What is 14/27 plus 15/21? (Answer: 233/189)

Exact Answer

==================================================
Problem: What is 14/27 plus 15/21?
Formula / Expression: 14/27 + 15/21
Final Answer: 1 44/189 (233/189)
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 27 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 189 (which is smaller than their product 27 × 21 = 567, keeping the calculation simpler).
Working: LCD(27, 21) = 189

Step 2: Convert to Equivalent Fractions with Common Denominator 189
Multiply the numerator and denominator of 14/27 by 7, and multiply the numerator and denominator of 15/21 by 9 so both fractions share the common base 189.
Working: 14 × 7/27 × 7 = 98/189 and 15 × 9/21 × 9 = 135/189

Step 3: Add the Numerators
Now add the numerators (98 + 135 = 233) and keep the common denominator 189 unchanged.
Working: 98 + 135/189 = 233/189

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 233 and 189 is 1, confirming that 233/189 cannot be reduced further—it is already in its simplest irreducible form.
Working: 233/189

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (233) is greater than the denominator (189), divide 233 by 189: it goes in 1 whole time(s) with a remainder of 44, giving the mixed number 1 44/189.
Working: 233/189 = 1 44/189

Step 6: Decimal & Percentage Representation
Dividing the numerator 233 by denominator 189 produces a repeating decimal (approximately 1.232804, or 123.2804%).
Working: 233 ÷ 189 = 1.232804 (123.2804%)

Key Values:
- Simplified Fraction: 233/189
- Mixed Number Form: 1 44/189
- Decimal Value: 1.232804
- Percentage: 123.2804%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-14-27-plus-15-21/
==================================================

14/27 + 15/21 = 233/189

Simplified Fraction

233/189

Mixed Number

1 44/189

Decimal Value

1.232804

Percentage

123.2804%

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: 14/27 + 15/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 27 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 189 (which is smaller than their product 27 × 21 = 567, keeping the calculation simpler).

LCD(27, 21) = 189

Step 2

Convert to Equivalent Fractions with Common Denominator 189

Multiply the numerator and denominator of 14/27 by 7, and multiply the numerator and denominator of 15/21 by 9 so both fractions share the common base 189.

14 × 7/27 × 7 = 98/189 and 15 × 9/21 × 9 = 135/189

Step 3

Add the Numerators

Now add the numerators (98 + 135 = 233) and keep the common denominator 189 unchanged.

98 + 135/189 = 233/189

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 233 and 189 is 1, confirming that 233/189 cannot be reduced further—it is already in its simplest irreducible form.

233/189

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (233) is greater than the denominator (189), divide 233 by 189: it goes in 1 whole time(s) with a remainder of 44, giving the mixed number 1 44/189.

233/189 = 144/189

Step 6

Decimal & Percentage Representation

Dividing the numerator 233 by denominator 189 produces a repeating decimal (approximately 1.232804, or 123.2804%).

233 ÷ 189 = 1.232804 (123.2804%)

Visual Representation

The diagram below illustrates 14/27 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`233/189`
Mixed Number Form	`1 44/189`
Decimal Form	`1.232804`
Percentage	`123.2804%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 14/27 plus 15/21 as a fraction?

14/27 + 15/21 in simplest fraction form is 233/189 (or 1 44/189 as a mixed number).

What is 14/27 plus 15/21 as a decimal?

14/27 + 15/21 converted to a decimal is 1.232804.

What is 14/27 plus 15/21 as a percentage?

14/27 + 15/21 expressed as a percentage is 123.2804%.

How do you write 14/27 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 233/189 can be written as the mixed number 1 44/189.

Does 14/27 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.232804...) because the denominator contains prime factors other than 2 and 5.