What is 8/36 plus 9/21? (Answer: 41/63)

Exact Answer

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Problem: What is 8/36 plus 9/21?
Formula / Expression: 8/36 + 9/21
Final Answer: 41/63
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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 8/36 by 7, and multiply the numerator and denominator of 9/21 by 12 so both fractions share the common base 252.
Working: 8 × 7/36 × 7 = 56/252 and 9 × 12/21 × 12 = 108/252

Step 3: Add the Numerators
Now add the numerators (56 + 108 = 164) and keep the common denominator 252 unchanged.
Working: 56 + 108/252 = 164/252

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 164 and 252, which is 4. Divide both the numerator and denominator by 4.
Working: 164 ÷ 4/252 ÷ 4 = 41/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 63 produces a repeating decimal (approximately 0.650794, or 65.0794%).
Working: 41 ÷ 63 = 0.650794 (65.0794%)

Key Values:
- Simplified Fraction: 41/63
- Mixed Number Form: 41/63
- Decimal Value: 0.650794
- Percentage: 65.0794%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-36-plus-9-21/
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8/36 + 9/21 = 41/63

Simplified Fraction

41/63

Mixed Number

Proper (41/63)

Decimal Value

0.650794

Percentage

65.0794%

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Step-by-Step Solution: 8/36 + 9/21

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 8/36 by 7, and multiply the numerator and denominator of 9/21 by 12 so both fractions share the common base 252.

8 × 7/36 × 7 = 56/252 and 9 × 12/21 × 12 = 108/252

Step 3

Add the Numerators

Now add the numerators (56 + 108 = 164) and keep the common denominator 252 unchanged.

56 + 108/252 = 164/252

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 164 and 252, which is 4. Divide both the numerator and denominator by 4.

164 ÷ 4/252 ÷ 4 = 41/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 63 produces a repeating decimal (approximately 0.650794, or 65.0794%).

41 ÷ 63 = 0.650794 (65.0794%)

Visual Representation

The diagram below illustrates 8/36 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/63`
Mixed Number Form	`41/63`
Decimal Form	`0.650794`
Percentage	`65.0794%`

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Frequently Asked Questions

What is 8/36 plus 9/21 as a fraction?

8/36 + 9/21 in simplest fraction form is 41/63.

What is 8/36 plus 9/21 as a decimal?

8/36 + 9/21 converted to a decimal is 0.650794.

What is 8/36 plus 9/21 as a percentage?

8/36 + 9/21 expressed as a percentage is 65.0794%.

Does 8/36 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.650794...) because the denominator contains prime factors other than 2 and 5.