What is 22/36 plus 15/21? (Answer: 167/126)

Exact Answer

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Problem: What is 22/36 plus 15/21?
Formula / Expression: 22/36 + 15/21
Final Answer: 1 41/126 (167/126)
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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 22/36 by 7, and multiply the numerator and denominator of 15/21 by 12 so both fractions share the common base 252.
Working: 22 × 7/36 × 7 = 154/252 and 15 × 12/21 × 12 = 180/252

Step 3: Add the Numerators
Now add the numerators (154 + 180 = 334) and keep the common denominator 252 unchanged.
Working: 154 + 180/252 = 334/252

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 334 and 252, which is 2. Divide both the numerator and denominator by 2.
Working: 334 ÷ 2/252 ÷ 2 = 167/126

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (167) is greater than the denominator (126), divide 167 by 126: it goes in 1 whole time(s) with a remainder of 41, giving the mixed number 1 41/126.
Working: 167/126 = 1 41/126

Step 6: Decimal & Percentage Representation
Dividing the numerator 167 by denominator 126 produces a repeating decimal (approximately 1.325397, or 132.5397%).
Working: 167 ÷ 126 = 1.325397 (132.5397%)

Key Values:
- Simplified Fraction: 167/126
- Mixed Number Form: 1 41/126
- Decimal Value: 1.325397
- Percentage: 132.5397%

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Solved with FractionsCalc:
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22/36 + 15/21 = 167/126

Simplified Fraction

167/126

Mixed Number

1 41/126

Decimal Value

1.325397

Percentage

132.5397%

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Step-by-Step Solution: 22/36 + 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 22/36 by 7, and multiply the numerator and denominator of 15/21 by 12 so both fractions share the common base 252.

22 × 7/36 × 7 = 154/252 and 15 × 12/21 × 12 = 180/252

Step 3

Add the Numerators

Now add the numerators (154 + 180 = 334) and keep the common denominator 252 unchanged.

154 + 180/252 = 334/252

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 334 and 252, which is 2. Divide both the numerator and denominator by 2.

334 ÷ 2/252 ÷ 2 = 167/126

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (167) is greater than the denominator (126), divide 167 by 126: it goes in 1 whole time(s) with a remainder of 41, giving the mixed number 1 41/126.

167/126 = 141/126

Step 6

Decimal & Percentage Representation

Dividing the numerator 167 by denominator 126 produces a repeating decimal (approximately 1.325397, or 132.5397%).

167 ÷ 126 = 1.325397 (132.5397%)

Visual Representation

The diagram below illustrates 22/36 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`167/126`
Mixed Number Form	`1 41/126`
Decimal Form	`1.325397`
Percentage	`132.5397%`

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Frequently Asked Questions

What is 22/36 plus 15/21 as a fraction?

22/36 + 15/21 in simplest fraction form is 167/126 (or 1 41/126 as a mixed number).

What is 22/36 plus 15/21 as a decimal?

22/36 + 15/21 converted to a decimal is 1.325397.

What is 22/36 plus 15/21 as a percentage?

22/36 + 15/21 expressed as a percentage is 132.5397%.

How do you write 22/36 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 167/126 can be written as the mixed number 1 41/126.

Does 22/36 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.325397...) because the denominator contains prime factors other than 2 and 5.