What is 16/35 plus 12/21? (Answer: 36/35)

Exact Answer

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Problem: What is 16/35 plus 12/21?
Formula / Expression: 16/35 + 12/21
Final Answer: 1 1/35 (36/35)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 35 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 35 × 21 = 735, keeping the calculation simpler).
Working: LCD(35, 21) = 105

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 16/35 by 3, and multiply the numerator and denominator of 12/21 by 5 so both fractions share the common base 105.
Working: 16 × 3/35 × 3 = 48/105 and 12 × 5/21 × 5 = 60/105

Step 3: Add the Numerators
Now add the numerators (48 + 60 = 108) and keep the common denominator 105 unchanged.
Working: 48 + 60/105 = 108/105

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 108 and 105, which is 3. Divide both the numerator and denominator by 3.
Working: 108 ÷ 3/105 ÷ 3 = 36/35

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (36) is greater than the denominator (35), divide 36 by 35: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/35.
Working: 36/35 = 1 1/35

Step 6: Decimal & Percentage Representation
Dividing the numerator 36 by denominator 35 produces a repeating decimal (approximately 1.028571, or 102.8571%).
Working: 36 ÷ 35 = 1.028571 (102.8571%)

Key Values:
- Simplified Fraction: 36/35
- Mixed Number Form: 1 1/35
- Decimal Value: 1.028571
- Percentage: 102.8571%

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Solved with FractionsCalc:
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16/35 + 12/21 = 36/35

Simplified Fraction

36/35

Mixed Number

1 1/35

Decimal Value

1.028571

Percentage

102.8571%

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Step-by-Step Solution: 16/35 + 12/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 35 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 35 × 21 = 735, keeping the calculation simpler).

LCD(35, 21) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 16/35 by 3, and multiply the numerator and denominator of 12/21 by 5 so both fractions share the common base 105.

16 × 3/35 × 3 = 48/105 and 12 × 5/21 × 5 = 60/105

Step 3

Add the Numerators

Now add the numerators (48 + 60 = 108) and keep the common denominator 105 unchanged.

48 + 60/105 = 108/105

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 108 and 105, which is 3. Divide both the numerator and denominator by 3.

108 ÷ 3/105 ÷ 3 = 36/35

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (36) is greater than the denominator (35), divide 36 by 35: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/35.

36/35 = 11/35

Step 6

Decimal & Percentage Representation

Dividing the numerator 36 by denominator 35 produces a repeating decimal (approximately 1.028571, or 102.8571%).

36 ÷ 35 = 1.028571 (102.8571%)

Visual Representation

The diagram below illustrates 16/35 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`36/35`
Mixed Number Form	`1 1/35`
Decimal Form	`1.028571`
Percentage	`102.8571%`

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Frequently Asked Questions

What is 16/35 plus 12/21 as a fraction?

16/35 + 12/21 in simplest fraction form is 36/35 (or 1 1/35 as a mixed number).

What is 16/35 plus 12/21 as a decimal?

16/35 + 12/21 converted to a decimal is 1.028571.

What is 16/35 plus 12/21 as a percentage?

16/35 + 12/21 expressed as a percentage is 102.8571%.

How do you write 16/35 plus 12/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 36/35 can be written as the mixed number 1 1/35.

Does 16/35 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.028571...) because the denominator contains prime factors other than 2 and 5.