What is 1/3 divided by 7/8? (Answer: 8/21)

Exact Answer

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Problem: What is 1/3 divided by 7/8?
Formula / Expression: 1/3 ÷ 7/8
Final Answer: 8/21
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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: 1/3 ÷ 7/8 = 1/3 × 8/7

Step 2: Multiply the Numerators and Denominators
Multiply the new numerators (1 × 8 = 8) and denominators (3 × 7 = 21).
Working: 1 × 8/3 × 7 = 8/21

Step 3: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 8 and 21 is 1, confirming that 8/21 cannot be reduced further—it is already in its simplest irreducible form.
Working: 8/21

Step 4: Decimal & Percentage Representation
Dividing the numerator 8 by denominator 21 produces a repeating decimal (approximately 0.380952, or 38.0952%).
Working: 8 ÷ 21 = 0.380952 (38.0952%)

Key Values:
- Simplified Fraction: 8/21
- Mixed Number Form: 8/21
- Decimal Value: 0.380952
- Percentage: 38.0952%

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1/3 ÷ 7/8 = 8/21

Simplified Fraction

8/21

Mixed Number

Proper (8/21)

Decimal Value

0.380952

Percentage

38.0952%

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Step-by-Step Solution: 1/3 ÷ 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.

1/3 ÷ 7/8 = 1/3 × 8/7

Step 2

Multiply the Numerators and Denominators

Multiply the new numerators (1 × 8 = 8) and denominators (3 × 7 = 21).

1 × 8/3 × 7 = 8/21

Step 3

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 8 and 21 is 1, confirming that 8/21 cannot be reduced further—it is already in its simplest irreducible form.

8/21

Step 4

Decimal & Percentage Representation

Dividing the numerator 8 by denominator 21 produces a repeating decimal (approximately 0.380952, or 38.0952%).

8 ÷ 21 = 0.380952 (38.0952%)

Visual Representation

The diagram below illustrates 1/3 divided by 7/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`8/21`
Mixed Number Form	`8/21`
Decimal Form	`0.380952`
Percentage	`38.0952%`

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Frequently Asked Questions

What is 1/3 divided by 7/8 as a fraction?

1/3 ÷ 7/8 in simplest fraction form is 8/21.

What is 1/3 divided by 7/8 as a decimal?

1/3 ÷ 7/8 converted to a decimal is 0.380952.

What is 1/3 divided by 7/8 as a percentage?

1/3 ÷ 7/8 expressed as a percentage is 38.0952%.

Does 1/3 divided by 7/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.380952...) because the denominator contains prime factors other than 2 and 5.