What is 7/15 plus 15/21? (Answer: 124/105)

Exact Answer

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Problem: What is 7/15 plus 15/21?
Formula / Expression: 7/15 + 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 15 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 15 × 21 = 315, keeping the calculation simpler).
Working: LCD(15, 21) = 105

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 7/15 by 7, and multiply the numerator and denominator of 15/21 by 5 so both fractions share the common base 105.
Working: 7 × 7/15 × 7 = 49/105 and 15 × 5/21 × 5 = 75/105

Step 3: Add the Numerators
Now add the numerators (49 + 75 = 124) and keep the common denominator 105 unchanged.
Working: 49 + 75/105 = 124/105

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 124 and 105 is 1, confirming that 124/105 cannot be reduced further—it is already in its simplest irreducible form.
Working: 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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Solved with FractionsCalc:
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7/15 + 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: 7/15 + 15/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 15 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 15 × 21 = 315, keeping the calculation simpler).

LCD(15, 21) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 7/15 by 7, and multiply the numerator and denominator of 15/21 by 5 so both fractions share the common base 105.

7 × 7/15 × 7 = 49/105 and 15 × 5/21 × 5 = 75/105

Step 3

Add the Numerators

Now add the numerators (49 + 75 = 124) and keep the common denominator 105 unchanged.

49 + 75/105 = 124/105

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 124 and 105 is 1, confirming that 124/105 cannot be reduced further—it is already in its simplest irreducible form.

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 7/15 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 7/15 plus 15/21 as a fraction?

7/15 + 15/21 in simplest fraction form is 124/105 (or 1 19/105 as a mixed number).

What is 7/15 plus 15/21 as a decimal?

7/15 + 15/21 converted to a decimal is 1.180952.

What is 7/15 plus 15/21 as a percentage?

7/15 + 15/21 expressed as a percentage is 118.0952%.

How do you write 7/15 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 7/15 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.