Question

Mackenzie solve the problem one. 35×1.4 which shows the correct work to find the product A (135 x 1/10) x (14 x 1/10)
(135 x 14) x (1/10 x 1/10)
B (135 x 1/100) x (14 x 1/10)
(135 x 14) x (1/100 x 1/10)
C (135×1/10) × (14×1/10)
(135×14) × (1/10×1/100)
D (135×1/100) × (14 x 1/100)
(135×14) × (1/100×1/100)

Answer 1

To solve the problem \( 35 \times 1.4 \), let's rewrite it in a more manageable form.

We can express \( 35 \) and \( 1.4 \) in terms of their factors:

\[
35 = 135 \times \frac{1}{10} \quad \text{and} \quad 1.4 = 14 \times \frac{1}{10}
\]

Now, multiplying those two gives us:

\[
35 \times 1.4 = (135 \times \frac{1}{10}) \times (14 \times \frac{1}{10})
\]

Using properties of multiplication, we can rearrange this:

\[
= (135 \times 14) \times \left(\frac{1}{10} \times \frac{1}{10}\right)
\]

This matches choice A:

\[
A\ (135 \times \frac{1}{10}) \times (14 \times \frac{1}{10}) \implies (135 \times 14) \times \left(\frac{1}{10} \times \frac{1}{10}\right)
\]

Now let's analyze the other choices:

- **B**: \( (135 \times \frac{1}{100}) \times (14 \times \frac{1}{10}) \) leads to a term \( \frac{1}{100} \), which is not applicable here.

- **C**: \( (135 \times \frac{1}{10}) \times (14 \times \frac{1}{10}) \) gives \( (135 \times 14) \times \left(\frac{1}{10} \times \frac{1}{10}\right) \), and this also matches.

- **D**: \( (135 \times \frac{1}{100}) \times (14 \times \frac{1}{100}) \) will also not apply here since it incorrectly uses \( \frac{1}{100} \).

So the correct options include both **A** and **C**.

But if you strictly follow the consistent representation, it would be most appropriate to say **A** is the best representation:

\[
\text{The answer is: } A
\]