What is 3/36 plus 15/21? (Answer: 67/84)

Exact Answer

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Problem: What is 3/36 plus 15/21?
Formula / Expression: 3/36 + 15/21
Final Answer: 67/84
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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 3/36 by 7, and multiply the numerator and denominator of 15/21 by 12 so both fractions share the common base 252.
Working: 3 × 7/36 × 7 = 21/252 and 15 × 12/21 × 12 = 180/252

Step 3: Add the Numerators
Now add the numerators (21 + 180 = 201) and keep the common denominator 252 unchanged.
Working: 21 + 180/252 = 201/252

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 201 and 252, which is 3. Divide both the numerator and denominator by 3.
Working: 201 ÷ 3/252 ÷ 3 = 67/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 67 by denominator 84 produces a repeating decimal (approximately 0.797619, or 79.7619%).
Working: 67 ÷ 84 = 0.797619 (79.7619%)

Key Values:
- Simplified Fraction: 67/84
- Mixed Number Form: 67/84
- Decimal Value: 0.797619
- Percentage: 79.7619%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-36-plus-15-21/
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3/36 + 15/21 = 67/84

Simplified Fraction

67/84

Mixed Number

Proper (67/84)

Decimal Value

0.797619

Percentage

79.7619%

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Step-by-Step Solution: 3/36 + 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 3/36 by 7, and multiply the numerator and denominator of 15/21 by 12 so both fractions share the common base 252.

3 × 7/36 × 7 = 21/252 and 15 × 12/21 × 12 = 180/252

Step 3

Add the Numerators

Now add the numerators (21 + 180 = 201) and keep the common denominator 252 unchanged.

21 + 180/252 = 201/252

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 201 and 252, which is 3. Divide both the numerator and denominator by 3.

201 ÷ 3/252 ÷ 3 = 67/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 67 by denominator 84 produces a repeating decimal (approximately 0.797619, or 79.7619%).

67 ÷ 84 = 0.797619 (79.7619%)

Visual Representation

The diagram below illustrates 3/36 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`67/84`
Mixed Number Form	`67/84`
Decimal Form	`0.797619`
Percentage	`79.7619%`

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Frequently Asked Questions

What is 3/36 plus 15/21 as a fraction?

3/36 + 15/21 in simplest fraction form is 67/84.

What is 3/36 plus 15/21 as a decimal?

3/36 + 15/21 converted to a decimal is 0.797619.

What is 3/36 plus 15/21 as a percentage?

3/36 + 15/21 expressed as a percentage is 79.7619%.

Does 3/36 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.797619...) because the denominator contains prime factors other than 2 and 5.