What is 13/36 plus 10/21? (Answer: 211/252)

Exact Answer

==================================================
Problem: What is 13/36 plus 10/21?
Formula / Expression: 13/36 + 10/21
Final Answer: 211/252
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 36 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 252 (which is smaller than their product 36 × 21 = 756, keeping the calculation simpler).
Working: LCD(36, 21) = 252

Step 2: Convert to Equivalent Fractions with Common Denominator 252
Multiply the numerator and denominator of 13/36 by 7, and multiply the numerator and denominator of 10/21 by 12 so both fractions share the common base 252.
Working: 13 × 7/36 × 7 = 91/252 and 10 × 12/21 × 12 = 120/252

Step 3: Add the Numerators
Now add the numerators (91 + 120 = 211) and keep the common denominator 252 unchanged.
Working: 91 + 120/252 = 211/252

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 211 and 252 is 1, confirming that 211/252 cannot be reduced further—it is already in its simplest irreducible form.
Working: 211/252

Step 5: Decimal & Percentage Representation
Dividing the numerator 211 by denominator 252 produces a repeating decimal (approximately 0.837302, or 83.7302%).
Working: 211 ÷ 252 = 0.837302 (83.7302%)

Key Values:
- Simplified Fraction: 211/252
- Mixed Number Form: 211/252
- Decimal Value: 0.837302
- Percentage: 83.7302%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-36-plus-10-21/
==================================================

13/36 + 10/21 = 211/252

Simplified Fraction

211/252

Mixed Number

Proper (211/252)

Decimal Value

0.837302

Percentage

83.7302%

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: 13/36 + 10/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 36 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 252 (which is smaller than their product 36 × 21 = 756, keeping the calculation simpler).

LCD(36, 21) = 252

Step 2

Convert to Equivalent Fractions with Common Denominator 252

Multiply the numerator and denominator of 13/36 by 7, and multiply the numerator and denominator of 10/21 by 12 so both fractions share the common base 252.

13 × 7/36 × 7 = 91/252 and 10 × 12/21 × 12 = 120/252

Step 3

Add the Numerators

Now add the numerators (91 + 120 = 211) and keep the common denominator 252 unchanged.

91 + 120/252 = 211/252

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 211 and 252 is 1, confirming that 211/252 cannot be reduced further—it is already in its simplest irreducible form.

211/252

Step 5

Decimal & Percentage Representation

Dividing the numerator 211 by denominator 252 produces a repeating decimal (approximately 0.837302, or 83.7302%).

211 ÷ 252 = 0.837302 (83.7302%)

Visual Representation

The diagram below illustrates 13/36 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`211/252`
Mixed Number Form	`211/252`
Decimal Form	`0.837302`
Percentage	`83.7302%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 13/36 plus 10/21 as a fraction?

13/36 + 10/21 in simplest fraction form is 211/252.

What is 13/36 plus 10/21 as a decimal?

13/36 + 10/21 converted to a decimal is 0.837302.

What is 13/36 plus 10/21 as a percentage?

13/36 + 10/21 expressed as a percentage is 83.7302%.

Does 13/36 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.837302...) because the denominator contains prime factors other than 2 and 5.