Question

The value of a ratio is 4 to 3. The second quantity in the ratio is how many times the first quantity in the ratio? Explain your reasoning

Answer 1

The second quantity in the ratio of 4 to 3 is three-fourths or 0.75 times the first quantity. This is found by dividing the second quantity (3) by the first quantity (4).

Step-by-step explanation:

The student's question "The second quantity in the ratio is how many times the first quantity in the ratio?" revolves around understanding the ratio relationship. A ratio compares two quantities, which can be written as fractions, with a colon, or with the word "to". In this case, the ratio given is 4 to 3, or 4:3, which can also be written as the fraction 4/3.

To determine the relationship between the second quantity and the first, consider the fraction 4/3. This implies that for every 4 parts of the first quantity, there are 3 parts of the second quantity. To find how many times the second quantity is of the first, you would set up a proportion or equation to isolate the second quantity in terms of the first. Essentially, you divide the second quantity (3) by the first quantity (4), to get 3/4, which means the second quantity is three-fourths or 0.75 times the first quantity.

Answer 2

The second quantity is 1.3333 times the first quantity in the ratio.

Solution:

A ratio is given to us which is 4:3.

What we need to find out is, the second quantity in the ratio is how many times the first quantity in the ratio.

The definition of ratio is, the quantitative relation between two amounts showing the number of times one value contains or is contained within the other.

So according to the definition of ratio we get:

So we can say that 4 contains 3, 1.3333 times in it.

So the second quantity is 1.3333 times the first quantity in the ratio.

Step-by-step explanation: