What is 22/45 plus 9/13? (Answer: 691/585)

Exact Answer

==================================================
Problem: What is 22/45 plus 9/13?
Formula / Expression: 22/45 + 9/13
Final Answer: 1 106/585 (691/585)
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 45 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 45 × 13 = 585.
Working: LCD(45, 13) = 585

Step 2: Convert to Equivalent Fractions with Common Denominator 585
Multiply the numerator and denominator of 22/45 by 13, and multiply the numerator and denominator of 9/13 by 45 so both fractions share the common base 585.
Working: 22 × 13/45 × 13 = 286/585 and 9 × 45/13 × 45 = 405/585

Step 3: Add the Numerators
Now add the numerators (286 + 405 = 691) and keep the common denominator 585 unchanged.
Working: 286 + 405/585 = 691/585

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 691 and 585 is 1, confirming that 691/585 cannot be reduced further—it is already in its simplest irreducible form.
Working: 691/585

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (691) is greater than the denominator (585), divide 691 by 585: it goes in 1 whole time(s) with a remainder of 106, giving the mixed number 1 106/585.
Working: 691/585 = 1 106/585

Step 6: Decimal & Percentage Representation
Dividing the numerator 691 by denominator 585 produces a repeating decimal (approximately 1.181197, or 118.1197%).
Working: 691 ÷ 585 = 1.181197 (118.1197%)

Key Values:
- Simplified Fraction: 691/585
- Mixed Number Form: 1 106/585
- Decimal Value: 1.181197
- Percentage: 118.1197%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-22-45-plus-9-13/
==================================================

22/45 + 9/13 = 691/585

Simplified Fraction

691/585

Mixed Number

1 106/585

Decimal Value

1.181197

Percentage

118.1197%

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: 22/45 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 45 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 45 × 13 = 585.

LCD(45, 13) = 585

Step 2

Convert to Equivalent Fractions with Common Denominator 585

Multiply the numerator and denominator of 22/45 by 13, and multiply the numerator and denominator of 9/13 by 45 so both fractions share the common base 585.

22 × 13/45 × 13 = 286/585 and 9 × 45/13 × 45 = 405/585

Step 3

Add the Numerators

Now add the numerators (286 + 405 = 691) and keep the common denominator 585 unchanged.

286 + 405/585 = 691/585

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 691 and 585 is 1, confirming that 691/585 cannot be reduced further—it is already in its simplest irreducible form.

691/585

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (691) is greater than the denominator (585), divide 691 by 585: it goes in 1 whole time(s) with a remainder of 106, giving the mixed number 1 106/585.

691/585 = 1106/585

Step 6

Decimal & Percentage Representation

Dividing the numerator 691 by denominator 585 produces a repeating decimal (approximately 1.181197, or 118.1197%).

691 ÷ 585 = 1.181197 (118.1197%)

Visual Representation

The diagram below illustrates 22/45 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`691/585`
Mixed Number Form	`1 106/585`
Decimal Form	`1.181197`
Percentage	`118.1197%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 22/45 plus 9/13 as a fraction?

22/45 + 9/13 in simplest fraction form is 691/585 (or 1 106/585 as a mixed number).

What is 22/45 plus 9/13 as a decimal?

22/45 + 9/13 converted to a decimal is 1.181197.

What is 22/45 plus 9/13 as a percentage?

22/45 + 9/13 expressed as a percentage is 118.1197%.

How do you write 22/45 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 691/585 can be written as the mixed number 1 106/585.

Does 22/45 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.181197...) because the denominator contains prime factors other than 2 and 5.