What is 9/36 plus 15/21? (Answer: 27/28)

Exact Answer

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Problem: What is 9/36 plus 15/21?
Formula / Expression: 9/36 + 15/21
Final Answer: 27/28
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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 9/36 by 7, and multiply the numerator and denominator of 15/21 by 12 so both fractions share the common base 252.
Working: 9 × 7/36 × 7 = 63/252 and 15 × 12/21 × 12 = 180/252

Step 3: Add the Numerators
Now add the numerators (63 + 180 = 243) and keep the common denominator 252 unchanged.
Working: 63 + 180/252 = 243/252

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 243 and 252, which is 9. Divide both the numerator and denominator by 9.
Working: 243 ÷ 9/252 ÷ 9 = 27/28

Step 5: Decimal & Percentage Representation
Dividing the numerator 27 by denominator 28 produces a repeating decimal (approximately 0.964286, or 96.4286%).
Working: 27 ÷ 28 = 0.964286 (96.4286%)

Key Values:
- Simplified Fraction: 27/28
- Mixed Number Form: 27/28
- Decimal Value: 0.964286
- Percentage: 96.4286%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-36-plus-15-21/
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9/36 + 15/21 = 27/28

Simplified Fraction

27/28

Mixed Number

Proper (27/28)

Decimal Value

0.964286

Percentage

96.4286%

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Step-by-Step Solution: 9/36 + 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 9/36 by 7, and multiply the numerator and denominator of 15/21 by 12 so both fractions share the common base 252.

9 × 7/36 × 7 = 63/252 and 15 × 12/21 × 12 = 180/252

Step 3

Add the Numerators

Now add the numerators (63 + 180 = 243) and keep the common denominator 252 unchanged.

63 + 180/252 = 243/252

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 243 and 252, which is 9. Divide both the numerator and denominator by 9.

243 ÷ 9/252 ÷ 9 = 27/28

Step 5

Decimal & Percentage Representation

Dividing the numerator 27 by denominator 28 produces a repeating decimal (approximately 0.964286, or 96.4286%).

27 ÷ 28 = 0.964286 (96.4286%)

Visual Representation

The diagram below illustrates 9/36 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`27/28`
Mixed Number Form	`27/28`
Decimal Form	`0.964286`
Percentage	`96.4286%`

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Frequently Asked Questions

What is 9/36 plus 15/21 as a fraction?

9/36 + 15/21 in simplest fraction form is 27/28.

What is 9/36 plus 15/21 as a decimal?

9/36 + 15/21 converted to a decimal is 0.964286.

What is 9/36 plus 15/21 as a percentage?

9/36 + 15/21 expressed as a percentage is 96.4286%.

Does 9/36 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.964286...) because the denominator contains prime factors other than 2 and 5.