What is 14/24 plus 15/21? (Answer: 109/84)

Exact Answer

==================================================
Problem: What is 14/24 plus 15/21?
Formula / Expression: 14/24 + 15/21
Final Answer: 1 25/84 (109/84)
==================================================

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 14/24 by 7, and multiply the numerator and denominator of 15/21 by 8 so both fractions share the common base 168.
Working: 14 × 7/24 × 7 = 98/168 and 15 × 8/21 × 8 = 120/168

Step 3: Add the Numerators
Now add the numerators (98 + 120 = 218) and keep the common denominator 168 unchanged.
Working: 98 + 120/168 = 218/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 218 and 168, which is 2. Divide both the numerator and denominator by 2.
Working: 218 ÷ 2/168 ÷ 2 = 109/84

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (109) is greater than the denominator (84), divide 109 by 84: it goes in 1 whole time(s) with a remainder of 25, giving the mixed number 1 25/84.
Working: 109/84 = 1 25/84

Step 6: Decimal & Percentage Representation
Dividing the numerator 109 by denominator 84 produces a repeating decimal (approximately 1.297619, or 129.7619%).
Working: 109 ÷ 84 = 1.297619 (129.7619%)

Key Values:
- Simplified Fraction: 109/84
- Mixed Number Form: 1 25/84
- Decimal Value: 1.297619
- Percentage: 129.7619%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-14-24-plus-15-21/
==================================================

14/24 + 15/21 = 109/84

Simplified Fraction

109/84

Mixed Number

1 25/84

Decimal Value

1.297619

Percentage

129.7619%

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: 14/24 + 15/21

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 14/24 by 7, and multiply the numerator and denominator of 15/21 by 8 so both fractions share the common base 168.

14 × 7/24 × 7 = 98/168 and 15 × 8/21 × 8 = 120/168

Step 3

Add the Numerators

Now add the numerators (98 + 120 = 218) and keep the common denominator 168 unchanged.

98 + 120/168 = 218/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 218 and 168, which is 2. Divide both the numerator and denominator by 2.

218 ÷ 2/168 ÷ 2 = 109/84

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (109) is greater than the denominator (84), divide 109 by 84: it goes in 1 whole time(s) with a remainder of 25, giving the mixed number 1 25/84.

109/84 = 125/84

Step 6

Decimal & Percentage Representation

Dividing the numerator 109 by denominator 84 produces a repeating decimal (approximately 1.297619, or 129.7619%).

109 ÷ 84 = 1.297619 (129.7619%)

Visual Representation

The diagram below illustrates 14/24 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`109/84`
Mixed Number Form	`1 25/84`
Decimal Form	`1.297619`
Percentage	`129.7619%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 14/24 plus 15/21 as a fraction?

14/24 + 15/21 in simplest fraction form is 109/84 (or 1 25/84 as a mixed number).

What is 14/24 plus 15/21 as a decimal?

14/24 + 15/21 converted to a decimal is 1.297619.

What is 14/24 plus 15/21 as a percentage?

14/24 + 15/21 expressed as a percentage is 129.7619%.

How do you write 14/24 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 109/84 can be written as the mixed number 1 25/84.

Does 14/24 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.297619...) because the denominator contains prime factors other than 2 and 5.