What is 1/33 plus 10/21? (Answer: 39/77)

Exact Answer

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Problem: What is 1/33 plus 10/21?
Formula / Expression: 1/33 + 10/21
Final Answer: 39/77
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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 1/33 by 7, and multiply the numerator and denominator of 10/21 by 11 so both fractions share the common base 231.
Working: 1 × 7/33 × 7 = 7/231 and 10 × 11/21 × 11 = 110/231

Step 3: Add the Numerators
Now add the numerators (7 + 110 = 117) and keep the common denominator 231 unchanged.
Working: 7 + 110/231 = 117/231

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 117 and 231, which is 3. Divide both the numerator and denominator by 3.
Working: 117 ÷ 3/231 ÷ 3 = 39/77

Step 5: Decimal & Percentage Representation
Dividing the numerator 39 by denominator 77 produces a repeating decimal (approximately 0.506494, or 50.6494%).
Working: 39 ÷ 77 = 0.506494 (50.6494%)

Key Values:
- Simplified Fraction: 39/77
- Mixed Number Form: 39/77
- Decimal Value: 0.506494
- Percentage: 50.6494%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-33-plus-10-21/
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1/33 + 10/21 = 39/77

Simplified Fraction

39/77

Mixed Number

Proper (39/77)

Decimal Value

0.506494

Percentage

50.6494%

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Step-by-Step Solution: 1/33 + 10/21

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 10/21 by 11 so both fractions share the common base 231.

1 × 7/33 × 7 = 7/231 and 10 × 11/21 × 11 = 110/231

Step 3

Add the Numerators

Now add the numerators (7 + 110 = 117) and keep the common denominator 231 unchanged.

7 + 110/231 = 117/231

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 117 and 231, which is 3. Divide both the numerator and denominator by 3.

117 ÷ 3/231 ÷ 3 = 39/77

Step 5

Decimal & Percentage Representation

Dividing the numerator 39 by denominator 77 produces a repeating decimal (approximately 0.506494, or 50.6494%).

39 ÷ 77 = 0.506494 (50.6494%)

Visual Representation

The diagram below illustrates 1/33 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`39/77`
Mixed Number Form	`39/77`
Decimal Form	`0.506494`
Percentage	`50.6494%`

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Frequently Asked Questions

What is 1/33 plus 10/21 as a fraction?

1/33 + 10/21 in simplest fraction form is 39/77.

What is 1/33 plus 10/21 as a decimal?

1/33 + 10/21 converted to a decimal is 0.506494.

What is 1/33 plus 10/21 as a percentage?

1/33 + 10/21 expressed as a percentage is 50.6494%.

Does 1/33 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.506494...) because the denominator contains prime factors other than 2 and 5.