What is 17/42 plus 9/21? (Answer: 5/6)

Exact Answer

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Problem: What is 17/42 plus 9/21?
Formula / Expression: 17/42 + 9/21
Final Answer: 5/6
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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 17/42 by 1, and multiply the numerator and denominator of 9/21 by 2 so both fractions share the common base 42.
Working: 17 × 1/42 × 1 = 17/42 and 9 × 2/21 × 2 = 18/42

Step 3: Add the Numerators
Now add the numerators (17 + 18 = 35) and keep the common denominator 42 unchanged.
Working: 17 + 18/42 = 35/42

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 35 and 42, which is 7. Divide both the numerator and denominator by 7.
Working: 35 ÷ 7/42 ÷ 7 = 5/6

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 6 produces a repeating decimal (approximately 0.833333, or 83.3333%).
Working: 5 ÷ 6 = 0.833333 (83.3333%)

Key Values:
- Simplified Fraction: 5/6
- Mixed Number Form: 5/6
- Decimal Value: 0.833333
- Percentage: 83.3333%

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Solved with FractionsCalc:
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17/42 + 9/21 = 5/6

Simplified Fraction

5/6

Mixed Number

Proper (5/6)

Decimal Value

0.833333

Percentage

83.3333%

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Step-by-Step Solution: 17/42 + 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 17/42 by 1, and multiply the numerator and denominator of 9/21 by 2 so both fractions share the common base 42.

17 × 1/42 × 1 = 17/42 and 9 × 2/21 × 2 = 18/42

Step 3

Add the Numerators

Now add the numerators (17 + 18 = 35) and keep the common denominator 42 unchanged.

17 + 18/42 = 35/42

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 35 and 42, which is 7. Divide both the numerator and denominator by 7.

35 ÷ 7/42 ÷ 7 = 5/6

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 6 produces a repeating decimal (approximately 0.833333, or 83.3333%).

5 ÷ 6 = 0.833333 (83.3333%)

Visual Representation

The diagram below illustrates 17/42 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/6`
Mixed Number Form	`5/6`
Decimal Form	`0.833333`
Percentage	`83.3333%`

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Frequently Asked Questions

What is 17/42 plus 9/21 as a fraction?

17/42 + 9/21 in simplest fraction form is 5/6.

What is 17/42 plus 9/21 as a decimal?

17/42 + 9/21 converted to a decimal is 0.833333.

What is 17/42 plus 9/21 as a percentage?

17/42 + 9/21 expressed as a percentage is 83.3333%.

Does 17/42 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.833333...) because the denominator contains prime factors other than 2 and 5.