What is 9/16 plus 5/8? (Answer: 19/16)

Exact Answer

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Problem: What is 9/16 plus 5/8?
Formula / Expression: 9/16 + 5/8
Final Answer: 1 3/16 (19/16)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 16 is an exact multiple of 8 (8 × 2 = 16). The Least Common Denominator (LCD) is simply 16, meaning we only need to scale one fraction.
Working: LCD(16, 8) = 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 5/8 by 2 so both fractions share the common base 16.
Working: 9 × 1/16 × 1 = 9/16 and 5 × 2/8 × 2 = 10/16

Step 3: Add the Numerators
Now add the numerators (9 + 10 = 19) and keep the common denominator 16 unchanged.
Working: 9 + 10/16 = 19/16

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 19 and 16 is 1, confirming that 19/16 cannot be reduced further—it is already in its simplest irreducible form.
Working: 19/16

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (19) is greater than the denominator (16), divide 19 by 16: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/16.
Working: 19/16 = 1 3/16

Step 6: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 16 yields an exact terminating decimal of 1.1875 (or 118.75%).
Working: 19 ÷ 16 = 1.1875 (118.75%)

Key Values:
- Simplified Fraction: 19/16
- Mixed Number Form: 1 3/16
- Decimal Value: 1.1875
- Percentage: 118.75%

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Solved with FractionsCalc:
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9/16 + 5/8 = 19/16

Simplified Fraction

19/16

Mixed Number

1 3/16

Decimal Value

1.1875

Percentage

118.75%

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Step-by-Step Solution: 9/16 + 5/8

Step 1

Find the Least Common Denominator (LCD)

Notice that 16 is an exact multiple of 8 (8 × 2 = 16). The Least Common Denominator (LCD) is simply 16, meaning we only need to scale one fraction.

LCD(16, 8) = 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 5/8 by 2 so both fractions share the common base 16.

9 × 1/16 × 1 = 9/16 and 5 × 2/8 × 2 = 10/16

Step 3

Add the Numerators

Now add the numerators (9 + 10 = 19) and keep the common denominator 16 unchanged.

9 + 10/16 = 19/16

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 19 and 16 is 1, confirming that 19/16 cannot be reduced further—it is already in its simplest irreducible form.

19/16

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (19) is greater than the denominator (16), divide 19 by 16: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/16.

19/16 = 13/16

Step 6

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 16 yields an exact terminating decimal of 1.1875 (or 118.75%).

19 ÷ 16 = 1.1875 (118.75%)

Visual Representation

The diagram below illustrates 9/16 plus 5/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/16`
Mixed Number Form	`1 3/16`
Decimal Form	`1.1875`
Percentage	`118.75%`

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Frequently Asked Questions

What is 9/16 plus 5/8 as a fraction?

9/16 + 5/8 in simplest fraction form is 19/16 (or 1 3/16 as a mixed number).

What is 9/16 plus 5/8 as a decimal?

9/16 + 5/8 converted to a decimal is 1.1875.

What is 9/16 plus 5/8 as a percentage?

9/16 + 5/8 expressed as a percentage is 118.75%.

How do you write 9/16 plus 5/8 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 19/16 can be written as the mixed number 1 3/16.

Does 9/16 plus 5/8 result in a terminating or repeating decimal?

It results in an exact terminating decimal (1.1875) because the denominator in simplest terms contains only prime factors 2 and/or 5.