What is 18/45 plus 9/21? (Answer: 29/35)

Exact Answer

==================================================
Problem: What is 18/45 plus 9/21?
Formula / Expression: 18/45 + 9/21
Final Answer: 29/35
==================================================

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 18/45 by 7, and multiply the numerator and denominator of 9/21 by 15 so both fractions share the common base 315.
Working: 18 × 7/45 × 7 = 126/315 and 9 × 15/21 × 15 = 135/315

Step 3: Add the Numerators
Now add the numerators (126 + 135 = 261) and keep the common denominator 315 unchanged.
Working: 126 + 135/315 = 261/315

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 261 and 315, which is 9. Divide both the numerator and denominator by 9.
Working: 261 ÷ 9/315 ÷ 9 = 29/35

Step 5: Decimal & Percentage Representation
Dividing the numerator 29 by denominator 35 produces a repeating decimal (approximately 0.828571, or 82.8571%).
Working: 29 ÷ 35 = 0.828571 (82.8571%)

Key Values:
- Simplified Fraction: 29/35
- Mixed Number Form: 29/35
- Decimal Value: 0.828571
- Percentage: 82.8571%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-18-45-plus-9-21/
==================================================

18/45 + 9/21 = 29/35

Simplified Fraction

29/35

Mixed Number

Proper (29/35)

Decimal Value

0.828571

Percentage

82.8571%

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: 18/45 + 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 18/45 by 7, and multiply the numerator and denominator of 9/21 by 15 so both fractions share the common base 315.

18 × 7/45 × 7 = 126/315 and 9 × 15/21 × 15 = 135/315

Step 3

Add the Numerators

Now add the numerators (126 + 135 = 261) and keep the common denominator 315 unchanged.

126 + 135/315 = 261/315

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 261 and 315, which is 9. Divide both the numerator and denominator by 9.

261 ÷ 9/315 ÷ 9 = 29/35

Step 5

Decimal & Percentage Representation

Dividing the numerator 29 by denominator 35 produces a repeating decimal (approximately 0.828571, or 82.8571%).

29 ÷ 35 = 0.828571 (82.8571%)

Visual Representation

The diagram below illustrates 18/45 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`29/35`
Mixed Number Form	`29/35`
Decimal Form	`0.828571`
Percentage	`82.8571%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 18/45 plus 9/21 as a fraction?

18/45 + 9/21 in simplest fraction form is 29/35.

What is 18/45 plus 9/21 as a decimal?

18/45 + 9/21 converted to a decimal is 0.828571.

What is 18/45 plus 9/21 as a percentage?

18/45 + 9/21 expressed as a percentage is 82.8571%.

Does 18/45 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.828571...) because the denominator contains prime factors other than 2 and 5.