Find the Other Number Given Product and One Number

The question asks us to find the value of one number when the product of two numbers and the value of the other number are given. This is a common type of problem involving the relationship between multiplication and division.

We know the following:

• Product of two numbers = 0.432
• One of the numbers = 1.6

Let the other number be represented by 'x'. The relationship between the two numbers and their product can be written as:

\( \text{One number} \times \text{Other number} = \text{Product} \)

Substituting the given values, we get:

\( 1.6 \times x = 0.432 \)

To find the value of 'x', we need to isolate 'x' by dividing the product by the given number:

\( x = \frac{\text{Product}}{\text{One number}} \)

\( x = \frac{0.432}{1.6} \)

To perform the division of decimals, it is helpful to remove the decimal from the divisor (1.6). We can do this by multiplying both the numerator and the denominator by 10:

\( x = \frac{0.432 \times 10}{1.6 \times 10} \)

\( x = \frac{4.32}{16} \)

Now, we can perform the division:

\( \begin{array}{r} 0.27 \\ 16 \overline{) 4.32} \\ -3.2 \downarrow \\ \hline 1.12 \\ -1.12 \\ \hline 0 \\ \end{array} \)

So, the other number is 0.27.

Let's check this answer by multiplying the two numbers:

\( 1.6 \times 0.27 \)

\( 1.6 \times 0.27 = 0.432 \)

This matches the given product, so our calculation is correct.

Comparing our result with the given options:

• Option 1: 2.7
• Option 2: 0.027
• Option 3: 0.27
• Option 4: 27

The calculated other number, 0.27, matches Option 3.

Revision Table: Key Concepts

Additional Information on Decimal Division

Dividing decimals can sometimes seem tricky, but you can simplify it by converting the divisor into a whole number. Here’s how:

1. Identify the divisor: This is the number you are dividing by.
2. Count decimal places in the divisor: See how many digits are after the decimal point.
3. Move the decimal point: Move the decimal point in the divisor to the right until it becomes a whole number. The number of places you move it is equal to the number of decimal places you counted in step 2.
4. Move the decimal point in the dividend: Move the decimal point in the dividend (the number being divided) the same number of places to the right as you did for the divisor. Add zeros if necessary.
5. Perform standard division: Now you can perform long division as you would with whole numbers.
6. Place the decimal point in the quotient: Place the decimal point in the quotient (the answer) directly above where the decimal point is now located in the dividend.

In our problem, we divided 0.432 by 1.6.

• Divisor is 1.6 (one decimal place).
• Move decimal in 1.6 one place right to get 16.
• Move decimal in 0.432 one place right to get 4.32.
• Divide 4.32 by 16, which gave us 0.27.

This method makes the division process much clearer and easier to manage.