What is 10/21 plus 16/33? (Answer: 74/77)

Exact Answer

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Problem: What is 10/21 plus 16/33?
Formula / Expression: 10/21 + 16/33
Final Answer: 74/77
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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 10/21 by 11, and multiply the numerator and denominator of 16/33 by 7 so both fractions share the common base 231.
Working: 10 × 11/21 × 11 = 110/231 and 16 × 7/33 × 7 = 112/231

Step 3: Add the Numerators
Now add the numerators (110 + 112 = 222) and keep the common denominator 231 unchanged.
Working: 110 + 112/231 = 222/231

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 222 and 231, which is 3. Divide both the numerator and denominator by 3.
Working: 222 ÷ 3/231 ÷ 3 = 74/77

Step 5: Decimal & Percentage Representation
Dividing the numerator 74 by denominator 77 produces a repeating decimal (approximately 0.961039, or 96.1039%).
Working: 74 ÷ 77 = 0.961039 (96.1039%)

Key Values:
- Simplified Fraction: 74/77
- Mixed Number Form: 74/77
- Decimal Value: 0.961039
- Percentage: 96.1039%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-21-plus-16-33/
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10/21 + 16/33 = 74/77

Simplified Fraction

74/77

Mixed Number

Proper (74/77)

Decimal Value

0.961039

Percentage

96.1039%

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Step-by-Step Solution: 10/21 + 16/33

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 10/21 by 11, and multiply the numerator and denominator of 16/33 by 7 so both fractions share the common base 231.

10 × 11/21 × 11 = 110/231 and 16 × 7/33 × 7 = 112/231

Step 3

Add the Numerators

Now add the numerators (110 + 112 = 222) and keep the common denominator 231 unchanged.

110 + 112/231 = 222/231

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 222 and 231, which is 3. Divide both the numerator and denominator by 3.

222 ÷ 3/231 ÷ 3 = 74/77

Step 5

Decimal & Percentage Representation

Dividing the numerator 74 by denominator 77 produces a repeating decimal (approximately 0.961039, or 96.1039%).

74 ÷ 77 = 0.961039 (96.1039%)

Visual Representation

The diagram below illustrates 10/21 plus 16/33 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`74/77`
Mixed Number Form	`74/77`
Decimal Form	`0.961039`
Percentage	`96.1039%`

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Frequently Asked Questions

What is 10/21 plus 16/33 as a fraction?

10/21 + 16/33 in simplest fraction form is 74/77.

What is 10/21 plus 16/33 as a decimal?

10/21 + 16/33 converted to a decimal is 0.961039.

What is 10/21 plus 16/33 as a percentage?

10/21 + 16/33 expressed as a percentage is 96.1039%.

Does 10/21 plus 16/33 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.961039...) because the denominator contains prime factors other than 2 and 5.