What is 18/35 plus 12/21? (Answer: 38/35)

Exact Answer

==================================================
Problem: What is 18/35 plus 12/21?
Formula / Expression: 18/35 + 12/21
Final Answer: 1 3/35 (38/35)
==================================================

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 18/35 by 3, and multiply the numerator and denominator of 12/21 by 5 so both fractions share the common base 105.
Working: 18 × 3/35 × 3 = 54/105 and 12 × 5/21 × 5 = 60/105

Step 3: Add the Numerators
Now add the numerators (54 + 60 = 114) and keep the common denominator 105 unchanged.
Working: 54 + 60/105 = 114/105

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 114 and 105, which is 3. Divide both the numerator and denominator by 3.
Working: 114 ÷ 3/105 ÷ 3 = 38/35

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (38) is greater than the denominator (35), divide 38 by 35: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/35.
Working: 38/35 = 1 3/35

Step 6: Decimal & Percentage Representation
Dividing the numerator 38 by denominator 35 produces a repeating decimal (approximately 1.085714, or 108.5714%).
Working: 38 ÷ 35 = 1.085714 (108.5714%)

Key Values:
- Simplified Fraction: 38/35
- Mixed Number Form: 1 3/35
- Decimal Value: 1.085714
- Percentage: 108.5714%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-18-35-plus-12-21/
==================================================

18/35 + 12/21 = 38/35

Simplified Fraction

38/35

Mixed Number

1 3/35

Decimal Value

1.085714

Percentage

108.5714%

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: 18/35 + 12/21

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 18/35 by 3, and multiply the numerator and denominator of 12/21 by 5 so both fractions share the common base 105.

18 × 3/35 × 3 = 54/105 and 12 × 5/21 × 5 = 60/105

Step 3

Add the Numerators

Now add the numerators (54 + 60 = 114) and keep the common denominator 105 unchanged.

54 + 60/105 = 114/105

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 114 and 105, which is 3. Divide both the numerator and denominator by 3.

114 ÷ 3/105 ÷ 3 = 38/35

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (38) is greater than the denominator (35), divide 38 by 35: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/35.

38/35 = 13/35

Step 6

Decimal & Percentage Representation

Dividing the numerator 38 by denominator 35 produces a repeating decimal (approximately 1.085714, or 108.5714%).

38 ÷ 35 = 1.085714 (108.5714%)

Visual Representation

The diagram below illustrates 18/35 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`38/35`
Mixed Number Form	`1 3/35`
Decimal Form	`1.085714`
Percentage	`108.5714%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 18/35 plus 12/21 as a fraction?

18/35 + 12/21 in simplest fraction form is 38/35 (or 1 3/35 as a mixed number).

What is 18/35 plus 12/21 as a decimal?

18/35 + 12/21 converted to a decimal is 1.085714.

What is 18/35 plus 12/21 as a percentage?

18/35 + 12/21 expressed as a percentage is 108.5714%.

How do you write 18/35 plus 12/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 38/35 can be written as the mixed number 1 3/35.

Does 18/35 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.085714...) because the denominator contains prime factors other than 2 and 5.