Equivalent Ratios

Front

What is an equivalent ratio?

Back

An equivalent ratio is a ratio that expresses the same relationship between two quantities, even if the numbers are different. For example, the ratios 1:2 and 2:4 are equivalent.

Front

If a class has a ratio of boys to girls as 5:6, how can you find the number of girls if you know the total number of students?

Back

To find the number of girls, first add the parts of the ratio (5 + 6 = 11). Then, divide the total number of students by the total parts (33 ÷ 11 = 3). Multiply the number of girls' parts by this result (6 × 3 = 18).

Front

How do you determine if two ratios are equivalent?

Back

Two ratios are equivalent if their cross products are equal. For example, for the ratios a:b and c:d, they are equivalent if a*d = b*c.

Front

What is the ratio of 18 to 27 in simplest form?

Back

The simplest form of the ratio 18:27 is 2:3, since both numbers can be divided by 9.

Front

If a photographer's enlargement chart shows a width of 16 inches and a length of 24 inches, what is the ratio of width to length?

Back

The ratio of width to length is 16:24, which simplifies to 2:3.

Front

How can you use a table to find equivalent ratios?

Back

You can use a table to list pairs of quantities and check if the ratios formed by these pairs are equivalent by simplifying them or checking their cross products.

Front

What is the relationship between the number of cakes and the number of eggs needed if 4 cakes require 8 eggs?

Back

The relationship is a ratio of 4 cakes to 8 eggs, which simplifies to 1 cake requiring 2 eggs.

Front

If a group of 12 people pays $72, what is the cost per person?

Back

The cost per person is $72 ÷ 12 = $6.

Front

What is the importance of understanding equivalent ratios in real-life situations?

Back

Understanding equivalent ratios helps in making comparisons, scaling recipes, budgeting, and analyzing data in various real-life contexts.

Front

How do you find the missing dimensions in a proportional relationship?

Back

You can set up a proportion using the known dimensions and solve for the missing dimension by cross-multiplying.