What is 5/21 plus 8/33? (Answer: 37/77)

Exact Answer

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Problem: What is 5/21 plus 8/33?
Formula / Expression: 5/21 + 8/33
Final Answer: 37/77
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 33 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 231 (which is smaller than their product 21 × 33 = 693, keeping the calculation simpler).
Working: LCD(21, 33) = 231

Step 2: Convert to Equivalent Fractions with Common Denominator 231
Multiply the numerator and denominator of 5/21 by 11, and multiply the numerator and denominator of 8/33 by 7 so both fractions share the common base 231.
Working: 5 × 11/21 × 11 = 55/231 and 8 × 7/33 × 7 = 56/231

Step 3: Add the Numerators
Now add the numerators (55 + 56 = 111) and keep the common denominator 231 unchanged.
Working: 55 + 56/231 = 111/231

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 111 and 231, which is 3. Divide both the numerator and denominator by 3.
Working: 111 ÷ 3/231 ÷ 3 = 37/77

Step 5: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 77 produces a repeating decimal (approximately 0.480519, or 48.0519%).
Working: 37 ÷ 77 = 0.480519 (48.0519%)

Key Values:
- Simplified Fraction: 37/77
- Mixed Number Form: 37/77
- Decimal Value: 0.480519
- Percentage: 48.0519%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-21-plus-8-33/
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5/21 + 8/33 = 37/77

Simplified Fraction

37/77

Mixed Number

Proper (37/77)

Decimal Value

0.480519

Percentage

48.0519%

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Step-by-Step Solution: 5/21 + 8/33

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 33 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 231 (which is smaller than their product 21 × 33 = 693, keeping the calculation simpler).

LCD(21, 33) = 231

Step 2

Convert to Equivalent Fractions with Common Denominator 231

Multiply the numerator and denominator of 5/21 by 11, and multiply the numerator and denominator of 8/33 by 7 so both fractions share the common base 231.

5 × 11/21 × 11 = 55/231 and 8 × 7/33 × 7 = 56/231

Step 3

Add the Numerators

Now add the numerators (55 + 56 = 111) and keep the common denominator 231 unchanged.

55 + 56/231 = 111/231

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 111 and 231, which is 3. Divide both the numerator and denominator by 3.

111 ÷ 3/231 ÷ 3 = 37/77

Step 5

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 77 produces a repeating decimal (approximately 0.480519, or 48.0519%).

37 ÷ 77 = 0.480519 (48.0519%)

Visual Representation

The diagram below illustrates 5/21 plus 8/33 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/77`
Mixed Number Form	`37/77`
Decimal Form	`0.480519`
Percentage	`48.0519%`

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Frequently Asked Questions

What is 5/21 plus 8/33 as a fraction?

5/21 + 8/33 in simplest fraction form is 37/77.

What is 5/21 plus 8/33 as a decimal?

5/21 + 8/33 converted to a decimal is 0.480519.

What is 5/21 plus 8/33 as a percentage?

5/21 + 8/33 expressed as a percentage is 48.0519%.

Does 5/21 plus 8/33 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.480519...) because the denominator contains prime factors other than 2 and 5.