What is 3/24 plus 8/21? (Answer: 85/168)

Exact Answer

==================================================
Problem: What is 3/24 plus 8/21?
Formula / Expression: 3/24 + 8/21
Final Answer: 85/168
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 24 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 168 (which is smaller than their product 24 × 21 = 504, keeping the calculation simpler).
Working: LCD(24, 21) = 168

Step 2: Convert to Equivalent Fractions with Common Denominator 168
Multiply the numerator and denominator of 3/24 by 7, and multiply the numerator and denominator of 8/21 by 8 so both fractions share the common base 168.
Working: 3 × 7/24 × 7 = 21/168 and 8 × 8/21 × 8 = 64/168

Step 3: Add the Numerators
Now add the numerators (21 + 64 = 85) and keep the common denominator 168 unchanged.
Working: 21 + 64/168 = 85/168

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 85 and 168 is 1, confirming that 85/168 cannot be reduced further—it is already in its simplest irreducible form.
Working: 85/168

Step 5: Decimal & Percentage Representation
Dividing the numerator 85 by denominator 168 produces a repeating decimal (approximately 0.505952, or 50.5952%).
Working: 85 ÷ 168 = 0.505952 (50.5952%)

Key Values:
- Simplified Fraction: 85/168
- Mixed Number Form: 85/168
- Decimal Value: 0.505952
- Percentage: 50.5952%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-24-plus-8-21/
==================================================

3/24 + 8/21 = 85/168

Simplified Fraction

85/168

Mixed Number

Proper (85/168)

Decimal Value

0.505952

Percentage

50.5952%

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: 3/24 + 8/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 24 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 168 (which is smaller than their product 24 × 21 = 504, keeping the calculation simpler).

LCD(24, 21) = 168

Step 2

Convert to Equivalent Fractions with Common Denominator 168

Multiply the numerator and denominator of 3/24 by 7, and multiply the numerator and denominator of 8/21 by 8 so both fractions share the common base 168.

3 × 7/24 × 7 = 21/168 and 8 × 8/21 × 8 = 64/168

Step 3

Add the Numerators

Now add the numerators (21 + 64 = 85) and keep the common denominator 168 unchanged.

21 + 64/168 = 85/168

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 85 and 168 is 1, confirming that 85/168 cannot be reduced further—it is already in its simplest irreducible form.

85/168

Step 5

Decimal & Percentage Representation

Dividing the numerator 85 by denominator 168 produces a repeating decimal (approximately 0.505952, or 50.5952%).

85 ÷ 168 = 0.505952 (50.5952%)

Visual Representation

The diagram below illustrates 3/24 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`85/168`
Mixed Number Form	`85/168`
Decimal Form	`0.505952`
Percentage	`50.5952%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 3/24 plus 8/21 as a fraction?

3/24 + 8/21 in simplest fraction form is 85/168.

What is 3/24 plus 8/21 as a decimal?

3/24 + 8/21 converted to a decimal is 0.505952.

What is 3/24 plus 8/21 as a percentage?

3/24 + 8/21 expressed as a percentage is 50.5952%.

Does 3/24 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.505952...) because the denominator contains prime factors other than 2 and 5.