What is 3/7 divided by 8/21? (Answer: 9/8)

Exact Answer

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Problem: What is 3/7 divided by 8/21?
Formula / Expression: 3/7 ÷ 8/21
Final Answer: 1 1/8 (9/8)
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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 8/21 to get 21/8.
Working: 3/7 ÷ 8/21 = 3/7 × 21/8

Step 2: Multiply the Numerators and Denominators
Multiply the new numerators (3 × 21 = 63) and denominators (7 × 8 = 56).
Working: 3 × 21/7 × 8 = 63/56

Step 3: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 63 and 56, which is 7. Divide both the numerator and denominator by 7.
Working: 63 ÷ 7/56 ÷ 7 = 9/8

Step 4: Convert Improper Fraction to a Mixed Number
Since the numerator (9) is greater than the denominator (8), divide 9 by 8: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/8.
Working: 9/8 = 1 1/8

Step 5: Decimal & Percentage Representation
Dividing the numerator 9 by denominator 8 yields an exact terminating decimal of 1.125 (or 112.5%).
Working: 9 ÷ 8 = 1.125 (112.5%)

Key Values:
- Simplified Fraction: 9/8
- Mixed Number Form: 1 1/8
- Decimal Value: 1.125
- Percentage: 112.5%

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3/7 ÷ 8/21 = 9/8

Simplified Fraction

9/8

Mixed Number

1 1/8

Decimal Value

1.125

Percentage

112.5%

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Step-by-Step Solution: 3/7 ÷ 8/21

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 8/21 to get 21/8.

3/7 ÷ 8/21 = 3/7 × 21/8

Step 2

Multiply the Numerators and Denominators

Multiply the new numerators (3 × 21 = 63) and denominators (7 × 8 = 56).

3 × 21/7 × 8 = 63/56

Step 3

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 63 and 56, which is 7. Divide both the numerator and denominator by 7.

63 ÷ 7/56 ÷ 7 = 9/8

Step 4

Convert Improper Fraction to a Mixed Number

Since the numerator (9) is greater than the denominator (8), divide 9 by 8: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/8.

9/8 = 11/8

Step 5

Decimal & Percentage Representation

Dividing the numerator 9 by denominator 8 yields an exact terminating decimal of 1.125 (or 112.5%).

9 ÷ 8 = 1.125 (112.5%)

Visual Representation

The diagram below illustrates 3/7 divided by 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`9/8`
Mixed Number Form	`1 1/8`
Decimal Form	`1.125`
Percentage	`112.5%`

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Frequently Asked Questions

What is 3/7 divided by 8/21 as a fraction?

3/7 ÷ 8/21 in simplest fraction form is 9/8 (or 1 1/8 as a mixed number).

What is 3/7 divided by 8/21 as a decimal?

3/7 ÷ 8/21 converted to a decimal is 1.125.

What is 3/7 divided by 8/21 as a percentage?

3/7 ÷ 8/21 expressed as a percentage is 112.5%.

How do you write 3/7 divided by 8/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 9/8 can be written as the mixed number 1 1/8.

Does 3/7 divided by 8/21 result in a terminating or repeating decimal?

It results in an exact terminating decimal (1.125) because the denominator in simplest terms contains only prime factors 2 and/or 5.