Conversions, Ratios, and Number Line Concepts

The video tutorial covers three math problems. The first problem involves converting milliliters to cups using a ratio and cross-multiplication. The second problem requires finding a point on a number line by calculating increments. The third problem involves determining the least common multiple of numbers to divide textbooks into groups. Each problem is solved step-by-step, demonstrating mathematical reasoning and calculation techniques.

How can you set up a ratio to convert 205 milliliters to cups if 100 milliliters is approximately 0.4 cups?

• 100 milliliters is to x cups as 205 milliliters is to 0.4 cups

• 205 milliliters is to x cups as 100 milliliters is to 0.4 cups

• 205 milliliters is to 0.4 cups as 100 milliliters is to x cups

• 100 milliliters is to 0.4 cups as 205 milliliters is to x cups

What is the result of cross-multiplying to solve for x in the milliliters to cups conversion problem?

• 100x = 205 * 0.4

• 100x = 200 * 0.4

• 205x = 200 * 0.4

• 205x = 100 * 0.4

Which option correctly represents 205% of 0.4?

• 2.05 * 0.4

• 1.05 * 0.4

• 0.105 * 0.4

• 0.205 * 0.4

How many increments are there between 0.003 and 0.004 on the number line?

• 5 increments

• 8 increments

• 6 increments

• 7 increments

What is the value of each increment on the number line between 0.003 and 0.004?

• 0.000125

• 0.00025

• 0.0005

• 0.001

What is the value of point P on the number line if it is two increments past 0.003?

• 0.003125

• 0.00325

• 0.0035

• 0.00375

What is the least common multiple of 12, 15, and 18?

• 210

• 180

• 150

• 120

Which of the following is a prime factorization of 12?

• 2 * 2 * 5

• 2 * 2 * 3

• 3 * 3 * 2

• 2 * 3 * 5

What additional factor is needed to make the number divisible by 18 when finding the least common multiple of 12, 15, and 18?

• Another 7

• Another 2

• Another 3

• Another 5

Which inequality is satisfied if N is the smallest possible total number of textbooks divisible by 12, 15, and 18?

• N > 250

• N < 150

• 150 < N < 200

• 200 < N < 250