What is 24/45 plus 12/21? (Answer: 116/105)

Exact Answer

==================================================
Problem: What is 24/45 plus 12/21?
Formula / Expression: 24/45 + 12/21
Final Answer: 1 11/105 (116/105)
==================================================

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 24/45 by 7, and multiply the numerator and denominator of 12/21 by 15 so both fractions share the common base 315.
Working: 24 × 7/45 × 7 = 168/315 and 12 × 15/21 × 15 = 180/315

Step 3: Add the Numerators
Now add the numerators (168 + 180 = 348) and keep the common denominator 315 unchanged.
Working: 168 + 180/315 = 348/315

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 348 and 315, which is 3. Divide both the numerator and denominator by 3.
Working: 348 ÷ 3/315 ÷ 3 = 116/105

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (116) is greater than the denominator (105), divide 116 by 105: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/105.
Working: 116/105 = 1 11/105

Step 6: Decimal & Percentage Representation
Dividing the numerator 116 by denominator 105 produces a repeating decimal (approximately 1.104762, or 110.4762%).
Working: 116 ÷ 105 = 1.104762 (110.4762%)

Key Values:
- Simplified Fraction: 116/105
- Mixed Number Form: 1 11/105
- Decimal Value: 1.104762
- Percentage: 110.4762%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-24-45-plus-12-21/
==================================================

24/45 + 12/21 = 116/105

Simplified Fraction

116/105

Mixed Number

1 11/105

Decimal Value

1.104762

Percentage

110.4762%

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: 24/45 + 12/21

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 24/45 by 7, and multiply the numerator and denominator of 12/21 by 15 so both fractions share the common base 315.

24 × 7/45 × 7 = 168/315 and 12 × 15/21 × 15 = 180/315

Step 3

Add the Numerators

Now add the numerators (168 + 180 = 348) and keep the common denominator 315 unchanged.

168 + 180/315 = 348/315

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 348 and 315, which is 3. Divide both the numerator and denominator by 3.

348 ÷ 3/315 ÷ 3 = 116/105

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (116) is greater than the denominator (105), divide 116 by 105: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/105.

116/105 = 111/105

Step 6

Decimal & Percentage Representation

Dividing the numerator 116 by denominator 105 produces a repeating decimal (approximately 1.104762, or 110.4762%).

116 ÷ 105 = 1.104762 (110.4762%)

Visual Representation

The diagram below illustrates 24/45 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`116/105`
Mixed Number Form	`1 11/105`
Decimal Form	`1.104762`
Percentage	`110.4762%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 24/45 plus 12/21 as a fraction?

24/45 + 12/21 in simplest fraction form is 116/105 (or 1 11/105 as a mixed number).

What is 24/45 plus 12/21 as a decimal?

24/45 + 12/21 converted to a decimal is 1.104762.

What is 24/45 plus 12/21 as a percentage?

24/45 + 12/21 expressed as a percentage is 110.4762%.

How do you write 24/45 plus 12/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 116/105 can be written as the mixed number 1 11/105.

Does 24/45 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.104762...) because the denominator contains prime factors other than 2 and 5.