What is 9/33 plus 2/7? (Answer: 43/77)

Exact Answer

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Problem: What is 9/33 plus 2/7?
Formula / Expression: 9/33 + 2/7
Final Answer: 43/77
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 33 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 33 × 7 = 231.
Working: LCD(33, 7) = 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 2/7 by 33 so both fractions share the common base 231.
Working: 9 × 7/33 × 7 = 63/231 and 2 × 33/7 × 33 = 66/231

Step 3: Add the Numerators
Now add the numerators (63 + 66 = 129) and keep the common denominator 231 unchanged.
Working: 63 + 66/231 = 129/231

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 129 and 231, which is 3. Divide both the numerator and denominator by 3.
Working: 129 ÷ 3/231 ÷ 3 = 43/77

Step 5: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 77 produces a repeating decimal (approximately 0.558442, or 55.8442%).
Working: 43 ÷ 77 = 0.558442 (55.8442%)

Key Values:
- Simplified Fraction: 43/77
- Mixed Number Form: 43/77
- Decimal Value: 0.558442
- Percentage: 55.8442%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-33-plus-2-7/
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9/33 + 2/7 = 43/77

Simplified Fraction

43/77

Mixed Number

Proper (43/77)

Decimal Value

0.558442

Percentage

55.8442%

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Step-by-Step Solution: 9/33 + 2/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 33 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 33 × 7 = 231.

LCD(33, 7) = 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 2/7 by 33 so both fractions share the common base 231.

9 × 7/33 × 7 = 63/231 and 2 × 33/7 × 33 = 66/231

Step 3

Add the Numerators

Now add the numerators (63 + 66 = 129) and keep the common denominator 231 unchanged.

63 + 66/231 = 129/231

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 129 and 231, which is 3. Divide both the numerator and denominator by 3.

129 ÷ 3/231 ÷ 3 = 43/77

Step 5

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 77 produces a repeating decimal (approximately 0.558442, or 55.8442%).

43 ÷ 77 = 0.558442 (55.8442%)

Visual Representation

The diagram below illustrates 9/33 plus 2/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/77`
Mixed Number Form	`43/77`
Decimal Form	`0.558442`
Percentage	`55.8442%`

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Frequently Asked Questions

What is 9/33 plus 2/7 as a fraction?

9/33 + 2/7 in simplest fraction form is 43/77.

What is 9/33 plus 2/7 as a decimal?

9/33 + 2/7 converted to a decimal is 0.558442.

What is 9/33 plus 2/7 as a percentage?

9/33 + 2/7 expressed as a percentage is 55.8442%.

Does 9/33 plus 2/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.558442...) because the denominator contains prime factors other than 2 and 5.