Question

Write a multiplication equation that represents the question: how many 3/8's are in 5/4?

Answer 1

The multiplication equation representing "how many 3/8's are in 5/4" is
`\( (5)/(4) * (8)/(3) = (10)/(3) \)`.

Step-by-step explanation:

To determine how many
`\( (3)/(8) \)'s` are in
`\( (5)/(4) \)`, we use the concept of division as a multiplication of the reciprocal. This can be written as
`\( (5)/(4) * (8)/(3) \)`. To solve, multiply the numerators (5 * 8) to get 40, and multiply the denominators (4 * 3) to get 12. The result,
`\( (40)/(12) \)`, simplifies to
`\( (10)/(3) \)`.

Understanding this calculation involves converting the whole number
`\( (5)/(4) \)` into a fraction. This means
`\( (5)/(4) \)` can be expressed as
`\( (5)/(1) / (4)/(1) \)`, which is
`\( (5)/(1) * (1)/(4) \)`. We want to find how many groups of
`\( (3)/(8) \)` are in
`\( (5)/(4) \)`, hence the multiplication by
`\( (8)/(3) \)`. This calculation yields
`\( (10)/(3) \)`, indicating that
`\( (10)/(3) \)` of
`\( (3)/(8) \)` are present in
`\( (5)/(4) \)`.

Therefore,
`\( (10)/(3) \)` represents the number of
`\( (3)/(8) \)'s` present within
`\( (5)/(4) \)`. It implies that within
`\( (5)/(4) \)`, there are
`\( (10)/(3) \)` groups of
`\( (3)/(8) \)`.