What is 7/24 plus 7/21? (Answer: 5/8)

Exact Answer

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Problem: What is 7/24 plus 7/21?
Formula / Expression: 7/24 + 7/21
Final Answer: 5/8
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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 7/21 by 8 so both fractions share the common base 168.
Working: 7 × 7/24 × 7 = 49/168 and 7 × 8/21 × 8 = 56/168

Step 3: Add the Numerators
Now add the numerators (49 + 56 = 105) and keep the common denominator 168 unchanged.
Working: 49 + 56/168 = 105/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 105 and 168, which is 21. Divide both the numerator and denominator by 21.
Working: 105 ÷ 21/168 ÷ 21 = 5/8

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 8 yields an exact terminating decimal of 0.625 (or 62.5%).
Working: 5 ÷ 8 = 0.625 (62.5%)

Key Values:
- Simplified Fraction: 5/8
- Mixed Number Form: 5/8
- Decimal Value: 0.625
- Percentage: 62.5%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-24-plus-7-21/
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7/24 + 7/21 = 5/8

Simplified Fraction

5/8

Mixed Number

Proper (5/8)

Decimal Value

0.625

Percentage

62.5%

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

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 7/21 by 8 so both fractions share the common base 168.

7 × 7/24 × 7 = 49/168 and 7 × 8/21 × 8 = 56/168

Step 3

Add the Numerators

Now add the numerators (49 + 56 = 105) and keep the common denominator 168 unchanged.

49 + 56/168 = 105/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 105 and 168, which is 21. Divide both the numerator and denominator by 21.

105 ÷ 21/168 ÷ 21 = 5/8

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 8 yields an exact terminating decimal of 0.625 (or 62.5%).

5 ÷ 8 = 0.625 (62.5%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/8`
Mixed Number Form	`5/8`
Decimal Form	`0.625`
Percentage	`62.5%`

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Frequently Asked Questions

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

7/24 + 7/21 in simplest fraction form is 5/8.

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

7/24 + 7/21 converted to a decimal is 0.625.

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

7/24 + 7/21 expressed as a percentage is 62.5%.

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

It results in an exact terminating decimal (0.625) because the denominator in simplest terms contains only prime factors 2 and/or 5.