What is 4/24 plus 10/21? (Answer: 9/14)

Exact Answer

==================================================
Problem: What is 4/24 plus 10/21?
Formula / Expression: 4/24 + 10/21
Final Answer: 9/14
==================================================

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 4/24 by 7, and multiply the numerator and denominator of 10/21 by 8 so both fractions share the common base 168.
Working: 4 × 7/24 × 7 = 28/168 and 10 × 8/21 × 8 = 80/168

Step 3: Add the Numerators
Now add the numerators (28 + 80 = 108) and keep the common denominator 168 unchanged.
Working: 28 + 80/168 = 108/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 108 and 168, which is 12. Divide both the numerator and denominator by 12.
Working: 108 ÷ 12/168 ÷ 12 = 9/14

Step 5: Decimal & Percentage Representation
Dividing the numerator 9 by denominator 14 produces a repeating decimal (approximately 0.642857, or 64.2857%).
Working: 9 ÷ 14 = 0.642857 (64.2857%)

Key Values:
- Simplified Fraction: 9/14
- Mixed Number Form: 9/14
- Decimal Value: 0.642857
- Percentage: 64.2857%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-24-plus-10-21/
==================================================

4/24 + 10/21 = 9/14

Simplified Fraction

9/14

Mixed Number

Proper (9/14)

Decimal Value

0.642857

Percentage

64.2857%

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: 4/24 + 10/21

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 4/24 by 7, and multiply the numerator and denominator of 10/21 by 8 so both fractions share the common base 168.

4 × 7/24 × 7 = 28/168 and 10 × 8/21 × 8 = 80/168

Step 3

Add the Numerators

Now add the numerators (28 + 80 = 108) and keep the common denominator 168 unchanged.

28 + 80/168 = 108/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 108 and 168, which is 12. Divide both the numerator and denominator by 12.

108 ÷ 12/168 ÷ 12 = 9/14

Step 5

Decimal & Percentage Representation

Dividing the numerator 9 by denominator 14 produces a repeating decimal (approximately 0.642857, or 64.2857%).

9 ÷ 14 = 0.642857 (64.2857%)

Visual Representation

The diagram below illustrates 4/24 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`9/14`
Mixed Number Form	`9/14`
Decimal Form	`0.642857`
Percentage	`64.2857%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 4/24 plus 10/21 as a fraction?

4/24 + 10/21 in simplest fraction form is 9/14.

What is 4/24 plus 10/21 as a decimal?

4/24 + 10/21 converted to a decimal is 0.642857.

What is 4/24 plus 10/21 as a percentage?

4/24 + 10/21 expressed as a percentage is 64.2857%.

Does 4/24 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.642857...) because the denominator contains prime factors other than 2 and 5.