What is 21/36 plus 15/21? (Answer: 109/84)

Exact Answer

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Problem: What is 21/36 plus 15/21?
Formula / Expression: 21/36 + 15/21
Final Answer: 1 25/84 (109/84)
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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 21/36 by 7, and multiply the numerator and denominator of 15/21 by 12 so both fractions share the common base 252.
Working: 21 × 7/36 × 7 = 147/252 and 15 × 12/21 × 12 = 180/252

Step 3: Add the Numerators
Now add the numerators (147 + 180 = 327) and keep the common denominator 252 unchanged.
Working: 147 + 180/252 = 327/252

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 327 and 252, which is 3. Divide both the numerator and denominator by 3.
Working: 327 ÷ 3/252 ÷ 3 = 109/84

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (109) is greater than the denominator (84), divide 109 by 84: it goes in 1 whole time(s) with a remainder of 25, giving the mixed number 1 25/84.
Working: 109/84 = 1 25/84

Step 6: Decimal & Percentage Representation
Dividing the numerator 109 by denominator 84 produces a repeating decimal (approximately 1.297619, or 129.7619%).
Working: 109 ÷ 84 = 1.297619 (129.7619%)

Key Values:
- Simplified Fraction: 109/84
- Mixed Number Form: 1 25/84
- Decimal Value: 1.297619
- Percentage: 129.7619%

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21/36 + 15/21 = 109/84

Simplified Fraction

109/84

Mixed Number

1 25/84

Decimal Value

1.297619

Percentage

129.7619%

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

21 × 7/36 × 7 = 147/252 and 15 × 12/21 × 12 = 180/252

Step 3

Add the Numerators

Now add the numerators (147 + 180 = 327) and keep the common denominator 252 unchanged.

147 + 180/252 = 327/252

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 327 and 252, which is 3. Divide both the numerator and denominator by 3.

327 ÷ 3/252 ÷ 3 = 109/84

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (109) is greater than the denominator (84), divide 109 by 84: it goes in 1 whole time(s) with a remainder of 25, giving the mixed number 1 25/84.

109/84 = 125/84

Step 6

Decimal & Percentage Representation

Dividing the numerator 109 by denominator 84 produces a repeating decimal (approximately 1.297619, or 129.7619%).

109 ÷ 84 = 1.297619 (129.7619%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`109/84`
Mixed Number Form	`1 25/84`
Decimal Form	`1.297619`
Percentage	`129.7619%`

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Frequently Asked Questions

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

21/36 + 15/21 in simplest fraction form is 109/84 (or 1 25/84 as a mixed number).

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

21/36 + 15/21 converted to a decimal is 1.297619.

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

21/36 + 15/21 expressed as a percentage is 129.7619%.

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

Because the numerator is greater than the denominator, the improper fraction 109/84 can be written as the mixed number 1 25/84.

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

It results in a repeating decimal (approximately 1.297619...) because the denominator contains prime factors other than 2 and 5.