction: 37/24
- Mixed Number Form: 1 13/24
- Decimal Value: 1.541667
- Percentage: 154.1667%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-3-plus-7-8/
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2/3 + 7/8 = 37/24

Simplified Fraction

37/24

Mixed Number

1 13/24

Decimal Value

1.541667

Percentage

154.1667%

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

Step 1

Find the Least Common Denominator (LCD)

The denominators 3 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 3 × 8 = 24.

LCD(3, 8) = 24

Step 2

Convert to Equivalent Fractions with Common Denominator 24

Multiply the numerator and denominator of 2/3 by 8, and multiply the numerator and denominator of 7/8 by 3 so both fractions share the common base 24.

2 × 8/3 × 8 = 16/24 and 7 × 3/8 × 3 = 21/24

Step 3

Add the Numerators

Now add the numerators (16 + 21 = 37) and keep the common denominator 24 unchanged.

16 + 21/24 = 37/24

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 37 and 24 is 1, confirming that 37/24 cannot be reduced further—it is already in its simplest irreducible form.

37/24

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (37) is greater than the denominator (24), divide 37 by 24: it goes in 1 whole time(s) with a remainder of 13, giving the mixed number 1 13/24.

37/24 = 113/24

Step 6

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 24 produces a repeating decimal (approximately 1.541667, or 154.1667%).

37 ÷ 24 = 1.541667 (154.1667%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/24`
Mixed Number Form	`1 13/24`
Decimal Form	`1.541667`
Percentage	`154.1667%`

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Frequently Asked Questions

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

2/3 + 7/8 in simplest fraction form is 37/24 (or 1 13/24 as a mixed number).

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

2/3 + 7/8 converted to a decimal is 1.541667.

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

2/3 + 7/8 expressed as a percentage is 154.1667%.

How do you write 2/3 plus 7/8 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 37/24 can be written as the mixed number 1 13/24.

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

It results in a repeating decimal (approximately 1.541667...) because the denominator contains prime factors other than 2 and 5.