What is 10/24 plus 15/21? (Answer: 95/84)

Exact Answer

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Problem: What is 10/24 plus 15/21?
Formula / Expression: 10/24 + 15/21
Final Answer: 1 11/84 (95/84)
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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 10/24 by 7, and multiply the numerator and denominator of 15/21 by 8 so both fractions share the common base 168.
Working: 10 × 7/24 × 7 = 70/168 and 15 × 8/21 × 8 = 120/168

Step 3: Add the Numerators
Now add the numerators (70 + 120 = 190) and keep the common denominator 168 unchanged.
Working: 70 + 120/168 = 190/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 190 and 168, which is 2. Divide both the numerator and denominator by 2.
Working: 190 ÷ 2/168 ÷ 2 = 95/84

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (95) is greater than the denominator (84), divide 95 by 84: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/84.
Working: 95/84 = 1 11/84

Step 6: Decimal & Percentage Representation
Dividing the numerator 95 by denominator 84 produces a repeating decimal (approximately 1.130952, or 113.0952%).
Working: 95 ÷ 84 = 1.130952 (113.0952%)

Key Values:
- Simplified Fraction: 95/84
- Mixed Number Form: 1 11/84
- Decimal Value: 1.130952
- Percentage: 113.0952%

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Solved with FractionsCalc:
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10/24 + 15/21 = 95/84

Simplified Fraction

95/84

Mixed Number

1 11/84

Decimal Value

1.130952

Percentage

113.0952%

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Step-by-Step Solution: 10/24 + 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 10/24 by 7, and multiply the numerator and denominator of 15/21 by 8 so both fractions share the common base 168.

10 × 7/24 × 7 = 70/168 and 15 × 8/21 × 8 = 120/168

Step 3

Add the Numerators

Now add the numerators (70 + 120 = 190) and keep the common denominator 168 unchanged.

70 + 120/168 = 190/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 190 and 168, which is 2. Divide both the numerator and denominator by 2.

190 ÷ 2/168 ÷ 2 = 95/84

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (95) is greater than the denominator (84), divide 95 by 84: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/84.

95/84 = 111/84

Step 6

Decimal & Percentage Representation

Dividing the numerator 95 by denominator 84 produces a repeating decimal (approximately 1.130952, or 113.0952%).

95 ÷ 84 = 1.130952 (113.0952%)

Visual Representation

The diagram below illustrates 10/24 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`95/84`
Mixed Number Form	`1 11/84`
Decimal Form	`1.130952`
Percentage	`113.0952%`

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Frequently Asked Questions

What is 10/24 plus 15/21 as a fraction?

10/24 + 15/21 in simplest fraction form is 95/84 (or 1 11/84 as a mixed number).

What is 10/24 plus 15/21 as a decimal?

10/24 + 15/21 converted to a decimal is 1.130952.

What is 10/24 plus 15/21 as a percentage?

10/24 + 15/21 expressed as a percentage is 113.0952%.

How do you write 10/24 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 95/84 can be written as the mixed number 1 11/84.

Does 10/24 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.130952...) because the denominator contains prime factors other than 2 and 5.