Question

Malcom wrote the equivalent ratios shown below. Find the scale factor he used to write the equivalent ratios

9/40 and 54/240

Answer 1

To find the scale factor Malcolm used for the ratios 9/40 and 54/240, we simplified the second ratio to 1/4.4 and then found that both terms of the first ratio, when multiplied by 6, yielded the second ratio, indicating that the scale factor is 6.

Step-by-step explanation:

To find the scale factor Malcolm used to write the equivalent ratios 9/40 and 54/240, we can simplify one of the ratios and determine how the numbers relate to the other ratio. First, let's simplify the second ratio:

• 54/240 can be simplified by dividing both the numerator and denominator by 54.
• 54 ÷ 54 = 1 and 240 ÷ 54 = 4.4, so the simplified ratio is 1/4.4.

Now let's look at the first ratio:

• 9/40 cannot be simplified any further where the denominator is a whole number, so we need to find what number 9 was multiplied by to get 54.
• 54 divided by 9 equals 6.
• To check if this is the scale factor, we divide 240 by 40, which also equals 6.

So, the scale factor Malcolm used is 6, because multiplying both terms of the first ratio (9/40) by 6 gives us the second ratio (54/240).

Answer 2

In this question, we're looking for the number Malcom used to scale the two numbers. We can see there's a pattern, 9 is 1/6 of 54 and 40 is 1/6 of 240!

(54 divided by 9 is 6 and 240 divided by 40 is 6!)

therefore, the scale factor must be 6