What is 15/21 plus 11/15? (Answer: 152/105)

Exact Answer

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Problem: What is 15/21 plus 11/15?
Formula / Expression: 15/21 + 11/15
Final Answer: 1 47/105 (152/105)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 15 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 21 × 15 = 315, keeping the calculation simpler).
Working: LCD(21, 15) = 105

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 15/21 by 5, and multiply the numerator and denominator of 11/15 by 7 so both fractions share the common base 105.
Working: 15 × 5/21 × 5 = 75/105 and 11 × 7/15 × 7 = 77/105

Step 3: Add the Numerators
Now add the numerators (75 + 77 = 152) and keep the common denominator 105 unchanged.
Working: 75 + 77/105 = 152/105

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 152 and 105 is 1, confirming that 152/105 cannot be reduced further—it is already in its simplest irreducible form.
Working: 152/105

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (152) is greater than the denominator (105), divide 152 by 105: it goes in 1 whole time(s) with a remainder of 47, giving the mixed number 1 47/105.
Working: 152/105 = 1 47/105

Step 6: Decimal & Percentage Representation
Dividing the numerator 152 by denominator 105 produces a repeating decimal (approximately 1.447619, or 144.7619%).
Working: 152 ÷ 105 = 1.447619 (144.7619%)

Key Values:
- Simplified Fraction: 152/105
- Mixed Number Form: 1 47/105
- Decimal Value: 1.447619
- Percentage: 144.7619%

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Solved with FractionsCalc:
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15/21 + 11/15 = 152/105

Simplified Fraction

152/105

Mixed Number

1 47/105

Decimal Value

1.447619

Percentage

144.7619%

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Step-by-Step Solution: 15/21 + 11/15

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 15) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 15/21 by 5, and multiply the numerator and denominator of 11/15 by 7 so both fractions share the common base 105.

15 × 5/21 × 5 = 75/105 and 11 × 7/15 × 7 = 77/105

Step 3

Add the Numerators

Now add the numerators (75 + 77 = 152) and keep the common denominator 105 unchanged.

75 + 77/105 = 152/105

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 152 and 105 is 1, confirming that 152/105 cannot be reduced further—it is already in its simplest irreducible form.

152/105

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (152) is greater than the denominator (105), divide 152 by 105: it goes in 1 whole time(s) with a remainder of 47, giving the mixed number 1 47/105.

152/105 = 147/105

Step 6

Decimal & Percentage Representation

Dividing the numerator 152 by denominator 105 produces a repeating decimal (approximately 1.447619, or 144.7619%).

152 ÷ 105 = 1.447619 (144.7619%)

Visual Representation

The diagram below illustrates 15/21 plus 11/15 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`152/105`
Mixed Number Form	`1 47/105`
Decimal Form	`1.447619`
Percentage	`144.7619%`

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Frequently Asked Questions

What is 15/21 plus 11/15 as a fraction?

15/21 + 11/15 in simplest fraction form is 152/105 (or 1 47/105 as a mixed number).

What is 15/21 plus 11/15 as a decimal?

15/21 + 11/15 converted to a decimal is 1.447619.

What is 15/21 plus 11/15 as a percentage?

15/21 + 11/15 expressed as a percentage is 144.7619%.

How do you write 15/21 plus 11/15 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 152/105 can be written as the mixed number 1 47/105.

Does 15/21 plus 11/15 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.447619...) because the denominator contains prime factors other than 2 and 5.