What is 7/24 plus 8/21? (Answer: 113/168)

Exact Answer

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Problem: What is 7/24 plus 8/21?
Formula / Expression: 7/24 + 8/21
Final Answer: 113/168
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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 8/21 by 8 so both fractions share the common base 168.
Working: 7 × 7/24 × 7 = 49/168 and 8 × 8/21 × 8 = 64/168

Step 3: Add the Numerators
Now add the numerators (49 + 64 = 113) and keep the common denominator 168 unchanged.
Working: 49 + 64/168 = 113/168

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 113 and 168 is 1, confirming that 113/168 cannot be reduced further—it is already in its simplest irreducible form.
Working: 113/168

Step 5: Decimal & Percentage Representation
Dividing the numerator 113 by denominator 168 produces a repeating decimal (approximately 0.672619, or 67.2619%).
Working: 113 ÷ 168 = 0.672619 (67.2619%)

Key Values:
- Simplified Fraction: 113/168
- Mixed Number Form: 113/168
- Decimal Value: 0.672619
- Percentage: 67.2619%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-24-plus-8-21/
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7/24 + 8/21 = 113/168

Simplified Fraction

113/168

Mixed Number

Proper (113/168)

Decimal Value

0.672619

Percentage

67.2619%

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Step-by-Step Solution: 7/24 + 8/21

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 8/21 by 8 so both fractions share the common base 168.

7 × 7/24 × 7 = 49/168 and 8 × 8/21 × 8 = 64/168

Step 3

Add the Numerators

Now add the numerators (49 + 64 = 113) and keep the common denominator 168 unchanged.

49 + 64/168 = 113/168

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 113 and 168 is 1, confirming that 113/168 cannot be reduced further—it is already in its simplest irreducible form.

113/168

Step 5

Decimal & Percentage Representation

Dividing the numerator 113 by denominator 168 produces a repeating decimal (approximately 0.672619, or 67.2619%).

113 ÷ 168 = 0.672619 (67.2619%)

Visual Representation

The diagram below illustrates 7/24 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`113/168`
Mixed Number Form	`113/168`
Decimal Form	`0.672619`
Percentage	`67.2619%`

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Frequently Asked Questions

What is 7/24 plus 8/21 as a fraction?

7/24 + 8/21 in simplest fraction form is 113/168.

What is 7/24 plus 8/21 as a decimal?

7/24 + 8/21 converted to a decimal is 0.672619.

What is 7/24 plus 8/21 as a percentage?

7/24 + 8/21 expressed as a percentage is 67.2619%.

Does 7/24 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.672619...) because the denominator contains prime factors other than 2 and 5.