What is 16/42 plus 9/21? (Answer: 17/21)

Exact Answer

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Problem: What is 16/42 plus 9/21?
Formula / Expression: 16/42 + 9/21
Final Answer: 17/21
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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(42, 21) = 42

Step 2: Convert to Equivalent Fractions with Common Denominator 42
Multiply the numerator and denominator of 16/42 by 1, and multiply the numerator and denominator of 9/21 by 2 so both fractions share the common base 42.
Working: 16 × 1/42 × 1 = 16/42 and 9 × 2/21 × 2 = 18/42

Step 3: Add the Numerators
Now add the numerators (16 + 18 = 34) and keep the common denominator 42 unchanged.
Working: 16 + 18/42 = 34/42

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 34 and 42, which is 2. Divide both the numerator and denominator by 2.
Working: 34 ÷ 2/42 ÷ 2 = 17/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 21 produces a repeating decimal (approximately 0.809524, or 80.9524%).
Working: 17 ÷ 21 = 0.809524 (80.9524%)

Key Values:
- Simplified Fraction: 17/21
- Mixed Number Form: 17/21
- Decimal Value: 0.809524
- Percentage: 80.9524%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-16-42-plus-9-21/
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16/42 + 9/21 = 17/21

Simplified Fraction

17/21

Mixed Number

Proper (17/21)

Decimal Value

0.809524

Percentage

80.9524%

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Step-by-Step Solution: 16/42 + 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 16/42 by 1, and multiply the numerator and denominator of 9/21 by 2 so both fractions share the common base 42.

16 × 1/42 × 1 = 16/42 and 9 × 2/21 × 2 = 18/42

Step 3

Add the Numerators

Now add the numerators (16 + 18 = 34) and keep the common denominator 42 unchanged.

16 + 18/42 = 34/42

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 34 and 42, which is 2. Divide both the numerator and denominator by 2.

34 ÷ 2/42 ÷ 2 = 17/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 21 produces a repeating decimal (approximately 0.809524, or 80.9524%).

17 ÷ 21 = 0.809524 (80.9524%)

Visual Representation

The diagram below illustrates 16/42 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/21`
Mixed Number Form	`17/21`
Decimal Form	`0.809524`
Percentage	`80.9524%`

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Frequently Asked Questions

What is 16/42 plus 9/21 as a fraction?

16/42 + 9/21 in simplest fraction form is 17/21.

What is 16/42 plus 9/21 as a decimal?

16/42 + 9/21 converted to a decimal is 0.809524.

What is 16/42 plus 9/21 as a percentage?

16/42 + 9/21 expressed as a percentage is 80.9524%.

Does 16/42 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.809524...) because the denominator contains prime factors other than 2 and 5.