Means and Extremes in Ratios and Proportions

Explore means and extremes in ratios and proportions with this Grade 12 math worksheet, featuring problems on geometric mean, harmonic mean, and solving proportions.

Grade 12 Math Percents, Ratios, and RatesMeans and Extremes

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Includes

Fill in the BlanksMultiple Choice2 Short AnswerTrue / False

Standards

CCSS.MATH.CONTENT.HSG.SRT.B.5CCSS.MATH.CONTENT.HSA.REI.A.2

Topics

ratiosproportionsmeansextremesgeometric meanharmonic meanalgebra

7 sections · Free to use · Printable

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Means and Extremes in Ratios and Proportions

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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.

1. In a proportion a:b = c:d, the terms 'a' and 'd' are called the , while 'b' and 'c' are called the .

2. The of two positive numbers 'x' and 'y' is the square root of their product.

1. Which of the following statements is true regarding the product of the means and extremes in a proportion?

The product of the means is always greater than the product of the extremes.

The product of the extremes is always greater than the product of the means.

The product of the means is equal to the product of the extremes.

There is no relationship between the product of the means and extremes.

2. If x is the geometric mean of 4 and 9, what is the value of x?

6.5

1. Find the value of x in the proportion: 5/x = 15/21.

2. The harmonic mean of two numbers 'a' and 'b' is given by the formula 2ab / (a + b). Calculate the harmonic mean of 4 and 6.

1. In the proportion 2:3 = 4:6, the means are 2 and 6.

True

False

1. The ratio of boys to girls in a class is 3:5. If there are 18 boys, how many girls are there?

2. A recipe calls for 2 cups of flour for every 3 cups of sugar. If you use 5 cups of flour, how much sugar do you need?