What is 17/33 plus 11/21? (Answer: 80/77)

Exact Answer

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Problem: What is 17/33 plus 11/21?
Formula / Expression: 17/33 + 11/21
Final Answer: 1 3/77 (80/77)
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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 17/33 by 7, and multiply the numerator and denominator of 11/21 by 11 so both fractions share the common base 231.
Working: 17 × 7/33 × 7 = 119/231 and 11 × 11/21 × 11 = 121/231

Step 3: Add the Numerators
Now add the numerators (119 + 121 = 240) and keep the common denominator 231 unchanged.
Working: 119 + 121/231 = 240/231

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 240 and 231, which is 3. Divide both the numerator and denominator by 3.
Working: 240 ÷ 3/231 ÷ 3 = 80/77

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (80) is greater than the denominator (77), divide 80 by 77: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/77.
Working: 80/77 = 1 3/77

Step 6: Decimal & Percentage Representation
Dividing the numerator 80 by denominator 77 produces a repeating decimal (approximately 1.038961, or 103.8961%).
Working: 80 ÷ 77 = 1.038961 (103.8961%)

Key Values:
- Simplified Fraction: 80/77
- Mixed Number Form: 1 3/77
- Decimal Value: 1.038961
- Percentage: 103.8961%

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Solved with FractionsCalc:
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17/33 + 11/21 = 80/77

Simplified Fraction

80/77

Mixed Number

1 3/77

Decimal Value

1.038961

Percentage

103.8961%

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Step-by-Step Solution: 17/33 + 11/21

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 17/33 by 7, and multiply the numerator and denominator of 11/21 by 11 so both fractions share the common base 231.

17 × 7/33 × 7 = 119/231 and 11 × 11/21 × 11 = 121/231

Step 3

Add the Numerators

Now add the numerators (119 + 121 = 240) and keep the common denominator 231 unchanged.

119 + 121/231 = 240/231

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 240 and 231, which is 3. Divide both the numerator and denominator by 3.

240 ÷ 3/231 ÷ 3 = 80/77

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (80) is greater than the denominator (77), divide 80 by 77: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/77.

80/77 = 13/77

Step 6

Decimal & Percentage Representation

Dividing the numerator 80 by denominator 77 produces a repeating decimal (approximately 1.038961, or 103.8961%).

80 ÷ 77 = 1.038961 (103.8961%)

Visual Representation

The diagram below illustrates 17/33 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`80/77`
Mixed Number Form	`1 3/77`
Decimal Form	`1.038961`
Percentage	`103.8961%`

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Frequently Asked Questions

What is 17/33 plus 11/21 as a fraction?

17/33 + 11/21 in simplest fraction form is 80/77 (or 1 3/77 as a mixed number).

What is 17/33 plus 11/21 as a decimal?

17/33 + 11/21 converted to a decimal is 1.038961.

What is 17/33 plus 11/21 as a percentage?

17/33 + 11/21 expressed as a percentage is 103.8961%.

How do you write 17/33 plus 11/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 80/77 can be written as the mixed number 1 3/77.

Does 17/33 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.038961...) because the denominator contains prime factors other than 2 and 5.