What is 1/4 plus 9/16? (Answer: 13/16)

Exact Answer

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Problem: What is 1/4 plus 9/16?
Formula / Expression: 1/4 + 9/16
Final Answer: 13/16
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 16 is an exact multiple of 4 (4 × 4 = 16). The Least Common Denominator (LCD) is simply 16, meaning we only need to scale one fraction.
Working: LCD(4, 16) = 16

Step 2: Convert to Equivalent Fractions with Common Denominator 16
Multiply the numerator and denominator of 1/4 by 4, and multiply the numerator and denominator of 9/16 by 1 so both fractions share the common base 16.
Working: 1 × 4/4 × 4 = 4/16 and 9 × 1/16 × 1 = 9/16

Step 3: Add the Numerators
Now add the numerators (4 + 9 = 13) and keep the common denominator 16 unchanged.
Working: 4 + 9/16 = 13/16

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 13 and 16 is 1, confirming that 13/16 cannot be reduced further—it is already in its simplest irreducible form.
Working: 13/16

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 16 yields an exact terminating decimal of 0.8125 (or 81.25%).
Working: 13 ÷ 16 = 0.8125 (81.25%)

Key Values:
- Simplified Fraction: 13/16
- Mixed Number Form: 13/16
- Decimal Value: 0.8125
- Percentage: 81.25%

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Solved with FractionsCalc:
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1/4 + 9/16 = 13/16

Simplified Fraction

13/16

Mixed Number

Proper (13/16)

Decimal Value

0.8125

Percentage

81.25%

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Step-by-Step Solution: 1/4 + 9/16

Step 1

Find the Least Common Denominator (LCD)

Notice that 16 is an exact multiple of 4 (4 × 4 = 16). The Least Common Denominator (LCD) is simply 16, meaning we only need to scale one fraction.

LCD(4, 16) = 16

Step 2

Convert to Equivalent Fractions with Common Denominator 16

Multiply the numerator and denominator of 1/4 by 4, and multiply the numerator and denominator of 9/16 by 1 so both fractions share the common base 16.

1 × 4/4 × 4 = 4/16 and 9 × 1/16 × 1 = 9/16

Step 3

Add the Numerators

Now add the numerators (4 + 9 = 13) and keep the common denominator 16 unchanged.

4 + 9/16 = 13/16

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 13 and 16 is 1, confirming that 13/16 cannot be reduced further—it is already in its simplest irreducible form.

13/16

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 16 yields an exact terminating decimal of 0.8125 (or 81.25%).

13 ÷ 16 = 0.8125 (81.25%)

Visual Representation

The diagram below illustrates 1/4 plus 9/16 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/16`
Mixed Number Form	`13/16`
Decimal Form	`0.8125`
Percentage	`81.25%`

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Frequently Asked Questions

What is 1/4 plus 9/16 as a fraction?

1/4 + 9/16 in simplest fraction form is 13/16.

What is 1/4 plus 9/16 as a decimal?

1/4 + 9/16 converted to a decimal is 0.8125.

What is 1/4 plus 9/16 as a percentage?

1/4 + 9/16 expressed as a percentage is 81.25%.

Does 1/4 plus 9/16 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.8125) because the denominator in simplest terms contains only prime factors 2 and/or 5.