What is 1/33 plus 7/21? (Answer: 4/11)

Exact Answer

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Problem: What is 1/33 plus 7/21?
Formula / Expression: 1/33 + 7/21
Final Answer: 4/11
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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 1/33 by 7, and multiply the numerator and denominator of 7/21 by 11 so both fractions share the common base 231.
Working: 1 × 7/33 × 7 = 7/231 and 7 × 11/21 × 11 = 77/231

Step 3: Add the Numerators
Now add the numerators (7 + 77 = 84) and keep the common denominator 231 unchanged.
Working: 7 + 77/231 = 84/231

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 84 and 231, which is 21. Divide both the numerator and denominator by 21.
Working: 84 ÷ 21/231 ÷ 21 = 4/11

Step 5: Decimal & Percentage Representation
Dividing the numerator 4 by denominator 11 produces a repeating decimal (approximately 0.363636, or 36.3636%).
Working: 4 ÷ 11 = 0.363636 (36.3636%)

Key Values:
- Simplified Fraction: 4/11
- Mixed Number Form: 4/11
- Decimal Value: 0.363636
- Percentage: 36.3636%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-33-plus-7-21/
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1/33 + 7/21 = 4/11

Simplified Fraction

4/11

Mixed Number

Proper (4/11)

Decimal Value

0.363636

Percentage

36.3636%

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Step-by-Step Solution: 1/33 + 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 1/33 by 7, and multiply the numerator and denominator of 7/21 by 11 so both fractions share the common base 231.

1 × 7/33 × 7 = 7/231 and 7 × 11/21 × 11 = 77/231

Step 3

Add the Numerators

Now add the numerators (7 + 77 = 84) and keep the common denominator 231 unchanged.

7 + 77/231 = 84/231

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 84 and 231, which is 21. Divide both the numerator and denominator by 21.

84 ÷ 21/231 ÷ 21 = 4/11

Step 5

Decimal & Percentage Representation

Dividing the numerator 4 by denominator 11 produces a repeating decimal (approximately 0.363636, or 36.3636%).

4 ÷ 11 = 0.363636 (36.3636%)

Visual Representation

The diagram below illustrates 1/33 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`4/11`
Mixed Number Form	`4/11`
Decimal Form	`0.363636`
Percentage	`36.3636%`

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Frequently Asked Questions

What is 1/33 plus 7/21 as a fraction?

1/33 + 7/21 in simplest fraction form is 4/11.

What is 1/33 plus 7/21 as a decimal?

1/33 + 7/21 converted to a decimal is 0.363636.

What is 1/33 plus 7/21 as a percentage?

1/33 + 7/21 expressed as a percentage is 36.3636%.

Does 1/33 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.363636...) because the denominator contains prime factors other than 2 and 5.