What is 5/9 plus 9/16? (Answer: 161/144)

Exact Answer

==================================================
Problem: What is 5/9 plus 9/16?
Formula / Expression: 5/9 + 9/16
Final Answer: 1 17/144 (161/144)
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 16 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 16 = 144.
Working: LCD(9, 16) = 144

Step 2: Convert to Equivalent Fractions with Common Denominator 144
Multiply the numerator and denominator of 5/9 by 16, and multiply the numerator and denominator of 9/16 by 9 so both fractions share the common base 144.
Working: 5 × 16/9 × 16 = 80/144 and 9 × 9/16 × 9 = 81/144

Step 3: Add the Numerators
Now add the numerators (80 + 81 = 161) and keep the common denominator 144 unchanged.
Working: 80 + 81/144 = 161/144

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 161 and 144 is 1, confirming that 161/144 cannot be reduced further—it is already in its simplest irreducible form.
Working: 161/144

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (161) is greater than the denominator (144), divide 161 by 144: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/144.
Working: 161/144 = 1 17/144

Step 6: Decimal & Percentage Representation
Dividing the numerator 161 by denominator 144 produces a repeating decimal (approximately 1.118056, or 111.8056%).
Working: 161 ÷ 144 = 1.118056 (111.8056%)

Key Values:
- Simplified Fraction: 161/144
- Mixed Number Form: 1 17/144
- Decimal Value: 1.118056
- Percentage: 111.8056%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-9-plus-9-16/
==================================================

5/9 + 9/16 = 161/144

Simplified Fraction

161/144

Mixed Number

1 17/144

Decimal Value

1.118056

Percentage

111.8056%

Reduce / Convert Fraction:

Convert Fraction:

Enter Decimal Number:

Enter Percentage: %

What is % of

From Value: To Value:

Simplify Ratio: :

Switch to Proportion / Missing X Solver (A/B = C/D) →

Enter 3 known numbers and leave 1 empty (or type x) to solve:

← Switch to Ratio Simplifier (A:B)

Provide any 2 values below to calculate the remaining:

Price before discount

Discount

Price after discount

You saved

+ Add Sales Tax & Extra Coupon (Optional)

Sales Tax: % Extra Off: %

Provide any 2 values below to calculate the remaining:

Cost

Markup

REVENUE

Gross Profit

Profit Margin

Bill Subtotal

Tip Percentage

Split (People)

👥

Quick Tip:

Total Bill

Split Between

👥

Tip % (Optional)

Include Tip:

Total Price

Quantity

Unit of Measure

← Discount & Sales Tax • Ratio Simplifier (A:B) →

First Number: Second Number:

Find All Factors of:

Dividend: ÷ Divisor:

Number to Round: To Nearest:

Method: Standard (5+ ↑) Always Up (Ceil) Always Down (Floor)

Presets:

√ Square Root of: OR Power (x^y): ^{^}

x² + x + = 0

Number (n! & log):

Circle Radius (r):

Side a: Side b:

Angle (Degrees): °

Numbers (comma separated):

Total Items (n): Choose (r):

Decimal Number:

Number (1–3999):

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

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 16 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 16 = 144.

LCD(9, 16) = 144

Step 2

Convert to Equivalent Fractions with Common Denominator 144

Multiply the numerator and denominator of 5/9 by 16, and multiply the numerator and denominator of 9/16 by 9 so both fractions share the common base 144.

5 × 16/9 × 16 = 80/144 and 9 × 9/16 × 9 = 81/144

Step 3

Add the Numerators

Now add the numerators (80 + 81 = 161) and keep the common denominator 144 unchanged.

80 + 81/144 = 161/144

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 161 and 144 is 1, confirming that 161/144 cannot be reduced further—it is already in its simplest irreducible form.

161/144

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (161) is greater than the denominator (144), divide 161 by 144: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/144.

161/144 = 117/144

Step 6

Decimal & Percentage Representation

Dividing the numerator 161 by denominator 144 produces a repeating decimal (approximately 1.118056, or 111.8056%).

161 ÷ 144 = 1.118056 (111.8056%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`161/144`
Mixed Number Form	`1 17/144`
Decimal Form	`1.118056`
Percentage	`111.8056%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

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

5/9 + 9/16 in simplest fraction form is 161/144 (or 1 17/144 as a mixed number).

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

5/9 + 9/16 converted to a decimal is 1.118056.

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

5/9 + 9/16 expressed as a percentage is 111.8056%.

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

Because the numerator is greater than the denominator, the improper fraction 161/144 can be written as the mixed number 1 17/144.

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

It results in a repeating decimal (approximately 1.118056...) because the denominator contains prime factors other than 2 and 5.