What is 7/33 plus 7/21? (Answer: 6/11)

Exact Answer

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Problem: What is 7/33 plus 7/21?
Formula / Expression: 7/33 + 7/21
Final Answer: 6/11
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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 7/33 by 7, and multiply the numerator and denominator of 7/21 by 11 so both fractions share the common base 231.
Working: 7 × 7/33 × 7 = 49/231 and 7 × 11/21 × 11 = 77/231

Step 3: Add the Numerators
Now add the numerators (49 + 77 = 126) and keep the common denominator 231 unchanged.
Working: 49 + 77/231 = 126/231

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 126 and 231, which is 21. Divide both the numerator and denominator by 21.
Working: 126 ÷ 21/231 ÷ 21 = 6/11

Step 5: Decimal & Percentage Representation
Dividing the numerator 6 by denominator 11 produces a repeating decimal (approximately 0.545455, or 54.5455%).
Working: 6 ÷ 11 = 0.545455 (54.5455%)

Key Values:
- Simplified Fraction: 6/11
- Mixed Number Form: 6/11
- Decimal Value: 0.545455
- Percentage: 54.5455%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-33-plus-7-21/
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7/33 + 7/21 = 6/11

Simplified Fraction

6/11

Mixed Number

Proper (6/11)

Decimal Value

0.545455

Percentage

54.5455%

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

7 × 7/33 × 7 = 49/231 and 7 × 11/21 × 11 = 77/231

Step 3

Add the Numerators

Now add the numerators (49 + 77 = 126) and keep the common denominator 231 unchanged.

49 + 77/231 = 126/231

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 126 and 231, which is 21. Divide both the numerator and denominator by 21.

126 ÷ 21/231 ÷ 21 = 6/11

Step 5

Decimal & Percentage Representation

Dividing the numerator 6 by denominator 11 produces a repeating decimal (approximately 0.545455, or 54.5455%).

6 ÷ 11 = 0.545455 (54.5455%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`6/11`
Mixed Number Form	`6/11`
Decimal Form	`0.545455`
Percentage	`54.5455%`

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Frequently Asked Questions

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

7/33 + 7/21 in simplest fraction form is 6/11.

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

7/33 + 7/21 converted to a decimal is 0.545455.

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

7/33 + 7/21 expressed as a percentage is 54.5455%.

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

It results in a repeating decimal (approximately 0.545455...) because the denominator contains prime factors other than 2 and 5.