What is 1/8 plus 7/21? (Answer: 11/24)

Exact Answer

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Problem: What is 1/8 plus 7/21?
Formula / Expression: 1/8 + 7/21
Final Answer: 11/24
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 8 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 21 = 168.
Working: LCD(8, 21) = 168

Step 2: Convert to Equivalent Fractions with Common Denominator 168
Multiply the numerator and denominator of 1/8 by 21, and multiply the numerator and denominator of 7/21 by 8 so both fractions share the common base 168.
Working: 1 × 21/8 × 21 = 21/168 and 7 × 8/21 × 8 = 56/168

Step 3: Add the Numerators
Now add the numerators (21 + 56 = 77) and keep the common denominator 168 unchanged.
Working: 21 + 56/168 = 77/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 77 and 168, which is 7. Divide both the numerator and denominator by 7.
Working: 77 ÷ 7/168 ÷ 7 = 11/24

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 24 produces a repeating decimal (approximately 0.458333, or 45.8333%).
Working: 11 ÷ 24 = 0.458333 (45.8333%)

Key Values:
- Simplified Fraction: 11/24
- Mixed Number Form: 11/24
- Decimal Value: 0.458333
- Percentage: 45.8333%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-8-plus-7-21/
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1/8 + 7/21 = 11/24

Simplified Fraction

11/24

Mixed Number

Proper (11/24)

Decimal Value

0.458333

Percentage

45.8333%

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Step-by-Step Solution: 1/8 + 7/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 8 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 21 = 168.

LCD(8, 21) = 168

Step 2

Convert to Equivalent Fractions with Common Denominator 168

Multiply the numerator and denominator of 1/8 by 21, and multiply the numerator and denominator of 7/21 by 8 so both fractions share the common base 168.

1 × 21/8 × 21 = 21/168 and 7 × 8/21 × 8 = 56/168

Step 3

Add the Numerators

Now add the numerators (21 + 56 = 77) and keep the common denominator 168 unchanged.

21 + 56/168 = 77/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 77 and 168, which is 7. Divide both the numerator and denominator by 7.

77 ÷ 7/168 ÷ 7 = 11/24

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 24 produces a repeating decimal (approximately 0.458333, or 45.8333%).

11 ÷ 24 = 0.458333 (45.8333%)

Visual Representation

The diagram below illustrates 1/8 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/24`
Mixed Number Form	`11/24`
Decimal Form	`0.458333`
Percentage	`45.8333%`

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Frequently Asked Questions

What is 1/8 plus 7/21 as a fraction?

1/8 + 7/21 in simplest fraction form is 11/24.

What is 1/8 plus 7/21 as a decimal?

1/8 + 7/21 converted to a decimal is 0.458333.

What is 1/8 plus 7/21 as a percentage?

1/8 + 7/21 expressed as a percentage is 45.8333%.

Does 1/8 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.458333...) because the denominator contains prime factors other than 2 and 5.