What is 18/36 plus 15/21? (Answer: 17/14)

Exact Answer

==================================================
Problem: What is 18/36 plus 15/21?
Formula / Expression: 18/36 + 15/21
Final Answer: 1 3/14 (17/14)
==================================================

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 18/36 by 7, and multiply the numerator and denominator of 15/21 by 12 so both fractions share the common base 252.
Working: 18 × 7/36 × 7 = 126/252 and 15 × 12/21 × 12 = 180/252

Step 3: Add the Numerators
Now add the numerators (126 + 180 = 306) and keep the common denominator 252 unchanged.
Working: 126 + 180/252 = 306/252

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 306 and 252, which is 18. Divide both the numerator and denominator by 18.
Working: 306 ÷ 18/252 ÷ 18 = 17/14

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (17) is greater than the denominator (14), divide 17 by 14: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/14.
Working: 17/14 = 1 3/14

Step 6: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 14 produces a repeating decimal (approximately 1.214286, or 121.4286%).
Working: 17 ÷ 14 = 1.214286 (121.4286%)

Key Values:
- Simplified Fraction: 17/14
- Mixed Number Form: 1 3/14
- Decimal Value: 1.214286
- Percentage: 121.4286%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-18-36-plus-15-21/
==================================================

18/36 + 15/21 = 17/14

Simplified Fraction

17/14

Mixed Number

1 3/14

Decimal Value

1.214286

Percentage

121.4286%

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: 18/36 + 15/21

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 18/36 by 7, and multiply the numerator and denominator of 15/21 by 12 so both fractions share the common base 252.

18 × 7/36 × 7 = 126/252 and 15 × 12/21 × 12 = 180/252

Step 3

Add the Numerators

Now add the numerators (126 + 180 = 306) and keep the common denominator 252 unchanged.

126 + 180/252 = 306/252

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 306 and 252, which is 18. Divide both the numerator and denominator by 18.

306 ÷ 18/252 ÷ 18 = 17/14

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (17) is greater than the denominator (14), divide 17 by 14: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/14.

17/14 = 13/14

Step 6

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 14 produces a repeating decimal (approximately 1.214286, or 121.4286%).

17 ÷ 14 = 1.214286 (121.4286%)

Visual Representation

The diagram below illustrates 18/36 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/14`
Mixed Number Form	`1 3/14`
Decimal Form	`1.214286`
Percentage	`121.4286%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 18/36 plus 15/21 as a fraction?

18/36 + 15/21 in simplest fraction form is 17/14 (or 1 3/14 as a mixed number).

What is 18/36 plus 15/21 as a decimal?

18/36 + 15/21 converted to a decimal is 1.214286.

What is 18/36 plus 15/21 as a percentage?

18/36 + 15/21 expressed as a percentage is 121.4286%.

How do you write 18/36 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 17/14 can be written as the mixed number 1 3/14.

Does 18/36 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.214286...) because the denominator contains prime factors other than 2 and 5.