What is 13/33 plus 10/21? (Answer: 67/77)

Exact Answer

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Problem: What is 13/33 plus 10/21?
Formula / Expression: 13/33 + 10/21
Final Answer: 67/77
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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 13/33 by 7, and multiply the numerator and denominator of 10/21 by 11 so both fractions share the common base 231.
Working: 13 × 7/33 × 7 = 91/231 and 10 × 11/21 × 11 = 110/231

Step 3: Add the Numerators
Now add the numerators (91 + 110 = 201) and keep the common denominator 231 unchanged.
Working: 91 + 110/231 = 201/231

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 201 and 231, which is 3. Divide both the numerator and denominator by 3.
Working: 201 ÷ 3/231 ÷ 3 = 67/77

Step 5: Decimal & Percentage Representation
Dividing the numerator 67 by denominator 77 produces a repeating decimal (approximately 0.87013, or 87.013%).
Working: 67 ÷ 77 = 0.87013 (87.013%)

Key Values:
- Simplified Fraction: 67/77
- Mixed Number Form: 67/77
- Decimal Value: 0.87013
- Percentage: 87.013%

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Solved with FractionsCalc:
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13/33 + 10/21 = 67/77

Simplified Fraction

67/77

Mixed Number

Proper (67/77)

Decimal Value

0.87013

Percentage

87.013%

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Step-by-Step Solution: 13/33 + 10/21

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 13/33 by 7, and multiply the numerator and denominator of 10/21 by 11 so both fractions share the common base 231.

13 × 7/33 × 7 = 91/231 and 10 × 11/21 × 11 = 110/231

Step 3

Add the Numerators

Now add the numerators (91 + 110 = 201) and keep the common denominator 231 unchanged.

91 + 110/231 = 201/231

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 201 and 231, which is 3. Divide both the numerator and denominator by 3.

201 ÷ 3/231 ÷ 3 = 67/77

Step 5

Decimal & Percentage Representation

Dividing the numerator 67 by denominator 77 produces a repeating decimal (approximately 0.87013, or 87.013%).

67 ÷ 77 = 0.87013 (87.013%)

Visual Representation

The diagram below illustrates 13/33 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`67/77`
Mixed Number Form	`67/77`
Decimal Form	`0.87013`
Percentage	`87.013%`

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Frequently Asked Questions

What is 13/33 plus 10/21 as a fraction?

13/33 + 10/21 in simplest fraction form is 67/77.

What is 13/33 plus 10/21 as a decimal?

13/33 + 10/21 converted to a decimal is 0.87013.

What is 13/33 plus 10/21 as a percentage?

13/33 + 10/21 expressed as a percentage is 87.013%.

Does 13/33 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.87013...) because the denominator contains prime factors other than 2 and 5.