What is 7/14 plus 11/21? (Answer: 43/42)

Exact Answer

==================================================
Problem: What is 7/14 plus 11/21?
Formula / Expression: 7/14 + 11/21
Final Answer: 1 1/42 (43/42)
==================================================

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 7/14 by 3, and multiply the numerator and denominator of 11/21 by 2 so both fractions share the common base 42.
Working: 7 × 3/14 × 3 = 21/42 and 11 × 2/21 × 2 = 22/42

Step 3: Add the Numerators
Now add the numerators (21 + 22 = 43) and keep the common denominator 42 unchanged.
Working: 21 + 22/42 = 43/42

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 43 and 42 is 1, confirming that 43/42 cannot be reduced further—it is already in its simplest irreducible form.
Working: 43/42

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (43) is greater than the denominator (42), divide 43 by 42: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/42.
Working: 43/42 = 1 1/42

Step 6: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 42 produces a repeating decimal (approximately 1.02381, or 102.381%).
Working: 43 ÷ 42 = 1.02381 (102.381%)

Key Values:
- Simplified Fraction: 43/42
- Mixed Number Form: 1 1/42
- Decimal Value: 1.02381
- Percentage: 102.381%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-14-plus-11-21/
==================================================

7/14 + 11/21 = 43/42

Simplified Fraction

43/42

Mixed Number

1 1/42

Decimal Value

1.02381

Percentage

102.381%

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: 7/14 + 11/21

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 7/14 by 3, and multiply the numerator and denominator of 11/21 by 2 so both fractions share the common base 42.

7 × 3/14 × 3 = 21/42 and 11 × 2/21 × 2 = 22/42

Step 3

Add the Numerators

Now add the numerators (21 + 22 = 43) and keep the common denominator 42 unchanged.

21 + 22/42 = 43/42

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 43 and 42 is 1, confirming that 43/42 cannot be reduced further—it is already in its simplest irreducible form.

43/42

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (43) is greater than the denominator (42), divide 43 by 42: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/42.

43/42 = 11/42

Step 6

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 42 produces a repeating decimal (approximately 1.02381, or 102.381%).

43 ÷ 42 = 1.02381 (102.381%)

Visual Representation

The diagram below illustrates 7/14 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/42`
Mixed Number Form	`1 1/42`
Decimal Form	`1.02381`
Percentage	`102.381%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 7/14 plus 11/21 as a fraction?

7/14 + 11/21 in simplest fraction form is 43/42 (or 1 1/42 as a mixed number).

What is 7/14 plus 11/21 as a decimal?

7/14 + 11/21 converted to a decimal is 1.02381.

What is 7/14 plus 11/21 as a percentage?

7/14 + 11/21 expressed as a percentage is 102.381%.

How do you write 7/14 plus 11/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 43/42 can be written as the mixed number 1 1/42.

Does 7/14 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.02381...) because the denominator contains prime factors other than 2 and 5.