What is 13/45 plus 9/21? (Answer: 226/315)

Exact Answer

==================================================
Problem: What is 13/45 plus 9/21?
Formula / Expression: 13/45 + 9/21
Final Answer: 226/315
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 45 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 315 (which is smaller than their product 45 × 21 = 945, keeping the calculation simpler).
Working: LCD(45, 21) = 315

Step 2: Convert to Equivalent Fractions with Common Denominator 315
Multiply the numerator and denominator of 13/45 by 7, and multiply the numerator and denominator of 9/21 by 15 so both fractions share the common base 315.
Working: 13 × 7/45 × 7 = 91/315 and 9 × 15/21 × 15 = 135/315

Step 3: Add the Numerators
Now add the numerators (91 + 135 = 226) and keep the common denominator 315 unchanged.
Working: 91 + 135/315 = 226/315

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 226 and 315 is 1, confirming that 226/315 cannot be reduced further—it is already in its simplest irreducible form.
Working: 226/315

Step 5: Decimal & Percentage Representation
Dividing the numerator 226 by denominator 315 produces a repeating decimal (approximately 0.71746, or 71.746%).
Working: 226 ÷ 315 = 0.71746 (71.746%)

Key Values:
- Simplified Fraction: 226/315
- Mixed Number Form: 226/315
- Decimal Value: 0.71746
- Percentage: 71.746%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-45-plus-9-21/
==================================================

13/45 + 9/21 = 226/315

Simplified Fraction

226/315

Mixed Number

Proper (226/315)

Decimal Value

0.71746

Percentage

71.746%

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: 13/45 + 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 45 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 315 (which is smaller than their product 45 × 21 = 945, keeping the calculation simpler).

LCD(45, 21) = 315

Step 2

Convert to Equivalent Fractions with Common Denominator 315

Multiply the numerator and denominator of 13/45 by 7, and multiply the numerator and denominator of 9/21 by 15 so both fractions share the common base 315.

13 × 7/45 × 7 = 91/315 and 9 × 15/21 × 15 = 135/315

Step 3

Add the Numerators

Now add the numerators (91 + 135 = 226) and keep the common denominator 315 unchanged.

91 + 135/315 = 226/315

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 226 and 315 is 1, confirming that 226/315 cannot be reduced further—it is already in its simplest irreducible form.

226/315

Step 5

Decimal & Percentage Representation

Dividing the numerator 226 by denominator 315 produces a repeating decimal (approximately 0.71746, or 71.746%).

226 ÷ 315 = 0.71746 (71.746%)

Visual Representation

The diagram below illustrates 13/45 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`226/315`
Mixed Number Form	`226/315`
Decimal Form	`0.71746`
Percentage	`71.746%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 13/45 plus 9/21 as a fraction?

13/45 + 9/21 in simplest fraction form is 226/315.

What is 13/45 plus 9/21 as a decimal?

13/45 + 9/21 converted to a decimal is 0.71746.

What is 13/45 plus 9/21 as a percentage?

13/45 + 9/21 expressed as a percentage is 71.746%.

Does 13/45 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.71746...) because the denominator contains prime factors other than 2 and 5.