What is 13/42 plus 10/21? (Answer: 11/14)

Exact Answer

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Problem: What is 13/42 plus 10/21?
Formula / Expression: 13/42 + 10/21
Final Answer: 11/14
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 42 is an exact multiple of 21 (21 × 2 = 42). The Least Common Denominator (LCD) is simply 42, meaning we only need to scale one fraction.
Working: LCD(42, 21) = 42

Step 2: Convert to Equivalent Fractions with Common Denominator 42
Multiply the numerator and denominator of 13/42 by 1, and multiply the numerator and denominator of 10/21 by 2 so both fractions share the common base 42.
Working: 13 × 1/42 × 1 = 13/42 and 10 × 2/21 × 2 = 20/42

Step 3: Add the Numerators
Now add the numerators (13 + 20 = 33) and keep the common denominator 42 unchanged.
Working: 13 + 20/42 = 33/42

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 33 and 42, which is 3. Divide both the numerator and denominator by 3.
Working: 33 ÷ 3/42 ÷ 3 = 11/14

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 14 produces a repeating decimal (approximately 0.785714, or 78.5714%).
Working: 11 ÷ 14 = 0.785714 (78.5714%)

Key Values:
- Simplified Fraction: 11/14
- Mixed Number Form: 11/14
- Decimal Value: 0.785714
- Percentage: 78.5714%

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Solved with FractionsCalc:
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13/42 + 10/21 = 11/14

Simplified Fraction

11/14

Mixed Number

Proper (11/14)

Decimal Value

0.785714

Percentage

78.5714%

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Step-by-Step Solution: 13/42 + 10/21

Step 1

Find the Least Common Denominator (LCD)

Notice that 42 is an exact multiple of 21 (21 × 2 = 42). The Least Common Denominator (LCD) is simply 42, meaning we only need to scale one fraction.

LCD(42, 21) = 42

Step 2

Convert to Equivalent Fractions with Common Denominator 42

Multiply the numerator and denominator of 13/42 by 1, and multiply the numerator and denominator of 10/21 by 2 so both fractions share the common base 42.

13 × 1/42 × 1 = 13/42 and 10 × 2/21 × 2 = 20/42

Step 3

Add the Numerators

Now add the numerators (13 + 20 = 33) and keep the common denominator 42 unchanged.

13 + 20/42 = 33/42

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 33 and 42, which is 3. Divide both the numerator and denominator by 3.

33 ÷ 3/42 ÷ 3 = 11/14

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 14 produces a repeating decimal (approximately 0.785714, or 78.5714%).

11 ÷ 14 = 0.785714 (78.5714%)

Visual Representation

The diagram below illustrates 13/42 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/14`
Mixed Number Form	`11/14`
Decimal Form	`0.785714`
Percentage	`78.5714%`

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Frequently Asked Questions

What is 13/42 plus 10/21 as a fraction?

13/42 + 10/21 in simplest fraction form is 11/14.

What is 13/42 plus 10/21 as a decimal?

13/42 + 10/21 converted to a decimal is 0.785714.

What is 13/42 plus 10/21 as a percentage?

13/42 + 10/21 expressed as a percentage is 78.5714%.

Does 13/42 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.785714...) because the denominator contains prime factors other than 2 and 5.