What is 4/33 plus 4/21? (Answer: 24/77)

Exact Answer

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Problem: What is 4/33 plus 4/21?
Formula / Expression: 4/33 + 4/21
Final Answer: 24/77
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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 4/33 by 7, and multiply the numerator and denominator of 4/21 by 11 so both fractions share the common base 231.
Working: 4 × 7/33 × 7 = 28/231 and 4 × 11/21 × 11 = 44/231

Step 3: Add the Numerators
Now add the numerators (28 + 44 = 72) and keep the common denominator 231 unchanged.
Working: 28 + 44/231 = 72/231

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 72 and 231, which is 3. Divide both the numerator and denominator by 3.
Working: 72 ÷ 3/231 ÷ 3 = 24/77

Step 5: Decimal & Percentage Representation
Dividing the numerator 24 by denominator 77 produces a repeating decimal (approximately 0.311688, or 31.1688%).
Working: 24 ÷ 77 = 0.311688 (31.1688%)

Key Values:
- Simplified Fraction: 24/77
- Mixed Number Form: 24/77
- Decimal Value: 0.311688
- Percentage: 31.1688%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-33-plus-4-21/
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4/33 + 4/21 = 24/77

Simplified Fraction

24/77

Mixed Number

Proper (24/77)

Decimal Value

0.311688

Percentage

31.1688%

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Step-by-Step Solution: 4/33 + 4/21

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 4/33 by 7, and multiply the numerator and denominator of 4/21 by 11 so both fractions share the common base 231.

4 × 7/33 × 7 = 28/231 and 4 × 11/21 × 11 = 44/231

Step 3

Add the Numerators

Now add the numerators (28 + 44 = 72) and keep the common denominator 231 unchanged.

28 + 44/231 = 72/231

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 72 and 231, which is 3. Divide both the numerator and denominator by 3.

72 ÷ 3/231 ÷ 3 = 24/77

Step 5

Decimal & Percentage Representation

Dividing the numerator 24 by denominator 77 produces a repeating decimal (approximately 0.311688, or 31.1688%).

24 ÷ 77 = 0.311688 (31.1688%)

Visual Representation

The diagram below illustrates 4/33 plus 4/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`24/77`
Mixed Number Form	`24/77`
Decimal Form	`0.311688`
Percentage	`31.1688%`

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Frequently Asked Questions

What is 4/33 plus 4/21 as a fraction?

4/33 + 4/21 in simplest fraction form is 24/77.

What is 4/33 plus 4/21 as a decimal?

4/33 + 4/21 converted to a decimal is 0.311688.

What is 4/33 plus 4/21 as a percentage?

4/33 + 4/21 expressed as a percentage is 31.1688%.

Does 4/33 plus 4/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.311688...) because the denominator contains prime factors other than 2 and 5.