What is 9/16 plus 3/4? (Answer: 21/16)

Exact Answer

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Problem: What is 9/16 plus 3/4?
Formula / Expression: 9/16 + 3/4
Final Answer: 1 5/16 (21/16)
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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(16, 4) = 16

Step 2: Convert to Equivalent Fractions with Common Denominator 16
Multiply the numerator and denominator of 9/16 by 1, and multiply the numerator and denominator of 3/4 by 4 so both fractions share the common base 16.
Working: 9 × 1/16 × 1 = 9/16 and 3 × 4/4 × 4 = 12/16

Step 3: Add the Numerators
Now add the numerators (9 + 12 = 21) and keep the common denominator 16 unchanged.
Working: 9 + 12/16 = 21/16

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 21 and 16 is 1, confirming that 21/16 cannot be reduced further—it is already in its simplest irreducible form.
Working: 21/16

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (21) is greater than the denominator (16), divide 21 by 16: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/16.
Working: 21/16 = 1 5/16

Step 6: Decimal & Percentage Representation
Dividing the numerator 21 by denominator 16 yields an exact terminating decimal of 1.3125 (or 131.25%).
Working: 21 ÷ 16 = 1.3125 (131.25%)

Key Values:
- Simplified Fraction: 21/16
- Mixed Number Form: 1 5/16
- Decimal Value: 1.3125
- Percentage: 131.25%

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Solved with FractionsCalc:
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9/16 + 3/4 = 21/16

Simplified Fraction

21/16

Mixed Number

1 5/16

Decimal Value

1.3125

Percentage

131.25%

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Step-by-Step Solution: 9/16 + 3/4

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(16, 4) = 16

Step 2

Convert to Equivalent Fractions with Common Denominator 16

Multiply the numerator and denominator of 9/16 by 1, and multiply the numerator and denominator of 3/4 by 4 so both fractions share the common base 16.

9 × 1/16 × 1 = 9/16 and 3 × 4/4 × 4 = 12/16

Step 3

Add the Numerators

Now add the numerators (9 + 12 = 21) and keep the common denominator 16 unchanged.

9 + 12/16 = 21/16

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 21 and 16 is 1, confirming that 21/16 cannot be reduced further—it is already in its simplest irreducible form.

21/16

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (21) is greater than the denominator (16), divide 21 by 16: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/16.

21/16 = 15/16

Step 6

Decimal & Percentage Representation

Dividing the numerator 21 by denominator 16 yields an exact terminating decimal of 1.3125 (or 131.25%).

21 ÷ 16 = 1.3125 (131.25%)

Visual Representation

The diagram below illustrates 9/16 plus 3/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`21/16`
Mixed Number Form	`1 5/16`
Decimal Form	`1.3125`
Percentage	`131.25%`

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Frequently Asked Questions

What is 9/16 plus 3/4 as a fraction?

9/16 + 3/4 in simplest fraction form is 21/16 (or 1 5/16 as a mixed number).

What is 9/16 plus 3/4 as a decimal?

9/16 + 3/4 converted to a decimal is 1.3125.

What is 9/16 plus 3/4 as a percentage?

9/16 + 3/4 expressed as a percentage is 131.25%.

How do you write 9/16 plus 3/4 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 21/16 can be written as the mixed number 1 5/16.

Does 9/16 plus 3/4 result in a terminating or repeating decimal?

It results in an exact terminating decimal (1.3125) because the denominator in simplest terms contains only prime factors 2 and/or 5.