What is 9/33 plus 7/21? (Answer: 20/33)

Exact Answer

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Problem: What is 9/33 plus 7/21?
Formula / Expression: 9/33 + 7/21
Final Answer: 20/33
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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 7/21 by 11 so both fractions share the common base 231.
Working: 9 × 7/33 × 7 = 63/231 and 7 × 11/21 × 11 = 77/231

Step 3: Add the Numerators
Now add the numerators (63 + 77 = 140) and keep the common denominator 231 unchanged.
Working: 63 + 77/231 = 140/231

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 140 and 231, which is 7. Divide both the numerator and denominator by 7.
Working: 140 ÷ 7/231 ÷ 7 = 20/33

Step 5: Decimal & Percentage Representation
Dividing the numerator 20 by denominator 33 produces a repeating decimal (approximately 0.606061, or 60.6061%).
Working: 20 ÷ 33 = 0.606061 (60.6061%)

Key Values:
- Simplified Fraction: 20/33
- Mixed Number Form: 20/33
- Decimal Value: 0.606061
- Percentage: 60.6061%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-33-plus-7-21/
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9/33 + 7/21 = 20/33

Simplified Fraction

20/33

Mixed Number

Proper (20/33)

Decimal Value

0.606061

Percentage

60.6061%

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Step-by-Step Solution: 9/33 + 7/21

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 7/21 by 11 so both fractions share the common base 231.

9 × 7/33 × 7 = 63/231 and 7 × 11/21 × 11 = 77/231

Step 3

Add the Numerators

Now add the numerators (63 + 77 = 140) and keep the common denominator 231 unchanged.

63 + 77/231 = 140/231

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 140 and 231, which is 7. Divide both the numerator and denominator by 7.

140 ÷ 7/231 ÷ 7 = 20/33

Step 5

Decimal & Percentage Representation

Dividing the numerator 20 by denominator 33 produces a repeating decimal (approximately 0.606061, or 60.6061%).

20 ÷ 33 = 0.606061 (60.6061%)

Visual Representation

The diagram below illustrates 9/33 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`20/33`
Mixed Number Form	`20/33`
Decimal Form	`0.606061`
Percentage	`60.6061%`

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Frequently Asked Questions

What is 9/33 plus 7/21 as a fraction?

9/33 + 7/21 in simplest fraction form is 20/33.

What is 9/33 plus 7/21 as a decimal?

9/33 + 7/21 converted to a decimal is 0.606061.

What is 9/33 plus 7/21 as a percentage?

9/33 + 7/21 expressed as a percentage is 60.6061%.

Does 9/33 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.606061...) because the denominator contains prime factors other than 2 and 5.