Ratio and Proportion

Ratio and proportion

Jim Quesada

targets

1. Solve problems involving ratios.

2. Solve for the missing term is a proportion (direct, inverse, and partitive).

3. Solve problems involving direct, inverse, and partitive proportions.

Mathematics

PISAY EDGE 2022

​The school will hold a Sports Festival. The students will be divided into 7 groups in such a way that each group has an equal number of male and female members. There are 91 males and 84 females in total. How many males and females are in each group?

ratio

A ratio is an expression used in comparing two numbers or quantities that have the same unit. A ratio of a to b can be expressed as:

Mathematics

PISAY EDGE 2022

Point to remember

Multiple Choice

Write $$45$$  to $$21$$  as a ratio.

• $$\frac{15}{7}$$  

• $$\frac{7}{15}$$  

Multiple Choice

Write $$0.8$$  to $$0.4$$  as a ratio.

• $$\frac{1}{2}$$  

• $$\frac{2}{1}$$  

• $$\frac{0.2}{0.1}$$  

Multiple Choice

Write $$1\ \frac{2}{3}$$  to $$2\ \frac{5}{6}$$  as a ratio.

• $$\frac{10}{17}$$  

• $$\frac{17}{10}$$  

• $$\frac{85}{18}$$  

• $$\frac{18}{85}$$  

Multiple Choice

A building inspector would oversee a newly-built health care facility if the contractor followed the prescribed ramp measurements. What is the ratio of rise to run if the prescription says that a ramp must have a maximum vertical height of 2.54 cm for a 30.48-cm horizontal run?

• $$\frac{1}{12}$$  

• $$\frac{12}{1}$$  

• $$\frac{5}{12}$$  

• $$\frac{12}{5}$$  

proportion

Mathematics

PISAY EDGE 2022

fundamental principle of proportion

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

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Mathematics

PISAY EDGE 2022

Fill in the Blanks

Determine the value of $x$ .

$\frac{x}{42}=\frac{2}{7}$  

Fill in the Blanks

Determine the value of $c$ .

$\frac{c}{28}=\frac{c+10}{42}$  

direct proportion

Mathematics

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example

4 kg of palay costs 118.50 pesos. How much will it cost to buy 10 kg of palay?

example

Marjorie finally went out on a trip with her family to Pagsanjan Falls in Laguna. One gallon of gasoline can cover a distance of 15 km. Their destination is 105 km from their home. How many gallons of gasoline do they need to reach Pagsanjan Falls?

inverse proportion

Mathematics

PISAY EDGE 2022

example

Jim drove to a beach at a speed of 60 kph for one and a half hours. On the way home, he decreased his speed to 50 kph. How many hours will it take him to go back home?

example

Boyle's law states that at a constant temperature, the volume of a gas is inversely proportional to the pressure of the gas. A certain gas was used for an experiment in a laboratory with a constant temperature inside. If 10 mL of this gas gives a pressure of 3.5 atm, how much of this gas gives 1 atm of pressure?

partitive proportion

In a partitive proportion, a whole is divided into parts that are proportional ​to a given ratio.

Mathematics

PISAY EDGE 2022

example

​At a wedding party, the ratio of female to male guests is 4 to 3. If there are 182 guests, how many of the guests are female?

example

For the opening of a new school year, Arniel decided to plant gumamela and yellow bells to welcome the students. He wanted to make some rectangular plots that have the same number of seeds of gumamela and yellow bells in each plot. The ratio of the number of seeds of gumamela to yellow bells is 5 to 3. If there are a total of 360 seeds, how many rectangular plots does Mario need to prepare?

Fill in the Blanks

You made your own rising flour from following a recipe. You put on $1\ \frac{1}{2}$  tbsp of baking powder and $\frac{1}{10}$  tbsp of salt. What is the ratio of baking power to salt in your rising flour?

Fill in the Blanks

In a women's get-together party, the ratio of the number of single to married is 7:4. If the total number of people in the party is 121, how many married women are there?

Fill in the Blanks

The lengths of the sides of a triangle are in the ratio 3:4:5. If the perimeter of the triangle is 72 cm, what is the length of the longest side?

Fill in the Blanks

Ten carpenters can finish 4 standard houses in the span of 4 months. How long will it take to finish the same work if two carpenters leave? (Assuming the carpenters have same work rate)

Fill in the Blanks

Five cans of paint can cover a 25-square-foot wall. How many cans of paint are needed to cover a 10-square-foot wall?

In summary:

Mathematics

PISAY EDGE 2022

• The two quantities compared in a ratio must have the same units of measurement.

• the antecedent and the consequent of a ratio should be expressed as whole numbers.

• The ratio of two numbers should be expressed in its lowest terms.

• A ratio is an abstract number, it has no unit.

• The order of the ratio is important.

In summary:

Mathematics

PISAY EDGE 2022

• In the proportion a:b::c:d, a and d are called the extremes, while b and c are called the means.

• Two rations that have the same value are called equivalent ratios.

• Proportion says that two ratios are equal.

• Direct proportion states that if one quantity increases, the other quantity also increases.

• Inverse proportion states that if one quantity increases, the other quantity decreases (or vise versa)

Reference

Mathematics

PISAY EDGE 2022

Fair, J. & Bragg, S. C. (1993). Algebra 1. New Jersey: Prentice Hall.

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Swokowski, E. W. & Cole, J. A. (2017). Precalculus: Functions and graphs. Canada: Cengage Learning.

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