What is 5/21 plus 10/42? (Answer: 10/21)

Exact Answer

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Problem: What is 5/21 plus 10/42?
Formula / Expression: 5/21 + 10/42
Final Answer: 10/21
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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(21, 42) = 42

Step 2: Convert to Equivalent Fractions with Common Denominator 42
Multiply the numerator and denominator of 5/21 by 2, and multiply the numerator and denominator of 10/42 by 1 so both fractions share the common base 42.
Working: 5 × 2/21 × 2 = 10/42 and 10 × 1/42 × 1 = 10/42

Step 3: Add the Numerators
Now add the numerators (10 + 10 = 20) and keep the common denominator 42 unchanged.
Working: 10 + 10/42 = 20/42

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 20 and 42, which is 2. Divide both the numerator and denominator by 2.
Working: 20 ÷ 2/42 ÷ 2 = 10/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 10 by denominator 21 produces a repeating decimal (approximately 0.47619, or 47.619%).
Working: 10 ÷ 21 = 0.47619 (47.619%)

Key Values:
- Simplified Fraction: 10/21
- Mixed Number Form: 10/21
- Decimal Value: 0.47619
- Percentage: 47.619%

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Solved with FractionsCalc:
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5/21 + 10/42 = 10/21

Simplified Fraction

10/21

Mixed Number

Proper (10/21)

Decimal Value

0.47619

Percentage

47.619%

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Step-by-Step Solution: 5/21 + 10/42

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(21, 42) = 42

Step 2

Convert to Equivalent Fractions with Common Denominator 42

Multiply the numerator and denominator of 5/21 by 2, and multiply the numerator and denominator of 10/42 by 1 so both fractions share the common base 42.

5 × 2/21 × 2 = 10/42 and 10 × 1/42 × 1 = 10/42

Step 3

Add the Numerators

Now add the numerators (10 + 10 = 20) and keep the common denominator 42 unchanged.

10 + 10/42 = 20/42

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 20 and 42, which is 2. Divide both the numerator and denominator by 2.

20 ÷ 2/42 ÷ 2 = 10/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 10 by denominator 21 produces a repeating decimal (approximately 0.47619, or 47.619%).

10 ÷ 21 = 0.47619 (47.619%)

Visual Representation

The diagram below illustrates 5/21 plus 10/42 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`10/21`
Mixed Number Form	`10/21`
Decimal Form	`0.47619`
Percentage	`47.619%`

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Frequently Asked Questions

What is 5/21 plus 10/42 as a fraction?

5/21 + 10/42 in simplest fraction form is 10/21.

What is 5/21 plus 10/42 as a decimal?

5/21 + 10/42 converted to a decimal is 0.47619.

What is 5/21 plus 10/42 as a percentage?

5/21 + 10/42 expressed as a percentage is 47.619%.

Does 5/21 plus 10/42 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.47619...) because the denominator contains prime factors other than 2 and 5.