What is 12/30 plus 15/21? (Answer: 39/35)

Exact Answer

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Problem: What is 12/30 plus 15/21?
Formula / Expression: 12/30 + 15/21
Final Answer: 1 4/35 (39/35)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 210
Multiply the numerator and denominator of 12/30 by 7, and multiply the numerator and denominator of 15/21 by 10 so both fractions share the common base 210.
Working: 12 × 7/30 × 7 = 84/210 and 15 × 10/21 × 10 = 150/210

Step 3: Add the Numerators
Now add the numerators (84 + 150 = 234) and keep the common denominator 210 unchanged.
Working: 84 + 150/210 = 234/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 234 and 210, which is 6. Divide both the numerator and denominator by 6.
Working: 234 ÷ 6/210 ÷ 6 = 39/35

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (39) is greater than the denominator (35), divide 39 by 35: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/35.
Working: 39/35 = 1 4/35

Step 6: Decimal & Percentage Representation
Dividing the numerator 39 by denominator 35 produces a repeating decimal (approximately 1.114286, or 111.4286%).
Working: 39 ÷ 35 = 1.114286 (111.4286%)

Key Values:
- Simplified Fraction: 39/35
- Mixed Number Form: 1 4/35
- Decimal Value: 1.114286
- Percentage: 111.4286%

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12/30 + 15/21 = 39/35

Simplified Fraction

39/35

Mixed Number

1 4/35

Decimal Value

1.114286

Percentage

111.4286%

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Step-by-Step Solution: 12/30 + 15/21

Step 1

Find the Least Common Denominator (LCD)

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

LCD(30, 21) = 210

Step 2

Convert to Equivalent Fractions with Common Denominator 210

Multiply the numerator and denominator of 12/30 by 7, and multiply the numerator and denominator of 15/21 by 10 so both fractions share the common base 210.

12 × 7/30 × 7 = 84/210 and 15 × 10/21 × 10 = 150/210

Step 3

Add the Numerators

Now add the numerators (84 + 150 = 234) and keep the common denominator 210 unchanged.

84 + 150/210 = 234/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 234 and 210, which is 6. Divide both the numerator and denominator by 6.

234 ÷ 6/210 ÷ 6 = 39/35

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (39) is greater than the denominator (35), divide 39 by 35: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/35.

39/35 = 14/35

Step 6

Decimal & Percentage Representation

Dividing the numerator 39 by denominator 35 produces a repeating decimal (approximately 1.114286, or 111.4286%).

39 ÷ 35 = 1.114286 (111.4286%)

Visual Representation

The diagram below illustrates 12/30 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`39/35`
Mixed Number Form	`1 4/35`
Decimal Form	`1.114286`
Percentage	`111.4286%`

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Frequently Asked Questions

What is 12/30 plus 15/21 as a fraction?

12/30 + 15/21 in simplest fraction form is 39/35 (or 1 4/35 as a mixed number).

What is 12/30 plus 15/21 as a decimal?

12/30 + 15/21 converted to a decimal is 1.114286.

What is 12/30 plus 15/21 as a percentage?

12/30 + 15/21 expressed as a percentage is 111.4286%.

How do you write 12/30 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 39/35 can be written as the mixed number 1 4/35.

Does 12/30 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.114286...) because the denominator contains prime factors other than 2 and 5.