What is 7/24 plus 10/21? (Answer: 43/56)

Exact Answer

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Problem: What is 7/24 plus 10/21?
Formula / Expression: 7/24 + 10/21
Final Answer: 43/56
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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 10/21 by 8 so both fractions share the common base 168.
Working: 7 × 7/24 × 7 = 49/168 and 10 × 8/21 × 8 = 80/168

Step 3: Add the Numerators
Now add the numerators (49 + 80 = 129) and keep the common denominator 168 unchanged.
Working: 49 + 80/168 = 129/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 129 and 168, which is 3. Divide both the numerator and denominator by 3.
Working: 129 ÷ 3/168 ÷ 3 = 43/56

Step 5: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 56 produces a repeating decimal (approximately 0.767857, or 76.7857%).
Working: 43 ÷ 56 = 0.767857 (76.7857%)

Key Values:
- Simplified Fraction: 43/56
- Mixed Number Form: 43/56
- Decimal Value: 0.767857
- Percentage: 76.7857%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-24-plus-10-21/
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7/24 + 10/21 = 43/56

Simplified Fraction

43/56

Mixed Number

Proper (43/56)

Decimal Value

0.767857

Percentage

76.7857%

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Step-by-Step Solution: 7/24 + 10/21

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 10/21 by 8 so both fractions share the common base 168.

7 × 7/24 × 7 = 49/168 and 10 × 8/21 × 8 = 80/168

Step 3

Add the Numerators

Now add the numerators (49 + 80 = 129) and keep the common denominator 168 unchanged.

49 + 80/168 = 129/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 129 and 168, which is 3. Divide both the numerator and denominator by 3.

129 ÷ 3/168 ÷ 3 = 43/56

Step 5

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 56 produces a repeating decimal (approximately 0.767857, or 76.7857%).

43 ÷ 56 = 0.767857 (76.7857%)

Visual Representation

The diagram below illustrates 7/24 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/56`
Mixed Number Form	`43/56`
Decimal Form	`0.767857`
Percentage	`76.7857%`

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Frequently Asked Questions

What is 7/24 plus 10/21 as a fraction?

7/24 + 10/21 in simplest fraction form is 43/56.

What is 7/24 plus 10/21 as a decimal?

7/24 + 10/21 converted to a decimal is 0.767857.

What is 7/24 plus 10/21 as a percentage?

7/24 + 10/21 expressed as a percentage is 76.7857%.

Does 7/24 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.767857...) because the denominator contains prime factors other than 2 and 5.