What is 13/30 plus 11/21? (Answer: 67/70)

Exact Answer

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Problem: What is 13/30 plus 11/21?
Formula / Expression: 13/30 + 11/21
Final Answer: 67/70
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 30 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 210 (which is smaller than their product 30 × 21 = 630, keeping the calculation simpler).
Working: LCD(30, 21) = 210

Step 2: Convert to Equivalent Fractions with Common Denominator 210
Multiply the numerator and denominator of 13/30 by 7, and multiply the numerator and denominator of 11/21 by 10 so both fractions share the common base 210.
Working: 13 × 7/30 × 7 = 91/210 and 11 × 10/21 × 10 = 110/210

Step 3: Add the Numerators
Now add the numerators (91 + 110 = 201) and keep the common denominator 210 unchanged.
Working: 91 + 110/210 = 201/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 201 and 210, which is 3. Divide both the numerator and denominator by 3.
Working: 201 ÷ 3/210 ÷ 3 = 67/70

Step 5: Decimal & Percentage Representation
Dividing the numerator 67 by denominator 70 produces a repeating decimal (approximately 0.957143, or 95.7143%).
Working: 67 ÷ 70 = 0.957143 (95.7143%)

Key Values:
- Simplified Fraction: 67/70
- Mixed Number Form: 67/70
- Decimal Value: 0.957143
- Percentage: 95.7143%

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Solved with FractionsCalc:
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13/30 + 11/21 = 67/70

Simplified Fraction

67/70

Mixed Number

Proper (67/70)

Decimal Value

0.957143

Percentage

95.7143%

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Step-by-Step Solution: 13/30 + 11/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 30 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 210 (which is smaller than their product 30 × 21 = 630, keeping the calculation simpler).

LCD(30, 21) = 210

Step 2

Convert to Equivalent Fractions with Common Denominator 210

Multiply the numerator and denominator of 13/30 by 7, and multiply the numerator and denominator of 11/21 by 10 so both fractions share the common base 210.

13 × 7/30 × 7 = 91/210 and 11 × 10/21 × 10 = 110/210

Step 3

Add the Numerators

Now add the numerators (91 + 110 = 201) and keep the common denominator 210 unchanged.

91 + 110/210 = 201/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 201 and 210, which is 3. Divide both the numerator and denominator by 3.

201 ÷ 3/210 ÷ 3 = 67/70

Step 5

Decimal & Percentage Representation

Dividing the numerator 67 by denominator 70 produces a repeating decimal (approximately 0.957143, or 95.7143%).

67 ÷ 70 = 0.957143 (95.7143%)

Visual Representation

The diagram below illustrates 13/30 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`67/70`
Mixed Number Form	`67/70`
Decimal Form	`0.957143`
Percentage	`95.7143%`

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Frequently Asked Questions

What is 13/30 plus 11/21 as a fraction?

13/30 + 11/21 in simplest fraction form is 67/70.

What is 13/30 plus 11/21 as a decimal?

13/30 + 11/21 converted to a decimal is 0.957143.

What is 13/30 plus 11/21 as a percentage?

13/30 + 11/21 expressed as a percentage is 95.7143%.

Does 13/30 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.957143...) because the denominator contains prime factors other than 2 and 5.