What is 2/9 plus 6/16? (Answer: 43/72)

Exact Answer

==================================================
Problem: What is 2/9 plus 6/16?
Formula / Expression: 2/9 + 6/16
Final Answer: 43/72
==================================================

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 2/9 by 16, and multiply the numerator and denominator of 6/16 by 9 so both fractions share the common base 144.
Working: 2 × 16/9 × 16 = 32/144 and 6 × 9/16 × 9 = 54/144

Step 3: Add the Numerators
Now add the numerators (32 + 54 = 86) and keep the common denominator 144 unchanged.
Working: 32 + 54/144 = 86/144

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 86 and 144, which is 2. Divide both the numerator and denominator by 2.
Working: 86 ÷ 2/144 ÷ 2 = 43/72

Step 5: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 72 produces a repeating decimal (approximately 0.597222, or 59.7222%).
Working: 43 ÷ 72 = 0.597222 (59.7222%)

Key Values:
- Simplified Fraction: 43/72
- Mixed Number Form: 43/72
- Decimal Value: 0.597222
- Percentage: 59.7222%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-9-plus-6-16/
==================================================

2/9 + 6/16 = 43/72

Simplified Fraction

43/72

Mixed Number

Proper (43/72)

Decimal Value

0.597222

Percentage

59.7222%

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: 2/9 + 6/16

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 2/9 by 16, and multiply the numerator and denominator of 6/16 by 9 so both fractions share the common base 144.

2 × 16/9 × 16 = 32/144 and 6 × 9/16 × 9 = 54/144

Step 3

Add the Numerators

Now add the numerators (32 + 54 = 86) and keep the common denominator 144 unchanged.

32 + 54/144 = 86/144

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 86 and 144, which is 2. Divide both the numerator and denominator by 2.

86 ÷ 2/144 ÷ 2 = 43/72

Step 5

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 72 produces a repeating decimal (approximately 0.597222, or 59.7222%).

43 ÷ 72 = 0.597222 (59.7222%)

Visual Representation

The diagram below illustrates 2/9 plus 6/16 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/72`
Mixed Number Form	`43/72`
Decimal Form	`0.597222`
Percentage	`59.7222%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 2/9 plus 6/16 as a fraction?

2/9 + 6/16 in simplest fraction form is 43/72.

What is 2/9 plus 6/16 as a decimal?

2/9 + 6/16 converted to a decimal is 0.597222.

What is 2/9 plus 6/16 as a percentage?

2/9 + 6/16 expressed as a percentage is 59.7222%.

Does 2/9 plus 6/16 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.597222...) because the denominator contains prime factors other than 2 and 5.