What is 14/52 plus 7/21? (Answer: 47/78)

Exact Answer

==================================================
Problem: What is 14/52 plus 7/21?
Formula / Expression: 14/52 + 7/21
Final Answer: 47/78
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 52 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 52 × 21 = 1092.
Working: LCD(52, 21) = 1092

Step 2: Convert to Equivalent Fractions with Common Denominator 1092
Multiply the numerator and denominator of 14/52 by 21, and multiply the numerator and denominator of 7/21 by 52 so both fractions share the common base 1092.
Working: 14 × 21/52 × 21 = 294/1092 and 7 × 52/21 × 52 = 364/1092

Step 3: Add the Numerators
Now add the numerators (294 + 364 = 658) and keep the common denominator 1092 unchanged.
Working: 294 + 364/1092 = 658/1092

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 658 and 1092, which is 14. Divide both the numerator and denominator by 14.
Working: 658 ÷ 14/1092 ÷ 14 = 47/78

Step 5: Decimal & Percentage Representation
Dividing the numerator 47 by denominator 78 produces a repeating decimal (approximately 0.602564, or 60.2564%).
Working: 47 ÷ 78 = 0.602564 (60.2564%)

Key Values:
- Simplified Fraction: 47/78
- Mixed Number Form: 47/78
- Decimal Value: 0.602564
- Percentage: 60.2564%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-14-52-plus-7-21/
==================================================

14/52 + 7/21 = 47/78

Simplified Fraction

47/78

Mixed Number

Proper (47/78)

Decimal Value

0.602564

Percentage

60.2564%

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: 14/52 + 7/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 52 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 52 × 21 = 1092.

LCD(52, 21) = 1092

Step 2

Convert to Equivalent Fractions with Common Denominator 1092

Multiply the numerator and denominator of 14/52 by 21, and multiply the numerator and denominator of 7/21 by 52 so both fractions share the common base 1092.

14 × 21/52 × 21 = 294/1092 and 7 × 52/21 × 52 = 364/1092

Step 3

Add the Numerators

Now add the numerators (294 + 364 = 658) and keep the common denominator 1092 unchanged.

294 + 364/1092 = 658/1092

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 658 and 1092, which is 14. Divide both the numerator and denominator by 14.

658 ÷ 14/1092 ÷ 14 = 47/78

Step 5

Decimal & Percentage Representation

Dividing the numerator 47 by denominator 78 produces a repeating decimal (approximately 0.602564, or 60.2564%).

47 ÷ 78 = 0.602564 (60.2564%)

Visual Representation

The diagram below illustrates 14/52 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`47/78`
Mixed Number Form	`47/78`
Decimal Form	`0.602564`
Percentage	`60.2564%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 14/52 plus 7/21 as a fraction?

14/52 + 7/21 in simplest fraction form is 47/78.

What is 14/52 plus 7/21 as a decimal?

14/52 + 7/21 converted to a decimal is 0.602564.

What is 14/52 plus 7/21 as a percentage?

14/52 + 7/21 expressed as a percentage is 60.2564%.

Does 14/52 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.602564...) because the denominator contains prime factors other than 2 and 5.