What is 2/3 divided by 7/8? (Answer: 16/21)

Exact Answer

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Problem: What is 2/3 divided by 7/8?
Formula / Expression: 2/3 ÷ 7/8
Final Answer: 16/21
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Step-by-Step Solution:

Step 1: Find the Reciprocal of the Second Fraction
Dividing by a fraction is equivalent to multiplying by its reciprocal ("Keep, Change, Flip"). Invert the second fraction 7/8 to get 8/7.
Working: 2/3 ÷ 7/8 = 2/3 × 8/7

Step 2: Multiply the Numerators and Denominators
Multiply the new numerators (2 × 8 = 16) and denominators (3 × 7 = 21).
Working: 2 × 8/3 × 7 = 16/21

Step 3: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 16 and 21 is 1, confirming that 16/21 cannot be reduced further—it is already in its simplest irreducible form.
Working: 16/21

Step 4: Decimal & Percentage Representation
Dividing the numerator 16 by denominator 21 produces a repeating decimal (approximately 0.761905, or 76.1905%).
Working: 16 ÷ 21 = 0.761905 (76.1905%)

Key Values:
- Simplified Fraction: 16/21
- Mixed Number Form: 16/21
- Decimal Value: 0.761905
- Percentage: 76.1905%

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2/3 ÷ 7/8 = 16/21

Simplified Fraction

16/21

Mixed Number

Proper (16/21)

Decimal Value

0.761905

Percentage

76.1905%

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Step-by-Step Solution: 2/3 ÷ 7/8

Step 1

Find the Reciprocal of the Second Fraction

Dividing by a fraction is equivalent to multiplying by its reciprocal ("Keep, Change, Flip"). Invert the second fraction 7/8 to get 8/7.

2/3 ÷ 7/8 = 2/3 × 8/7

Step 2

Multiply the Numerators and Denominators

Multiply the new numerators (2 × 8 = 16) and denominators (3 × 7 = 21).

2 × 8/3 × 7 = 16/21

Step 3

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 16 and 21 is 1, confirming that 16/21 cannot be reduced further—it is already in its simplest irreducible form.

16/21

Step 4

Decimal & Percentage Representation

Dividing the numerator 16 by denominator 21 produces a repeating decimal (approximately 0.761905, or 76.1905%).

16 ÷ 21 = 0.761905 (76.1905%)

Visual Representation

The diagram below illustrates 2/3 divided by 7/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`16/21`
Mixed Number Form	`16/21`
Decimal Form	`0.761905`
Percentage	`76.1905%`

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Frequently Asked Questions

What is 2/3 divided by 7/8 as a fraction?

2/3 ÷ 7/8 in simplest fraction form is 16/21.

What is 2/3 divided by 7/8 as a decimal?

2/3 ÷ 7/8 converted to a decimal is 0.761905.

What is 2/3 divided by 7/8 as a percentage?

2/3 ÷ 7/8 expressed as a percentage is 76.1905%.

Does 2/3 divided by 7/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.761905...) because the denominator contains prime factors other than 2 and 5.