What is 7/36 plus 2/9? (Answer: 5/12)

Exact Answer

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Problem: What is 7/36 plus 2/9?
Formula / Expression: 7/36 + 2/9
Final Answer: 5/12
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 36 is an exact multiple of 9 (9 × 4 = 36). The Least Common Denominator (LCD) is simply 36, meaning we only need to scale one fraction.
Working: LCD(36, 9) = 36

Step 2: Convert to Equivalent Fractions with Common Denominator 36
Multiply the numerator and denominator of 7/36 by 1, and multiply the numerator and denominator of 2/9 by 4 so both fractions share the common base 36.
Working: 7 × 1/36 × 1 = 7/36 and 2 × 4/9 × 4 = 8/36

Step 3: Add the Numerators
Now add the numerators (7 + 8 = 15) and keep the common denominator 36 unchanged.
Working: 7 + 8/36 = 15/36

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 15 and 36, which is 3. Divide both the numerator and denominator by 3.
Working: 15 ÷ 3/36 ÷ 3 = 5/12

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 12 produces a repeating decimal (approximately 0.416667, or 41.6667%).
Working: 5 ÷ 12 = 0.416667 (41.6667%)

Key Values:
- Simplified Fraction: 5/12
- Mixed Number Form: 5/12
- Decimal Value: 0.416667
- Percentage: 41.6667%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-36-plus-2-9/
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7/36 + 2/9 = 5/12

Simplified Fraction

5/12

Mixed Number

Proper (5/12)

Decimal Value

0.416667

Percentage

41.6667%

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Step-by-Step Solution: 7/36 + 2/9

Step 1

Find the Least Common Denominator (LCD)

Notice that 36 is an exact multiple of 9 (9 × 4 = 36). The Least Common Denominator (LCD) is simply 36, meaning we only need to scale one fraction.

LCD(36, 9) = 36

Step 2

Convert to Equivalent Fractions with Common Denominator 36

Multiply the numerator and denominator of 7/36 by 1, and multiply the numerator and denominator of 2/9 by 4 so both fractions share the common base 36.

7 × 1/36 × 1 = 7/36 and 2 × 4/9 × 4 = 8/36

Step 3

Add the Numerators

Now add the numerators (7 + 8 = 15) and keep the common denominator 36 unchanged.

7 + 8/36 = 15/36

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 15 and 36, which is 3. Divide both the numerator and denominator by 3.

15 ÷ 3/36 ÷ 3 = 5/12

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 12 produces a repeating decimal (approximately 0.416667, or 41.6667%).

5 ÷ 12 = 0.416667 (41.6667%)

Visual Representation

The diagram below illustrates 7/36 plus 2/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/12`
Mixed Number Form	`5/12`
Decimal Form	`0.416667`
Percentage	`41.6667%`

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Frequently Asked Questions

What is 7/36 plus 2/9 as a fraction?

7/36 + 2/9 in simplest fraction form is 5/12.

What is 7/36 plus 2/9 as a decimal?

7/36 + 2/9 converted to a decimal is 0.416667.

What is 7/36 plus 2/9 as a percentage?

7/36 + 2/9 expressed as a percentage is 41.6667%.

Does 7/36 plus 2/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.416667...) because the denominator contains prime factors other than 2 and 5.