What is 24/45 plus 15/21? (Answer: 131/105)

Exact Answer

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Problem: What is 24/45 plus 15/21?
Formula / Expression: 24/45 + 15/21
Final Answer: 1 26/105 (131/105)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 45 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 315 (which is smaller than their product 45 × 21 = 945, keeping the calculation simpler).
Working: LCD(45, 21) = 315

Step 2: Convert to Equivalent Fractions with Common Denominator 315
Multiply the numerator and denominator of 24/45 by 7, and multiply the numerator and denominator of 15/21 by 15 so both fractions share the common base 315.
Working: 24 × 7/45 × 7 = 168/315 and 15 × 15/21 × 15 = 225/315

Step 3: Add the Numerators
Now add the numerators (168 + 225 = 393) and keep the common denominator 315 unchanged.
Working: 168 + 225/315 = 393/315

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 393 and 315, which is 3. Divide both the numerator and denominator by 3.
Working: 393 ÷ 3/315 ÷ 3 = 131/105

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (131) is greater than the denominator (105), divide 131 by 105: it goes in 1 whole time(s) with a remainder of 26, giving the mixed number 1 26/105.
Working: 131/105 = 1 26/105

Step 6: Decimal & Percentage Representation
Dividing the numerator 131 by denominator 105 produces a repeating decimal (approximately 1.247619, or 124.7619%).
Working: 131 ÷ 105 = 1.247619 (124.7619%)

Key Values:
- Simplified Fraction: 131/105
- Mixed Number Form: 1 26/105
- Decimal Value: 1.247619
- Percentage: 124.7619%

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24/45 + 15/21 = 131/105

Simplified Fraction

131/105

Mixed Number

1 26/105

Decimal Value

1.247619

Percentage

124.7619%

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Step-by-Step Solution: 24/45 + 15/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 45 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 315 (which is smaller than their product 45 × 21 = 945, keeping the calculation simpler).

LCD(45, 21) = 315

Step 2

Convert to Equivalent Fractions with Common Denominator 315

Multiply the numerator and denominator of 24/45 by 7, and multiply the numerator and denominator of 15/21 by 15 so both fractions share the common base 315.

24 × 7/45 × 7 = 168/315 and 15 × 15/21 × 15 = 225/315

Step 3

Add the Numerators

Now add the numerators (168 + 225 = 393) and keep the common denominator 315 unchanged.

168 + 225/315 = 393/315

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 393 and 315, which is 3. Divide both the numerator and denominator by 3.

393 ÷ 3/315 ÷ 3 = 131/105

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (131) is greater than the denominator (105), divide 131 by 105: it goes in 1 whole time(s) with a remainder of 26, giving the mixed number 1 26/105.

131/105 = 126/105

Step 6

Decimal & Percentage Representation

Dividing the numerator 131 by denominator 105 produces a repeating decimal (approximately 1.247619, or 124.7619%).

131 ÷ 105 = 1.247619 (124.7619%)

Visual Representation

The diagram below illustrates 24/45 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`131/105`
Mixed Number Form	`1 26/105`
Decimal Form	`1.247619`
Percentage	`124.7619%`

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Frequently Asked Questions

What is 24/45 plus 15/21 as a fraction?

24/45 + 15/21 in simplest fraction form is 131/105 (or 1 26/105 as a mixed number).

What is 24/45 plus 15/21 as a decimal?

24/45 + 15/21 converted to a decimal is 1.247619.

What is 24/45 plus 15/21 as a percentage?

24/45 + 15/21 expressed as a percentage is 124.7619%.

How do you write 24/45 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 131/105 can be written as the mixed number 1 26/105.

Does 24/45 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.247619...) because the denominator contains prime factors other than 2 and 5.