What is 1/2 plus 5/8? (Answer: 9/8)

Exact Answer

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Problem: What is 1/2 plus 5/8?
Formula / Expression: 1/2 + 5/8
Final Answer: 1 1/8 (9/8)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 8 is an exact multiple of 2 (2 × 4 = 8). The Least Common Denominator (LCD) is simply 8, meaning we only need to scale one fraction.
Working: LCD(2, 8) = 8

Step 2: Convert to Equivalent Fractions with Common Denominator 8
Multiply the numerator and denominator of 1/2 by 4, and multiply the numerator and denominator of 5/8 by 1 so both fractions share the common base 8.
Working: 1 × 4/2 × 4 = 4/8 and 5 × 1/8 × 1 = 5/8

Step 3: Add the Numerators
Now add the numerators (4 + 5 = 9) and keep the common denominator 8 unchanged.
Working: 4 + 5/8 = 9/8

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 9 and 8 is 1, confirming that 9/8 cannot be reduced further—it is already in its simplest irreducible form.
Working: 9/8

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (9) is greater than the denominator (8), divide 9 by 8: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/8.
Working: 9/8 = 1 1/8

Step 6: Decimal & Percentage Representation
Dividing the numerator 9 by denominator 8 yields an exact terminating decimal of 1.125 (or 112.5%).
Working: 9 ÷ 8 = 1.125 (112.5%)

Key Values:
- Simplified Fraction: 9/8
- Mixed Number Form: 1 1/8
- Decimal Value: 1.125
- Percentage: 112.5%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-2-plus-5-8/
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1/2 + 5/8 = 9/8

Simplified Fraction

9/8

Mixed Number

1 1/8

Decimal Value

1.125

Percentage

112.5%

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Step-by-Step Solution: 1/2 + 5/8

Step 1

Find the Least Common Denominator (LCD)

Notice that 8 is an exact multiple of 2 (2 × 4 = 8). The Least Common Denominator (LCD) is simply 8, meaning we only need to scale one fraction.

LCD(2, 8) = 8

Step 2

Convert to Equivalent Fractions with Common Denominator 8

Multiply the numerator and denominator of 1/2 by 4, and multiply the numerator and denominator of 5/8 by 1 so both fractions share the common base 8.

1 × 4/2 × 4 = 4/8 and 5 × 1/8 × 1 = 5/8

Step 3

Add the Numerators

Now add the numerators (4 + 5 = 9) and keep the common denominator 8 unchanged.

4 + 5/8 = 9/8

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 9 and 8 is 1, confirming that 9/8 cannot be reduced further—it is already in its simplest irreducible form.

9/8

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (9) is greater than the denominator (8), divide 9 by 8: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/8.

9/8 = 11/8

Step 6

Decimal & Percentage Representation

Dividing the numerator 9 by denominator 8 yields an exact terminating decimal of 1.125 (or 112.5%).

9 ÷ 8 = 1.125 (112.5%)

Visual Representation

The diagram below illustrates 1/2 plus 5/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`9/8`
Mixed Number Form	`1 1/8`
Decimal Form	`1.125`
Percentage	`112.5%`

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Frequently Asked Questions

What is 1/2 plus 5/8 as a fraction?

1/2 + 5/8 in simplest fraction form is 9/8 (or 1 1/8 as a mixed number).

What is 1/2 plus 5/8 as a decimal?

1/2 + 5/8 converted to a decimal is 1.125.

What is 1/2 plus 5/8 as a percentage?

1/2 + 5/8 expressed as a percentage is 112.5%.

How do you write 1/2 plus 5/8 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 9/8 can be written as the mixed number 1 1/8.

Does 1/2 plus 5/8 result in a terminating or repeating decimal?

It results in an exact terminating decimal (1.125) because the denominator in simplest terms contains only prime factors 2 and/or 5.