What is 19/42 plus 10/21? (Answer: 13/14)

Exact Answer

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Problem: What is 19/42 plus 10/21?
Formula / Expression: 19/42 + 10/21
Final Answer: 13/14
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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 19/42 by 1, and multiply the numerator and denominator of 10/21 by 2 so both fractions share the common base 42.
Working: 19 × 1/42 × 1 = 19/42 and 10 × 2/21 × 2 = 20/42

Step 3: Add the Numerators
Now add the numerators (19 + 20 = 39) and keep the common denominator 42 unchanged.
Working: 19 + 20/42 = 39/42

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 39 and 42, which is 3. Divide both the numerator and denominator by 3.
Working: 39 ÷ 3/42 ÷ 3 = 13/14

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 14 produces a repeating decimal (approximately 0.928571, or 92.8571%).
Working: 13 ÷ 14 = 0.928571 (92.8571%)

Key Values:
- Simplified Fraction: 13/14
- Mixed Number Form: 13/14
- Decimal Value: 0.928571
- Percentage: 92.8571%

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Solved with FractionsCalc:
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19/42 + 10/21 = 13/14

Simplified Fraction

13/14

Mixed Number

Proper (13/14)

Decimal Value

0.928571

Percentage

92.8571%

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Step-by-Step Solution: 19/42 + 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 19/42 by 1, and multiply the numerator and denominator of 10/21 by 2 so both fractions share the common base 42.

19 × 1/42 × 1 = 19/42 and 10 × 2/21 × 2 = 20/42

Step 3

Add the Numerators

Now add the numerators (19 + 20 = 39) and keep the common denominator 42 unchanged.

19 + 20/42 = 39/42

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 39 and 42, which is 3. Divide both the numerator and denominator by 3.

39 ÷ 3/42 ÷ 3 = 13/14

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 14 produces a repeating decimal (approximately 0.928571, or 92.8571%).

13 ÷ 14 = 0.928571 (92.8571%)

Visual Representation

The diagram below illustrates 19/42 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/14`
Mixed Number Form	`13/14`
Decimal Form	`0.928571`
Percentage	`92.8571%`

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Frequently Asked Questions

What is 19/42 plus 10/21 as a fraction?

19/42 + 10/21 in simplest fraction form is 13/14.

What is 19/42 plus 10/21 as a decimal?

19/42 + 10/21 converted to a decimal is 0.928571.

What is 19/42 plus 10/21 as a percentage?

19/42 + 10/21 expressed as a percentage is 92.8571%.

Does 19/42 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.928571...) because the denominator contains prime factors other than 2 and 5.