What is 1/4 plus 5/8? (Answer: 7/8)

Exact Answer

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Problem: What is 1/4 plus 5/8?
Formula / Expression: 1/4 + 5/8
Final Answer: 7/8
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Step-by-Step Solution:

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

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

Step 3: Add the Numerators
Now add the numerators (2 + 5 = 7) and keep the common denominator 8 unchanged.
Working: 2 + 5/8 = 7/8

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 7 and 8 is 1, confirming that 7/8 cannot be reduced further—it is already in its simplest irreducible form.
Working: 7/8

Step 5: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 8 yields an exact terminating decimal of 0.875 (or 87.5%).
Working: 7 ÷ 8 = 0.875 (87.5%)

Key Values:
- Simplified Fraction: 7/8
- Mixed Number Form: 7/8
- Decimal Value: 0.875
- Percentage: 87.5%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-4-plus-5-8/
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1/4 + 5/8 = 7/8

Simplified Fraction

7/8

Mixed Number

Proper (7/8)

Decimal Value

0.875

Percentage

87.5%

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Step-by-Step Solution: 1/4 + 5/8

Step 1

Find the Least Common Denominator (LCD)

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

LCD(4, 8) = 8

Step 2

Convert to Equivalent Fractions with Common Denominator 8

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

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

Step 3

Add the Numerators

Now add the numerators (2 + 5 = 7) and keep the common denominator 8 unchanged.

2 + 5/8 = 7/8

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 7 and 8 is 1, confirming that 7/8 cannot be reduced further—it is already in its simplest irreducible form.

7/8

Step 5

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 8 yields an exact terminating decimal of 0.875 (or 87.5%).

7 ÷ 8 = 0.875 (87.5%)

Visual Representation

The diagram below illustrates 1/4 plus 5/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/8`
Mixed Number Form	`7/8`
Decimal Form	`0.875`
Percentage	`87.5%`

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Frequently Asked Questions

What is 1/4 plus 5/8 as a fraction?

1/4 + 5/8 in simplest fraction form is 7/8.

What is 1/4 plus 5/8 as a decimal?

1/4 + 5/8 converted to a decimal is 0.875.

What is 1/4 plus 5/8 as a percentage?

1/4 + 5/8 expressed as a percentage is 87.5%.

Does 1/4 plus 5/8 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.875) because the denominator in simplest terms contains only prime factors 2 and/or 5.