What is 9/33 plus 15/21? (Answer: 76/77)

Exact Answer

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Problem: What is 9/33 plus 15/21?
Formula / Expression: 9/33 + 15/21
Final Answer: 76/77
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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 9/33 by 7, and multiply the numerator and denominator of 15/21 by 11 so both fractions share the common base 231.
Working: 9 × 7/33 × 7 = 63/231 and 15 × 11/21 × 11 = 165/231

Step 3: Add the Numerators
Now add the numerators (63 + 165 = 228) and keep the common denominator 231 unchanged.
Working: 63 + 165/231 = 228/231

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 228 and 231, which is 3. Divide both the numerator and denominator by 3.
Working: 228 ÷ 3/231 ÷ 3 = 76/77

Step 5: Decimal & Percentage Representation
Dividing the numerator 76 by denominator 77 produces a repeating decimal (approximately 0.987013, or 98.7013%).
Working: 76 ÷ 77 = 0.987013 (98.7013%)

Key Values:
- Simplified Fraction: 76/77
- Mixed Number Form: 76/77
- Decimal Value: 0.987013
- Percentage: 98.7013%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-33-plus-15-21/
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9/33 + 15/21 = 76/77

Simplified Fraction

76/77

Mixed Number

Proper (76/77)

Decimal Value

0.987013

Percentage

98.7013%

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Step-by-Step Solution: 9/33 + 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 9/33 by 7, and multiply the numerator and denominator of 15/21 by 11 so both fractions share the common base 231.

9 × 7/33 × 7 = 63/231 and 15 × 11/21 × 11 = 165/231

Step 3

Add the Numerators

Now add the numerators (63 + 165 = 228) and keep the common denominator 231 unchanged.

63 + 165/231 = 228/231

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 228 and 231, which is 3. Divide both the numerator and denominator by 3.

228 ÷ 3/231 ÷ 3 = 76/77

Step 5

Decimal & Percentage Representation

Dividing the numerator 76 by denominator 77 produces a repeating decimal (approximately 0.987013, or 98.7013%).

76 ÷ 77 = 0.987013 (98.7013%)

Visual Representation

The diagram below illustrates 9/33 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`76/77`
Mixed Number Form	`76/77`
Decimal Form	`0.987013`
Percentage	`98.7013%`

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Frequently Asked Questions

What is 9/33 plus 15/21 as a fraction?

9/33 + 15/21 in simplest fraction form is 76/77.

What is 9/33 plus 15/21 as a decimal?

9/33 + 15/21 converted to a decimal is 0.987013.

What is 9/33 plus 15/21 as a percentage?

9/33 + 15/21 expressed as a percentage is 98.7013%.

Does 9/33 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.987013...) because the denominator contains prime factors other than 2 and 5.