What is 9/40 plus 5/21? (Answer: 389/840)

Exact Answer

==================================================
Problem: What is 9/40 plus 5/21?
Formula / Expression: 9/40 + 5/21
Final Answer: 389/840
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 40 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 21 = 840.
Working: LCD(40, 21) = 840

Step 2: Convert to Equivalent Fractions with Common Denominator 840
Multiply the numerator and denominator of 9/40 by 21, and multiply the numerator and denominator of 5/21 by 40 so both fractions share the common base 840.
Working: 9 × 21/40 × 21 = 189/840 and 5 × 40/21 × 40 = 200/840

Step 3: Add the Numerators
Now add the numerators (189 + 200 = 389) and keep the common denominator 840 unchanged.
Working: 189 + 200/840 = 389/840

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 389 and 840 is 1, confirming that 389/840 cannot be reduced further—it is already in its simplest irreducible form.
Working: 389/840

Step 5: Decimal & Percentage Representation
Dividing the numerator 389 by denominator 840 produces a repeating decimal (approximately 0.463095, or 46.3095%).
Working: 389 ÷ 840 = 0.463095 (46.3095%)

Key Values:
- Simplified Fraction: 389/840
- Mixed Number Form: 389/840
- Decimal Value: 0.463095
- Percentage: 46.3095%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-40-plus-5-21/
==================================================

9/40 + 5/21 = 389/840

Simplified Fraction

389/840

Mixed Number

Proper (389/840)

Decimal Value

0.463095

Percentage

46.3095%

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: 9/40 + 5/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 40 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 21 = 840.

LCD(40, 21) = 840

Step 2

Convert to Equivalent Fractions with Common Denominator 840

Multiply the numerator and denominator of 9/40 by 21, and multiply the numerator and denominator of 5/21 by 40 so both fractions share the common base 840.

9 × 21/40 × 21 = 189/840 and 5 × 40/21 × 40 = 200/840

Step 3

Add the Numerators

Now add the numerators (189 + 200 = 389) and keep the common denominator 840 unchanged.

189 + 200/840 = 389/840

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 389 and 840 is 1, confirming that 389/840 cannot be reduced further—it is already in its simplest irreducible form.

389/840

Step 5

Decimal & Percentage Representation

Dividing the numerator 389 by denominator 840 produces a repeating decimal (approximately 0.463095, or 46.3095%).

389 ÷ 840 = 0.463095 (46.3095%)

Visual Representation

The diagram below illustrates 9/40 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`389/840`
Mixed Number Form	`389/840`
Decimal Form	`0.463095`
Percentage	`46.3095%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 9/40 plus 5/21 as a fraction?

9/40 + 5/21 in simplest fraction form is 389/840.

What is 9/40 plus 5/21 as a decimal?

9/40 + 5/21 converted to a decimal is 0.463095.

What is 9/40 plus 5/21 as a percentage?

9/40 + 5/21 expressed as a percentage is 46.3095%.

Does 9/40 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.463095...) because the denominator contains prime factors other than 2 and 5.