What is 11/21 plus 16/30? (Answer: 37/35)

Exact Answer

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Problem: What is 11/21 plus 16/30?
Formula / Expression: 11/21 + 16/30
Final Answer: 1 2/35 (37/35)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 30 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 210 (which is smaller than their product 21 × 30 = 630, keeping the calculation simpler).
Working: LCD(21, 30) = 210

Step 2: Convert to Equivalent Fractions with Common Denominator 210
Multiply the numerator and denominator of 11/21 by 10, and multiply the numerator and denominator of 16/30 by 7 so both fractions share the common base 210.
Working: 11 × 10/21 × 10 = 110/210 and 16 × 7/30 × 7 = 112/210

Step 3: Add the Numerators
Now add the numerators (110 + 112 = 222) and keep the common denominator 210 unchanged.
Working: 110 + 112/210 = 222/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 222 and 210, which is 6. Divide both the numerator and denominator by 6.
Working: 222 ÷ 6/210 ÷ 6 = 37/35

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (37) is greater than the denominator (35), divide 37 by 35: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/35.
Working: 37/35 = 1 2/35

Step 6: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 35 produces a repeating decimal (approximately 1.057143, or 105.7143%).
Working: 37 ÷ 35 = 1.057143 (105.7143%)

Key Values:
- Simplified Fraction: 37/35
- Mixed Number Form: 1 2/35
- Decimal Value: 1.057143
- Percentage: 105.7143%

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11/21 + 16/30 = 37/35

Simplified Fraction

37/35

Mixed Number

1 2/35

Decimal Value

1.057143

Percentage

105.7143%

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Step-by-Step Solution: 11/21 + 16/30

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 30 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 210 (which is smaller than their product 21 × 30 = 630, keeping the calculation simpler).

LCD(21, 30) = 210

Step 2

Convert to Equivalent Fractions with Common Denominator 210

Multiply the numerator and denominator of 11/21 by 10, and multiply the numerator and denominator of 16/30 by 7 so both fractions share the common base 210.

11 × 10/21 × 10 = 110/210 and 16 × 7/30 × 7 = 112/210

Step 3

Add the Numerators

Now add the numerators (110 + 112 = 222) and keep the common denominator 210 unchanged.

110 + 112/210 = 222/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 222 and 210, which is 6. Divide both the numerator and denominator by 6.

222 ÷ 6/210 ÷ 6 = 37/35

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (37) is greater than the denominator (35), divide 37 by 35: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/35.

37/35 = 12/35

Step 6

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 35 produces a repeating decimal (approximately 1.057143, or 105.7143%).

37 ÷ 35 = 1.057143 (105.7143%)

Visual Representation

The diagram below illustrates 11/21 plus 16/30 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/35`
Mixed Number Form	`1 2/35`
Decimal Form	`1.057143`
Percentage	`105.7143%`

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Frequently Asked Questions

What is 11/21 plus 16/30 as a fraction?

11/21 + 16/30 in simplest fraction form is 37/35 (or 1 2/35 as a mixed number).

What is 11/21 plus 16/30 as a decimal?

11/21 + 16/30 converted to a decimal is 1.057143.

What is 11/21 plus 16/30 as a percentage?

11/21 + 16/30 expressed as a percentage is 105.7143%.

How do you write 11/21 plus 16/30 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 37/35 can be written as the mixed number 1 2/35.

Does 11/21 plus 16/30 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.057143...) because the denominator contains prime factors other than 2 and 5.