What is 10/33 plus 7/21? (Answer: 7/11)

Exact Answer

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

Step 3: Add the Numerators
Now add the numerators (70 + 77 = 147) and keep the common denominator 231 unchanged.
Working: 70 + 77/231 = 147/231

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 147 and 231, which is 21. Divide both the numerator and denominator by 21.
Working: 147 ÷ 21/231 ÷ 21 = 7/11

Step 5: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 11 produces a repeating decimal (approximately 0.636364, or 63.6364%).
Working: 7 ÷ 11 = 0.636364 (63.6364%)

Key Values:
- Simplified Fraction: 7/11
- Mixed Number Form: 7/11
- Decimal Value: 0.636364
- Percentage: 63.6364%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-33-plus-7-21/
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10/33 + 7/21 = 7/11

Simplified Fraction

7/11

Mixed Number

Proper (7/11)

Decimal Value

0.636364

Percentage

63.6364%

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Step-by-Step Solution: 10/33 + 7/21

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 7/21 by 11 so both fractions share the common base 231.

10 × 7/33 × 7 = 70/231 and 7 × 11/21 × 11 = 77/231

Step 3

Add the Numerators

Now add the numerators (70 + 77 = 147) and keep the common denominator 231 unchanged.

70 + 77/231 = 147/231

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 147 and 231, which is 21. Divide both the numerator and denominator by 21.

147 ÷ 21/231 ÷ 21 = 7/11

Step 5

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 11 produces a repeating decimal (approximately 0.636364, or 63.6364%).

7 ÷ 11 = 0.636364 (63.6364%)

Visual Representation

The diagram below illustrates 10/33 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/11`
Mixed Number Form	`7/11`
Decimal Form	`0.636364`
Percentage	`63.6364%`

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Frequently Asked Questions

What is 10/33 plus 7/21 as a fraction?

10/33 + 7/21 in simplest fraction form is 7/11.

What is 10/33 plus 7/21 as a decimal?

10/33 + 7/21 converted to a decimal is 0.636364.

What is 10/33 plus 7/21 as a percentage?

10/33 + 7/21 expressed as a percentage is 63.6364%.

Does 10/33 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.636364...) because the denominator contains prime factors other than 2 and 5.