What is 10/42 plus 9/21? (Answer: 2/3)

Exact Answer

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Problem: What is 10/42 plus 9/21?
Formula / Expression: 10/42 + 9/21
Final Answer: 2/3
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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 10/42 by 1, and multiply the numerator and denominator of 9/21 by 2 so both fractions share the common base 42.
Working: 10 × 1/42 × 1 = 10/42 and 9 × 2/21 × 2 = 18/42

Step 3: Add the Numerators
Now add the numerators (10 + 18 = 28) and keep the common denominator 42 unchanged.
Working: 10 + 18/42 = 28/42

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 28 and 42, which is 14. Divide both the numerator and denominator by 14.
Working: 28 ÷ 14/42 ÷ 14 = 2/3

Step 5: Decimal & Percentage Representation
Dividing the numerator 2 by denominator 3 produces a repeating decimal (approximately 0.666667, or 66.6667%).
Working: 2 ÷ 3 = 0.666667 (66.6667%)

Key Values:
- Simplified Fraction: 2/3
- Mixed Number Form: 2/3
- Decimal Value: 0.666667
- Percentage: 66.6667%

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Solved with FractionsCalc:
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10/42 + 9/21 = 2/3

Simplified Fraction

2/3

Mixed Number

Proper (2/3)

Decimal Value

0.666667

Percentage

66.6667%

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Step-by-Step Solution: 10/42 + 9/21

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 10/42 by 1, and multiply the numerator and denominator of 9/21 by 2 so both fractions share the common base 42.

10 × 1/42 × 1 = 10/42 and 9 × 2/21 × 2 = 18/42

Step 3

Add the Numerators

Now add the numerators (10 + 18 = 28) and keep the common denominator 42 unchanged.

10 + 18/42 = 28/42

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 28 and 42, which is 14. Divide both the numerator and denominator by 14.

28 ÷ 14/42 ÷ 14 = 2/3

Step 5

Decimal & Percentage Representation

Dividing the numerator 2 by denominator 3 produces a repeating decimal (approximately 0.666667, or 66.6667%).

2 ÷ 3 = 0.666667 (66.6667%)

Visual Representation

The diagram below illustrates 10/42 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`2/3`
Mixed Number Form	`2/3`
Decimal Form	`0.666667`
Percentage	`66.6667%`

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Frequently Asked Questions

What is 10/42 plus 9/21 as a fraction?

10/42 + 9/21 in simplest fraction form is 2/3.

What is 10/42 plus 9/21 as a decimal?

10/42 + 9/21 converted to a decimal is 0.666667.

What is 10/42 plus 9/21 as a percentage?

10/42 + 9/21 expressed as a percentage is 66.6667%.

Does 10/42 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.666667...) because the denominator contains prime factors other than 2 and 5.