What is 5/14 plus 9/21? (Answer: 11/14)

Exact Answer

==================================================
Problem: What is 5/14 plus 9/21?
Formula / Expression: 5/14 + 9/21
Final Answer: 11/14
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 14 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 42 (which is smaller than their product 14 × 21 = 294, keeping the calculation simpler).
Working: LCD(14, 21) = 42

Step 2: Convert to Equivalent Fractions with Common Denominator 42
Multiply the numerator and denominator of 5/14 by 3, and multiply the numerator and denominator of 9/21 by 2 so both fractions share the common base 42.
Working: 5 × 3/14 × 3 = 15/42 and 9 × 2/21 × 2 = 18/42

Step 3: Add the Numerators
Now add the numerators (15 + 18 = 33) and keep the common denominator 42 unchanged.
Working: 15 + 18/42 = 33/42

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 33 and 42, which is 3. Divide both the numerator and denominator by 3.
Working: 33 ÷ 3/42 ÷ 3 = 11/14

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 14 produces a repeating decimal (approximately 0.785714, or 78.5714%).
Working: 11 ÷ 14 = 0.785714 (78.5714%)

Key Values:
- Simplified Fraction: 11/14
- Mixed Number Form: 11/14
- Decimal Value: 0.785714
- Percentage: 78.5714%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-14-plus-9-21/
==================================================

5/14 + 9/21 = 11/14

Simplified Fraction

11/14

Mixed Number

Proper (11/14)

Decimal Value

0.785714

Percentage

78.5714%

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: 5/14 + 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 14 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 42 (which is smaller than their product 14 × 21 = 294, keeping the calculation simpler).

LCD(14, 21) = 42

Step 2

Convert to Equivalent Fractions with Common Denominator 42

Multiply the numerator and denominator of 5/14 by 3, and multiply the numerator and denominator of 9/21 by 2 so both fractions share the common base 42.

5 × 3/14 × 3 = 15/42 and 9 × 2/21 × 2 = 18/42

Step 3

Add the Numerators

Now add the numerators (15 + 18 = 33) and keep the common denominator 42 unchanged.

15 + 18/42 = 33/42

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 33 and 42, which is 3. Divide both the numerator and denominator by 3.

33 ÷ 3/42 ÷ 3 = 11/14

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 14 produces a repeating decimal (approximately 0.785714, or 78.5714%).

11 ÷ 14 = 0.785714 (78.5714%)

Visual Representation

The diagram below illustrates 5/14 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/14`
Mixed Number Form	`11/14`
Decimal Form	`0.785714`
Percentage	`78.5714%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 5/14 plus 9/21 as a fraction?

5/14 + 9/21 in simplest fraction form is 11/14.

What is 5/14 plus 9/21 as a decimal?

5/14 + 9/21 converted to a decimal is 0.785714.

What is 5/14 plus 9/21 as a percentage?

5/14 + 9/21 expressed as a percentage is 78.5714%.

Does 5/14 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.785714...) because the denominator contains prime factors other than 2 and 5.