What is 7/24 plus 15/21? (Answer: 169/168)

Exact Answer

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Problem: What is 7/24 plus 15/21?
Formula / Expression: 7/24 + 15/21
Final Answer: 1 1/168 (169/168)
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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 7/24 by 7, and multiply the numerator and denominator of 15/21 by 8 so both fractions share the common base 168.
Working: 7 × 7/24 × 7 = 49/168 and 15 × 8/21 × 8 = 120/168

Step 3: Add the Numerators
Now add the numerators (49 + 120 = 169) and keep the common denominator 168 unchanged.
Working: 49 + 120/168 = 169/168

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 169 and 168 is 1, confirming that 169/168 cannot be reduced further—it is already in its simplest irreducible form.
Working: 169/168

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (169) is greater than the denominator (168), divide 169 by 168: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/168.
Working: 169/168 = 1 1/168

Step 6: Decimal & Percentage Representation
Dividing the numerator 169 by denominator 168 produces a repeating decimal (approximately 1.005952, or 100.5952%).
Working: 169 ÷ 168 = 1.005952 (100.5952%)

Key Values:
- Simplified Fraction: 169/168
- Mixed Number Form: 1 1/168
- Decimal Value: 1.005952
- Percentage: 100.5952%

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Solved with FractionsCalc:
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7/24 + 15/21 = 169/168

Simplified Fraction

169/168

Mixed Number

1 1/168

Decimal Value

1.005952

Percentage

100.5952%

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Step-by-Step Solution: 7/24 + 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 7/24 by 7, and multiply the numerator and denominator of 15/21 by 8 so both fractions share the common base 168.

7 × 7/24 × 7 = 49/168 and 15 × 8/21 × 8 = 120/168

Step 3

Add the Numerators

Now add the numerators (49 + 120 = 169) and keep the common denominator 168 unchanged.

49 + 120/168 = 169/168

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 169 and 168 is 1, confirming that 169/168 cannot be reduced further—it is already in its simplest irreducible form.

169/168

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (169) is greater than the denominator (168), divide 169 by 168: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/168.

169/168 = 11/168

Step 6

Decimal & Percentage Representation

Dividing the numerator 169 by denominator 168 produces a repeating decimal (approximately 1.005952, or 100.5952%).

169 ÷ 168 = 1.005952 (100.5952%)

Visual Representation

The diagram below illustrates 7/24 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`169/168`
Mixed Number Form	`1 1/168`
Decimal Form	`1.005952`
Percentage	`100.5952%`

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Frequently Asked Questions

What is 7/24 plus 15/21 as a fraction?

7/24 + 15/21 in simplest fraction form is 169/168 (or 1 1/168 as a mixed number).

What is 7/24 plus 15/21 as a decimal?

7/24 + 15/21 converted to a decimal is 1.005952.

What is 7/24 plus 15/21 as a percentage?

7/24 + 15/21 expressed as a percentage is 100.5952%.

How do you write 7/24 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 169/168 can be written as the mixed number 1 1/168.

Does 7/24 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.005952...) because the denominator contains prime factors other than 2 and 5.