What is 21/40 plus 9/13? (Answer: 633/520)

Exact Answer

==================================================
Problem: What is 21/40 plus 9/13?
Formula / Expression: 21/40 + 9/13
Final Answer: 1 113/520 (633/520)
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 40 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 13 = 520.
Working: LCD(40, 13) = 520

Step 2: Convert to Equivalent Fractions with Common Denominator 520
Multiply the numerator and denominator of 21/40 by 13, and multiply the numerator and denominator of 9/13 by 40 so both fractions share the common base 520.
Working: 21 × 13/40 × 13 = 273/520 and 9 × 40/13 × 40 = 360/520

Step 3: Add the Numerators
Now add the numerators (273 + 360 = 633) and keep the common denominator 520 unchanged.
Working: 273 + 360/520 = 633/520

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 633 and 520 is 1, confirming that 633/520 cannot be reduced further—it is already in its simplest irreducible form.
Working: 633/520

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (633) is greater than the denominator (520), divide 633 by 520: it goes in 1 whole time(s) with a remainder of 113, giving the mixed number 1 113/520.
Working: 633/520 = 1 113/520

Step 6: Decimal & Percentage Representation
Dividing the numerator 633 by denominator 520 produces a repeating decimal (approximately 1.217308, or 121.7308%).
Working: 633 ÷ 520 = 1.217308 (121.7308%)

Key Values:
- Simplified Fraction: 633/520
- Mixed Number Form: 1 113/520
- Decimal Value: 1.217308
- Percentage: 121.7308%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-21-40-plus-9-13/
==================================================

21/40 + 9/13 = 633/520

Simplified Fraction

633/520

Mixed Number

1 113/520

Decimal Value

1.217308

Percentage

121.7308%

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: 21/40 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 40 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 13 = 520.

LCD(40, 13) = 520

Step 2

Convert to Equivalent Fractions with Common Denominator 520

Multiply the numerator and denominator of 21/40 by 13, and multiply the numerator and denominator of 9/13 by 40 so both fractions share the common base 520.

21 × 13/40 × 13 = 273/520 and 9 × 40/13 × 40 = 360/520

Step 3

Add the Numerators

Now add the numerators (273 + 360 = 633) and keep the common denominator 520 unchanged.

273 + 360/520 = 633/520

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 633 and 520 is 1, confirming that 633/520 cannot be reduced further—it is already in its simplest irreducible form.

633/520

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (633) is greater than the denominator (520), divide 633 by 520: it goes in 1 whole time(s) with a remainder of 113, giving the mixed number 1 113/520.

633/520 = 1113/520

Step 6

Decimal & Percentage Representation

Dividing the numerator 633 by denominator 520 produces a repeating decimal (approximately 1.217308, or 121.7308%).

633 ÷ 520 = 1.217308 (121.7308%)

Visual Representation

The diagram below illustrates 21/40 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`633/520`
Mixed Number Form	`1 113/520`
Decimal Form	`1.217308`
Percentage	`121.7308%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 21/40 plus 9/13 as a fraction?

21/40 + 9/13 in simplest fraction form is 633/520 (or 1 113/520 as a mixed number).

What is 21/40 plus 9/13 as a decimal?

21/40 + 9/13 converted to a decimal is 1.217308.

What is 21/40 plus 9/13 as a percentage?

21/40 + 9/13 expressed as a percentage is 121.7308%.

How do you write 21/40 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 633/520 can be written as the mixed number 1 113/520.

Does 21/40 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.217308...) because the denominator contains prime factors other than 2 and 5.