Question

Ratio and Proportion​

Answer 1

Answer:

A ratio is a way to compare two quantities by using division as in miles per hour where we compare miles and hours. A proportion on the other hand is an equation that says that two ratios are equivalent.

Step-by-step explanation:

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Answer 2

Ratio and Proportion

Parent Category: Math League Website Published: 16 September 2008

Ratio and Proportion

Ratio

Comparing ratios

Proportion

Rate

Converting rates

Average rate of speed

Ratio

A ratio is a comparison of two numbers. We generally separate the two numbers in the ratio with a colon (:). Suppose we want to write the ratio of 8 and 12.

We can write this as 8:12 or as a fraction 8/12, and we say the ratio is eight to twelve.

Examples:

Jeannine has a bag with 3 videocassettes, 4 marbles, 7 books, and 1 orange.

1) What is the ratio of books to marbles?

Expressed as a fraction, with the numerator equal to the first quantity and the denominator equal to the second, the answer would be 7/4.

Two other ways of writing the ratio are 7 to 4, and 7:4.

2) What is the ratio of videocassettes to the total number of items in the bag?

There are 3 videocassettes, and 3 + 4 + 7 + 1 = 15 items total.

The answer can be expressed as 3/15, 3 to 15, or 3:15.

Comparing Ratios

To compare ratios, write them as fractions. The ratios are equal if they are equal when written as fractions.

Example:

Are the ratios 3 to 4 and 6:8 equal?

The ratios are equal if 3/4 = 6/8.

These are equal if their cross products are equal; that is, if 3 × 8 = 4 × 6. Since both of these products equal 24, the answer is yes, the ratios are equal.

Remember to be careful! Order matters!

A ratio of 1:7 is not the same as a ratio of 7:1.

Examples:

Are the ratios 7:1 and 4:81 equal? No!

7/1 > 1, but 4/81 < 1, so the ratios can't be equal.

Are 7:14 and 36:72 equal?

Notice that 7/14 and 36/72 are both equal to 1/2, so the two ratios are equal.

Proportion

A proportion is an equation with a ratio on each side. It is a statement that two ratios are equal.

3/4 = 6/8 is an example of a proportion.

When one of the four numbers in a proportion is unknown, cross products may be used to find the unknown number. This is called solving the proportion. Question marks or letters are frequently used in place of the unknown number.

Example:

Solve for n: 1/2 = n/4.

Using cross products we see that 2 × n = 1 × 4 =4, so 2 × n = 4. Dividing both sides by 2, n = 4 ÷ 2 so that n = 2.