What is 14/30 plus 15/21? (Answer: 124/105)

Exact Answer

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Problem: What is 14/30 plus 15/21?
Formula / Expression: 14/30 + 15/21
Final Answer: 1 19/105 (124/105)
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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 14/30 by 7, and multiply the numerator and denominator of 15/21 by 10 so both fractions share the common base 210.
Working: 14 × 7/30 × 7 = 98/210 and 15 × 10/21 × 10 = 150/210

Step 3: Add the Numerators
Now add the numerators (98 + 150 = 248) and keep the common denominator 210 unchanged.
Working: 98 + 150/210 = 248/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 248 and 210, which is 2. Divide both the numerator and denominator by 2.
Working: 248 ÷ 2/210 ÷ 2 = 124/105

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (124) is greater than the denominator (105), divide 124 by 105: it goes in 1 whole time(s) with a remainder of 19, giving the mixed number 1 19/105.
Working: 124/105 = 1 19/105

Step 6: Decimal & Percentage Representation
Dividing the numerator 124 by denominator 105 produces a repeating decimal (approximately 1.180952, or 118.0952%).
Working: 124 ÷ 105 = 1.180952 (118.0952%)

Key Values:
- Simplified Fraction: 124/105
- Mixed Number Form: 1 19/105
- Decimal Value: 1.180952
- Percentage: 118.0952%

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14/30 + 15/21 = 124/105

Simplified Fraction

124/105

Mixed Number

1 19/105

Decimal Value

1.180952

Percentage

118.0952%

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Step-by-Step Solution: 14/30 + 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 14/30 by 7, and multiply the numerator and denominator of 15/21 by 10 so both fractions share the common base 210.

14 × 7/30 × 7 = 98/210 and 15 × 10/21 × 10 = 150/210

Step 3

Add the Numerators

Now add the numerators (98 + 150 = 248) and keep the common denominator 210 unchanged.

98 + 150/210 = 248/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 248 and 210, which is 2. Divide both the numerator and denominator by 2.

248 ÷ 2/210 ÷ 2 = 124/105

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (124) is greater than the denominator (105), divide 124 by 105: it goes in 1 whole time(s) with a remainder of 19, giving the mixed number 1 19/105.

124/105 = 119/105

Step 6

Decimal & Percentage Representation

Dividing the numerator 124 by denominator 105 produces a repeating decimal (approximately 1.180952, or 118.0952%).

124 ÷ 105 = 1.180952 (118.0952%)

Visual Representation

The diagram below illustrates 14/30 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`124/105`
Mixed Number Form	`1 19/105`
Decimal Form	`1.180952`
Percentage	`118.0952%`

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Frequently Asked Questions

What is 14/30 plus 15/21 as a fraction?

14/30 + 15/21 in simplest fraction form is 124/105 (or 1 19/105 as a mixed number).

What is 14/30 plus 15/21 as a decimal?

14/30 + 15/21 converted to a decimal is 1.180952.

What is 14/30 plus 15/21 as a percentage?

14/30 + 15/21 expressed as a percentage is 118.0952%.

How do you write 14/30 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 124/105 can be written as the mixed number 1 19/105.

Does 14/30 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.180952...) because the denominator contains prime factors other than 2 and 5.