What is 21/33 plus 15/21? (Answer: 104/77)

Exact Answer

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Problem: What is 21/33 plus 15/21?
Formula / Expression: 21/33 + 15/21
Final Answer: 1 27/77 (104/77)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 33 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 231 (which is smaller than their product 33 × 21 = 693, keeping the calculation simpler).
Working: LCD(33, 21) = 231

Step 2: Convert to Equivalent Fractions with Common Denominator 231
Multiply the numerator and denominator of 21/33 by 7, and multiply the numerator and denominator of 15/21 by 11 so both fractions share the common base 231.
Working: 21 × 7/33 × 7 = 147/231 and 15 × 11/21 × 11 = 165/231

Step 3: Add the Numerators
Now add the numerators (147 + 165 = 312) and keep the common denominator 231 unchanged.
Working: 147 + 165/231 = 312/231

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 312 and 231, which is 3. Divide both the numerator and denominator by 3.
Working: 312 ÷ 3/231 ÷ 3 = 104/77

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (104) is greater than the denominator (77), divide 104 by 77: it goes in 1 whole time(s) with a remainder of 27, giving the mixed number 1 27/77.
Working: 104/77 = 1 27/77

Step 6: Decimal & Percentage Representation
Dividing the numerator 104 by denominator 77 produces a repeating decimal (approximately 1.350649, or 135.0649%).
Working: 104 ÷ 77 = 1.350649 (135.0649%)

Key Values:
- Simplified Fraction: 104/77
- Mixed Number Form: 1 27/77
- Decimal Value: 1.350649
- Percentage: 135.0649%

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Solved with FractionsCalc:
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21/33 + 15/21 = 104/77

Simplified Fraction

104/77

Mixed Number

1 27/77

Decimal Value

1.350649

Percentage

135.0649%

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Step-by-Step Solution: 21/33 + 15/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 33 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 231 (which is smaller than their product 33 × 21 = 693, keeping the calculation simpler).

LCD(33, 21) = 231

Step 2

Convert to Equivalent Fractions with Common Denominator 231

Multiply the numerator and denominator of 21/33 by 7, and multiply the numerator and denominator of 15/21 by 11 so both fractions share the common base 231.

21 × 7/33 × 7 = 147/231 and 15 × 11/21 × 11 = 165/231

Step 3

Add the Numerators

Now add the numerators (147 + 165 = 312) and keep the common denominator 231 unchanged.

147 + 165/231 = 312/231

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 312 and 231, which is 3. Divide both the numerator and denominator by 3.

312 ÷ 3/231 ÷ 3 = 104/77

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (104) is greater than the denominator (77), divide 104 by 77: it goes in 1 whole time(s) with a remainder of 27, giving the mixed number 1 27/77.

104/77 = 127/77

Step 6

Decimal & Percentage Representation

Dividing the numerator 104 by denominator 77 produces a repeating decimal (approximately 1.350649, or 135.0649%).

104 ÷ 77 = 1.350649 (135.0649%)

Visual Representation

The diagram below illustrates 21/33 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`104/77`
Mixed Number Form	`1 27/77`
Decimal Form	`1.350649`
Percentage	`135.0649%`

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Frequently Asked Questions

What is 21/33 plus 15/21 as a fraction?

21/33 + 15/21 in simplest fraction form is 104/77 (or 1 27/77 as a mixed number).

What is 21/33 plus 15/21 as a decimal?

21/33 + 15/21 converted to a decimal is 1.350649.

What is 21/33 plus 15/21 as a percentage?

21/33 + 15/21 expressed as a percentage is 135.0649%.

How do you write 21/33 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 104/77 can be written as the mixed number 1 27/77.

Does 21/33 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.350649...) because the denominator contains prime factors other than 2 and 5.