What is 1/16 plus 2/9? (Answer: 41/144)

Exact Answer

==================================================
Problem: What is 1/16 plus 2/9?
Formula / Expression: 1/16 + 2/9
Final Answer: 41/144
==================================================

Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 144
Multiply the numerator and denominator of 1/16 by 9, and multiply the numerator and denominator of 2/9 by 16 so both fractions share the common base 144.
Working: 1 × 9/16 × 9 = 9/144 and 2 × 16/9 × 16 = 32/144

Step 3: Add the Numerators
Now add the numerators (9 + 32 = 41) and keep the common denominator 144 unchanged.
Working: 9 + 32/144 = 41/144

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 41 and 144 is 1, confirming that 41/144 cannot be reduced further—it is already in its simplest irreducible form.
Working: 41/144

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 144 produces a repeating decimal (approximately 0.284722, or 28.4722%).
Working: 41 ÷ 144 = 0.284722 (28.4722%)

Key Values:
- Simplified Fraction: 41/144
- Mixed Number Form: 41/144
- Decimal Value: 0.284722
- Percentage: 28.4722%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-16-plus-2-9/
==================================================

1/16 + 2/9 = 41/144

Simplified Fraction

41/144

Mixed Number

Proper (41/144)

Decimal Value

0.284722

Percentage

28.4722%

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: 1/16 + 2/9

Step 1

Find the Least Common Denominator (LCD)

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

LCD(16, 9) = 144

Step 2

Convert to Equivalent Fractions with Common Denominator 144

Multiply the numerator and denominator of 1/16 by 9, and multiply the numerator and denominator of 2/9 by 16 so both fractions share the common base 144.

1 × 9/16 × 9 = 9/144 and 2 × 16/9 × 16 = 32/144

Step 3

Add the Numerators

Now add the numerators (9 + 32 = 41) and keep the common denominator 144 unchanged.

9 + 32/144 = 41/144

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 41 and 144 is 1, confirming that 41/144 cannot be reduced further—it is already in its simplest irreducible form.

41/144

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 144 produces a repeating decimal (approximately 0.284722, or 28.4722%).

41 ÷ 144 = 0.284722 (28.4722%)

Visual Representation

The diagram below illustrates 1/16 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/144`
Mixed Number Form	`41/144`
Decimal Form	`0.284722`
Percentage	`28.4722%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 1/16 plus 2/9 as a fraction?

1/16 + 2/9 in simplest fraction form is 41/144.

What is 1/16 plus 2/9 as a decimal?

1/16 + 2/9 converted to a decimal is 0.284722.

What is 1/16 plus 2/9 as a percentage?

1/16 + 2/9 expressed as a percentage is 28.4722%.

Does 1/16 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.284722...) because the denominator contains prime factors other than 2 and 5.