A ratio compares two or more quantities. What is the primary purpose of using ratios?

Ratios help us understand relationships between different items or groups.

Fill in the blank: The ratio of cats to dogs can be expressed in colon form as ___:___ and in fraction form as ___/___ where there are 4 cats and 2 dogs.

4:2, 4/2

True or False: The total number of students in a class is the sum of the number of boys and girls.

True

If Raman's height is 175 cm and Radha's height is 1.35 m, what must be done before comparing their heights using a ratio?

Convert both heights to the same unit (either cm or m).

Riddle: I show the relationship between two quantities, expressing how much of one there is compared to another. What am I?

A ratio

What is the ratio of the number of boys to the total number of students if there are 35 boys and 25 girls?

The ratio is 35:60, which simplifies to 7:12.

Fill in the blank: To compare quantities with different units, it is necessary to convert them into the same ___.

Unit

Multiple Choice: Which of the following represents the ratio of 4 cats to 2 dogs in simplest form? A) 4:2 B) 2:1 C) 1:2 D) 1:4

B) 2:1

What is the process to find the lowest form of the ratio 25:100?

To find the lowest form, first convert the ratio into a fraction: 25/100. The greatest common factor of 25 and 100 is 25. Divide both the numerator and denominator by 25, resulting in the lowest form of the ratio as 1:4.

The equivalent ratio of 2/4 can be found by multiplying both the numerator and denominator by ___ or dividing by ___.

Any non-zero number or 2.

True or False: The only way to create equivalent ratios is by multiplying both terms of the ratio by the same number.

False. Equivalent ratios can also be created by dividing both terms by the same non-zero number.

If Radha's height is 1.35 m, what is her height in centimeters?

A ratio

Riddle: I can be expressed in many forms, but I represent the same part of a quantity. What am I?

Equivalent ratios.

Fill in the blank: The ratio of the height of Raman to Radha is found after converting both heights to the same unit, which in this case is ___.

Centimeters.

Explain how to find two equivalent ratios of 2/4.

To find two equivalent ratios of 2/4, you could multiply both the numerator and denominator by 2 to get 4/8, and divide both by 2 to get 1/2.

A proportion is defined as an equation that states that two ratios are ___.

Equal

Fill in the blanks: A proportion can be written as a: b : : c: d or a: b = c: d, which reads as '___ is to ___ as ___ is to ___.'

A, b, c, d

True or False: The first and fourth terms in a proportion are called the middle terms.

False. They are called extreme terms.

If the ratios 30 : 99 and 20 : 66 are equal, then the four terms are said to be in ___.

Proportion

What is the relationship between the ratios in a proportion?

The two ratios must be equal for the terms to be in proportion.

Riddle: I can express the relationship between two quantities, and I am often written with a colon. What am I?

A proportion

Find the ratio 30 cm to 4 m is proportional to 25 cm to 5 m. True or False?

True, because both ratios can be simplified to the same value.

In the proportion a : b = c : d, a and d are referred to as the ___ terms.

Extreme

How would you express the relationship '20 is to 40 as 2 is to 4' in the form of a proportion?

20 : 40 : : 2 : 4

What is the formula to check if the terms a, b, c, d are in proportion?

Check if a/b = c/d.