What is 10/52 plus 8/13? (Answer: 21/26)

Exact Answer

==================================================
Problem: What is 10/52 plus 8/13?
Formula / Expression: 10/52 + 8/13
Final Answer: 21/26
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 52 is an exact multiple of 13 (13 × 4 = 52). The Least Common Denominator (LCD) is simply 52, meaning we only need to scale one fraction.
Working: LCD(52, 13) = 52

Step 2: Convert to Equivalent Fractions with Common Denominator 52
Multiply the numerator and denominator of 10/52 by 1, and multiply the numerator and denominator of 8/13 by 4 so both fractions share the common base 52.
Working: 10 × 1/52 × 1 = 10/52 and 8 × 4/13 × 4 = 32/52

Step 3: Add the Numerators
Now add the numerators (10 + 32 = 42) and keep the common denominator 52 unchanged.
Working: 10 + 32/52 = 42/52

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 42 and 52, which is 2. Divide both the numerator and denominator by 2.
Working: 42 ÷ 2/52 ÷ 2 = 21/26

Step 5: Decimal & Percentage Representation
Dividing the numerator 21 by denominator 26 produces a repeating decimal (approximately 0.807692, or 80.7692%).
Working: 21 ÷ 26 = 0.807692 (80.7692%)

Key Values:
- Simplified Fraction: 21/26
- Mixed Number Form: 21/26
- Decimal Value: 0.807692
- Percentage: 80.7692%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-52-plus-8-13/
==================================================

10/52 + 8/13 = 21/26

Simplified Fraction

21/26

Mixed Number

Proper (21/26)

Decimal Value

0.807692

Percentage

80.7692%

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: 10/52 + 8/13

Step 1

Find the Least Common Denominator (LCD)

Notice that 52 is an exact multiple of 13 (13 × 4 = 52). The Least Common Denominator (LCD) is simply 52, meaning we only need to scale one fraction.

LCD(52, 13) = 52

Step 2

Convert to Equivalent Fractions with Common Denominator 52

Multiply the numerator and denominator of 10/52 by 1, and multiply the numerator and denominator of 8/13 by 4 so both fractions share the common base 52.

10 × 1/52 × 1 = 10/52 and 8 × 4/13 × 4 = 32/52

Step 3

Add the Numerators

Now add the numerators (10 + 32 = 42) and keep the common denominator 52 unchanged.

10 + 32/52 = 42/52

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 42 and 52, which is 2. Divide both the numerator and denominator by 2.

42 ÷ 2/52 ÷ 2 = 21/26

Step 5

Decimal & Percentage Representation

Dividing the numerator 21 by denominator 26 produces a repeating decimal (approximately 0.807692, or 80.7692%).

21 ÷ 26 = 0.807692 (80.7692%)

Visual Representation

The diagram below illustrates 10/52 plus 8/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`21/26`
Mixed Number Form	`21/26`
Decimal Form	`0.807692`
Percentage	`80.7692%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 10/52 plus 8/13 as a fraction?

10/52 + 8/13 in simplest fraction form is 21/26.

What is 10/52 plus 8/13 as a decimal?

10/52 + 8/13 converted to a decimal is 0.807692.

What is 10/52 plus 8/13 as a percentage?

10/52 + 8/13 expressed as a percentage is 80.7692%.

Does 10/52 plus 8/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.807692...) because the denominator contains prime factors other than 2 and 5.