What is 12/35 plus 11/21? (Answer: 13/15)

Exact Answer

==================================================
Problem: What is 12/35 plus 11/21?
Formula / Expression: 12/35 + 11/21
Final Answer: 13/15
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 35 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 35 × 21 = 735, keeping the calculation simpler).
Working: LCD(35, 21) = 105

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 12/35 by 3, and multiply the numerator and denominator of 11/21 by 5 so both fractions share the common base 105.
Working: 12 × 3/35 × 3 = 36/105 and 11 × 5/21 × 5 = 55/105

Step 3: Add the Numerators
Now add the numerators (36 + 55 = 91) and keep the common denominator 105 unchanged.
Working: 36 + 55/105 = 91/105

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 91 and 105, which is 7. Divide both the numerator and denominator by 7.
Working: 91 ÷ 7/105 ÷ 7 = 13/15

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 15 produces a repeating decimal (approximately 0.866667, or 86.6667%).
Working: 13 ÷ 15 = 0.866667 (86.6667%)

Key Values:
- Simplified Fraction: 13/15
- Mixed Number Form: 13/15
- Decimal Value: 0.866667
- Percentage: 86.6667%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-12-35-plus-11-21/
==================================================

12/35 + 11/21 = 13/15

Simplified Fraction

13/15

Mixed Number

Proper (13/15)

Decimal Value

0.866667

Percentage

86.6667%

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: 12/35 + 11/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 35 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 35 × 21 = 735, keeping the calculation simpler).

LCD(35, 21) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 12/35 by 3, and multiply the numerator and denominator of 11/21 by 5 so both fractions share the common base 105.

12 × 3/35 × 3 = 36/105 and 11 × 5/21 × 5 = 55/105

Step 3

Add the Numerators

Now add the numerators (36 + 55 = 91) and keep the common denominator 105 unchanged.

36 + 55/105 = 91/105

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 91 and 105, which is 7. Divide both the numerator and denominator by 7.

91 ÷ 7/105 ÷ 7 = 13/15

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 15 produces a repeating decimal (approximately 0.866667, or 86.6667%).

13 ÷ 15 = 0.866667 (86.6667%)

Visual Representation

The diagram below illustrates 12/35 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/15`
Mixed Number Form	`13/15`
Decimal Form	`0.866667`
Percentage	`86.6667%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 12/35 plus 11/21 as a fraction?

12/35 + 11/21 in simplest fraction form is 13/15.

What is 12/35 plus 11/21 as a decimal?

12/35 + 11/21 converted to a decimal is 0.866667.

What is 12/35 plus 11/21 as a percentage?

12/35 + 11/21 expressed as a percentage is 86.6667%.

Does 12/35 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.866667...) because the denominator contains prime factors other than 2 and 5.