What is 1/4 plus 11/21? (Answer: 65/84)

Exact Answer

==================================================
Problem: What is 1/4 plus 11/21?
Formula / Expression: 1/4 + 11/21
Final Answer: 65/84
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 4 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 4 × 21 = 84.
Working: LCD(4, 21) = 84

Step 2: Convert to Equivalent Fractions with Common Denominator 84
Multiply the numerator and denominator of 1/4 by 21, and multiply the numerator and denominator of 11/21 by 4 so both fractions share the common base 84.
Working: 1 × 21/4 × 21 = 21/84 and 11 × 4/21 × 4 = 44/84

Step 3: Add the Numerators
Now add the numerators (21 + 44 = 65) and keep the common denominator 84 unchanged.
Working: 21 + 44/84 = 65/84

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 65 and 84 is 1, confirming that 65/84 cannot be reduced further—it is already in its simplest irreducible form.
Working: 65/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 65 by denominator 84 produces a repeating decimal (approximately 0.77381, or 77.381%).
Working: 65 ÷ 84 = 0.77381 (77.381%)

Key Values:
- Simplified Fraction: 65/84
- Mixed Number Form: 65/84
- Decimal Value: 0.77381
- Percentage: 77.381%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-4-plus-11-21/
==================================================

1/4 + 11/21 = 65/84

Simplified Fraction

65/84

Mixed Number

Proper (65/84)

Decimal Value

0.77381

Percentage

77.381%

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: 1/4 + 11/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 4 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 4 × 21 = 84.

LCD(4, 21) = 84

Step 2

Convert to Equivalent Fractions with Common Denominator 84

Multiply the numerator and denominator of 1/4 by 21, and multiply the numerator and denominator of 11/21 by 4 so both fractions share the common base 84.

1 × 21/4 × 21 = 21/84 and 11 × 4/21 × 4 = 44/84

Step 3

Add the Numerators

Now add the numerators (21 + 44 = 65) and keep the common denominator 84 unchanged.

21 + 44/84 = 65/84

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 65 and 84 is 1, confirming that 65/84 cannot be reduced further—it is already in its simplest irreducible form.

65/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 65 by denominator 84 produces a repeating decimal (approximately 0.77381, or 77.381%).

65 ÷ 84 = 0.77381 (77.381%)

Visual Representation

The diagram below illustrates 1/4 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`65/84`
Mixed Number Form	`65/84`
Decimal Form	`0.77381`
Percentage	`77.381%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 1/4 plus 11/21 as a fraction?

1/4 + 11/21 in simplest fraction form is 65/84.

What is 1/4 plus 11/21 as a decimal?

1/4 + 11/21 converted to a decimal is 0.77381.

What is 1/4 plus 11/21 as a percentage?

1/4 + 11/21 expressed as a percentage is 77.381%.

Does 1/4 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.77381...) because the denominator contains prime factors other than 2 and 5.