What is 1/9 plus 4/16? (Answer: 13/36)

Exact Answer

==================================================
Problem: What is 1/9 plus 4/16?
Formula / Expression: 1/9 + 4/16
Final Answer: 13/36
==================================================

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 1/9 by 16, and multiply the numerator and denominator of 4/16 by 9 so both fractions share the common base 144.
Working: 1 × 16/9 × 16 = 16/144 and 4 × 9/16 × 9 = 36/144

Step 3: Add the Numerators
Now add the numerators (16 + 36 = 52) and keep the common denominator 144 unchanged.
Working: 16 + 36/144 = 52/144

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 52 and 144, which is 4. Divide both the numerator and denominator by 4.
Working: 52 ÷ 4/144 ÷ 4 = 13/36

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 36 produces a repeating decimal (approximately 0.361111, or 36.1111%).
Working: 13 ÷ 36 = 0.361111 (36.1111%)

Key Values:
- Simplified Fraction: 13/36
- Mixed Number Form: 13/36
- Decimal Value: 0.361111
- Percentage: 36.1111%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-9-plus-4-16/
==================================================

1/9 + 4/16 = 13/36

Simplified Fraction

13/36

Mixed Number

Proper (13/36)

Decimal Value

0.361111

Percentage

36.1111%

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: 1/9 + 4/16

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 1/9 by 16, and multiply the numerator and denominator of 4/16 by 9 so both fractions share the common base 144.

1 × 16/9 × 16 = 16/144 and 4 × 9/16 × 9 = 36/144

Step 3

Add the Numerators

Now add the numerators (16 + 36 = 52) and keep the common denominator 144 unchanged.

16 + 36/144 = 52/144

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 52 and 144, which is 4. Divide both the numerator and denominator by 4.

52 ÷ 4/144 ÷ 4 = 13/36

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 36 produces a repeating decimal (approximately 0.361111, or 36.1111%).

13 ÷ 36 = 0.361111 (36.1111%)

Visual Representation

The diagram below illustrates 1/9 plus 4/16 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/36`
Mixed Number Form	`13/36`
Decimal Form	`0.361111`
Percentage	`36.1111%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 1/9 plus 4/16 as a fraction?

1/9 + 4/16 in simplest fraction form is 13/36.

What is 1/9 plus 4/16 as a decimal?

1/9 + 4/16 converted to a decimal is 0.361111.

What is 1/9 plus 4/16 as a percentage?

1/9 + 4/16 expressed as a percentage is 36.1111%.

Does 1/9 plus 4/16 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.361111...) because the denominator contains prime factors other than 2 and 5.