What is 10/33 plus 10/21? (Answer: 60/77)

Exact Answer

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Problem: What is 10/33 plus 10/21?
Formula / Expression: 10/33 + 10/21
Final Answer: 60/77
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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 10/33 by 7, and multiply the numerator and denominator of 10/21 by 11 so both fractions share the common base 231.
Working: 10 × 7/33 × 7 = 70/231 and 10 × 11/21 × 11 = 110/231

Step 3: Add the Numerators
Now add the numerators (70 + 110 = 180) and keep the common denominator 231 unchanged.
Working: 70 + 110/231 = 180/231

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 180 and 231, which is 3. Divide both the numerator and denominator by 3.
Working: 180 ÷ 3/231 ÷ 3 = 60/77

Step 5: Decimal & Percentage Representation
Dividing the numerator 60 by denominator 77 produces a repeating decimal (approximately 0.779221, or 77.9221%).
Working: 60 ÷ 77 = 0.779221 (77.9221%)

Key Values:
- Simplified Fraction: 60/77
- Mixed Number Form: 60/77
- Decimal Value: 0.779221
- Percentage: 77.9221%

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Solved with FractionsCalc:
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10/33 + 10/21 = 60/77

Simplified Fraction

60/77

Mixed Number

Proper (60/77)

Decimal Value

0.779221

Percentage

77.9221%

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Step-by-Step Solution: 10/33 + 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 10/33 by 7, and multiply the numerator and denominator of 10/21 by 11 so both fractions share the common base 231.

10 × 7/33 × 7 = 70/231 and 10 × 11/21 × 11 = 110/231

Step 3

Add the Numerators

Now add the numerators (70 + 110 = 180) and keep the common denominator 231 unchanged.

70 + 110/231 = 180/231

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 180 and 231, which is 3. Divide both the numerator and denominator by 3.

180 ÷ 3/231 ÷ 3 = 60/77

Step 5

Decimal & Percentage Representation

Dividing the numerator 60 by denominator 77 produces a repeating decimal (approximately 0.779221, or 77.9221%).

60 ÷ 77 = 0.779221 (77.9221%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`60/77`
Mixed Number Form	`60/77`
Decimal Form	`0.779221`
Percentage	`77.9221%`

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Frequently Asked Questions

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

10/33 + 10/21 in simplest fraction form is 60/77.

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

10/33 + 10/21 converted to a decimal is 0.779221.

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

10/33 + 10/21 expressed as a percentage is 77.9221%.

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

It results in a repeating decimal (approximately 0.779221...) because the denominator contains prime factors other than 2 and 5.