What is 15/24 plus 15/21? (Answer: 75/56)

Exact Answer

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Problem: What is 15/24 plus 15/21?
Formula / Expression: 15/24 + 15/21
Final Answer: 1 19/56 (75/56)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 24 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 168 (which is smaller than their product 24 × 21 = 504, keeping the calculation simpler).
Working: LCD(24, 21) = 168

Step 2: Convert to Equivalent Fractions with Common Denominator 168
Multiply the numerator and denominator of 15/24 by 7, and multiply the numerator and denominator of 15/21 by 8 so both fractions share the common base 168.
Working: 15 × 7/24 × 7 = 105/168 and 15 × 8/21 × 8 = 120/168

Step 3: Add the Numerators
Now add the numerators (105 + 120 = 225) and keep the common denominator 168 unchanged.
Working: 105 + 120/168 = 225/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 225 and 168, which is 3. Divide both the numerator and denominator by 3.
Working: 225 ÷ 3/168 ÷ 3 = 75/56

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (75) is greater than the denominator (56), divide 75 by 56: it goes in 1 whole time(s) with a remainder of 19, giving the mixed number 1 19/56.
Working: 75/56 = 1 19/56

Step 6: Decimal & Percentage Representation
Dividing the numerator 75 by denominator 56 produces a repeating decimal (approximately 1.339286, or 133.9286%).
Working: 75 ÷ 56 = 1.339286 (133.9286%)

Key Values:
- Simplified Fraction: 75/56
- Mixed Number Form: 1 19/56
- Decimal Value: 1.339286
- Percentage: 133.9286%

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Solved with FractionsCalc:
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15/24 + 15/21 = 75/56

Simplified Fraction

75/56

Mixed Number

1 19/56

Decimal Value

1.339286

Percentage

133.9286%

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Step-by-Step Solution: 15/24 + 15/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 24 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 168 (which is smaller than their product 24 × 21 = 504, keeping the calculation simpler).

LCD(24, 21) = 168

Step 2

Convert to Equivalent Fractions with Common Denominator 168

Multiply the numerator and denominator of 15/24 by 7, and multiply the numerator and denominator of 15/21 by 8 so both fractions share the common base 168.

15 × 7/24 × 7 = 105/168 and 15 × 8/21 × 8 = 120/168

Step 3

Add the Numerators

Now add the numerators (105 + 120 = 225) and keep the common denominator 168 unchanged.

105 + 120/168 = 225/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 225 and 168, which is 3. Divide both the numerator and denominator by 3.

225 ÷ 3/168 ÷ 3 = 75/56

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (75) is greater than the denominator (56), divide 75 by 56: it goes in 1 whole time(s) with a remainder of 19, giving the mixed number 1 19/56.

75/56 = 119/56

Step 6

Decimal & Percentage Representation

Dividing the numerator 75 by denominator 56 produces a repeating decimal (approximately 1.339286, or 133.9286%).

75 ÷ 56 = 1.339286 (133.9286%)

Visual Representation

The diagram below illustrates 15/24 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`75/56`
Mixed Number Form	`1 19/56`
Decimal Form	`1.339286`
Percentage	`133.9286%`

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Frequently Asked Questions

What is 15/24 plus 15/21 as a fraction?

15/24 + 15/21 in simplest fraction form is 75/56 (or 1 19/56 as a mixed number).

What is 15/24 plus 15/21 as a decimal?

15/24 + 15/21 converted to a decimal is 1.339286.

What is 15/24 plus 15/21 as a percentage?

15/24 + 15/21 expressed as a percentage is 133.9286%.

How do you write 15/24 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 75/56 can be written as the mixed number 1 19/56.

Does 15/24 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.339286...) because the denominator contains prime factors other than 2 and 5.