Lesson 1: Expressing Ratio as a Fraction and Vice-Versa

1. Sketch three pictures that represent each of the following fractions:a.

b. 2/3

c. 5/8

Reflect: How well do you know fractions?

Five pupils are playing. Out of the total number of pupils, how many are boys? How many are girls?How do we express in another way the number of boys in the group? the number of girls in the group?Reflect: What do you want to know about ratio?

Exploration A

Get a piece of paper and fold it over three times. Press it hard to make a crease and open it. Into how many regions is the paper now divided into?

The paper is now divided into 8 regions as shown at the right. If you shade 3 parts of it, what part of the whole is shaded? What fraction does it represent?

In the fraction 3/8, what does the numerator 3 tell us? How about its denominator 8?

This time, lets separate the shaded regions from the original regions. Take note that the fraction represented by the figure is 3/8.Can we also say that there are 3 shaded regions for the set of 8 unshaded regions? In relation to the figure, what does the phrase 3 is to 8 mean? Does 3/8 also mean 3 is to 8?

Look at the figure, how many boys and girls are there? What fraction is represented by the figure?Using the phrase is to , how do you relate the number of boys to the number of girls? Is the same as 1 is to 2?

If the term ratio indicates the numerical relation between two things or quantities, can we say that the ratio of the number of boys to the number of girls is 1:2?

What objects are being compared on the right?Count the number of moon and stars on the right. What is the ratio of the number of moon to the number of stars? How many times larger is the number of stars as the number of moon? How did you get this?

If the ratio of the number of moon and stars is 2:6, how many times is the number of stars larger as the number of moon?

Given a ratio, how do you find the number of times one value is large as another?

Below are the ideas you should have learned in this lesson. Can you explain each one of them with one of your classmates? Check those you understood well and cross out those where you need further explanation.1. Ratio indicates the numerical relation between two things or quantities. In general, a ratio is written using the symbol of colon (:) written between the numbers of the two quantities being related.2. A fraction can be expressed as ratio. For example, the fraction 2/3 can be expressed as 2:3 read as 2 is to 3.

3. A ratio can be expressed as fraction. For example, the ratio 3:4

4. Both ratio and fraction can be represented using a figure. For example, the figure is expressed as fraction and ratio:5. In a ratio, to find how many times the second value is as large as the first value, we divide the larger value by the smaller first value. For example, in the ratio: 3:12 12 is 4 times as large as 3. To get 4, we divide 12 by 3; in the ratio 4:5 5 is 5/4 times as large as 4.

A. Complete the table.FRACTIONRATIOLANGUAGE

4/5

4:1

two is to five

B. Answer the following. 1. In a family of 5, the ratio of the number of parents to the number of children is 2:3. Express the ratio as fraction and draw the figure that represents it.2. The ratio of the height of the son and his father is 1:3. How many times taller is the father as the son?

3. Give real-life example for each of the following ratios: (1) 1:7 (2) 1:34. What ratio corresponds to the following situation: the number of moons of Jupiter is 63 times as many as the number of moons of the Earth.

A. Answer the following:1. Express the following as ratio: (a) (b) 5/3 (c) 4/7 (d) 9/2 (e) 3/11

2. Express the following as fraction: (a) 1:3 (b) 2:5 (c) 7:8 (d) 5:1 (e) 3:2

B. Read the following questions. Then explain your answers. 1. If the ratio of the number of boys to the number of girls in a class is 1:2, are there more boys than girls? 2. Give a real-life example of the ratio 1:1.3. Give examples of ratio that can be found in the parts of your body.

C. Express the following statements in symbol. Draw a figure to represent it.a. In the class, the ratio of the number of boys to the number of girls is 2:3.

b. Rafa has toy airplanes and cars. The ratio of the number of airplanes to the number of cars is 1:5

c. Dads tool box contains some pliers and screw drivers. The ratio of the number of pliers to the number of screw drivers is 2:5

D. Study the table below that shows the top 10 provinces in terms of land area. Answer the following:1. Express as ratio the area of Palawan to the area of North Cotabato. About how many times is Palawan as large as North Cotabato? Finally, express the areas in the simplest ratio.2. Express as ratio the area of Isabela to the area of Negros Occidental. About how many times is Isabela as large as North Occidental? Finally, express the areas in the simplest ratio. Pause & ReflectAre you happy with the result of your evaluation? Why?

What concepts are clear to you?

What concepts are still not clear to you?

What is the most desirable value or attitude that you have developed in this lesson?

Work in pairs. You need a meterstick, a cardboard and scissors. Do the following.

1. Cut out a rectangle 34 cm by 21 cm. Find the ratio of the length to the width. Use your calculator to express the ratio as a decimal. You do this by dividing the numerator by the denominator.2. Cut the rectangle into two such that one is the biggest square with a side equal to 21 cm by 21 cm and the other is a rectangle.

3. After setting aside the square, get the remaining rectangle. What are the dimensions of the rectangle? Do you see that the length is 21 cm and the width is 13 cm? Find the ratio of the length to the width, expressed in decimal.4. Repeat the steps 1 to 3.

5. Answer the questions below.

a. Do you see a pattern?b. Does the pattern true for any rectangle?c. If we call the original rectangle as a golden rectangle, what is the estimated value of the golden ratio (ratio of the length of the golden rectangle to its width?Elicit

Engage

Illustration:

2 boys and 3 girls playing

Explore

Draw a picture of one boy and 2 girls

Explain

2/3

2:3

two is to three the ratio of the number of triangles to the number circles is 2 is to 3.

Elaborate

Evaluate

PROVINCELAND AREA (SQ KM)REGION LOCATED1. Palawan 17, 030.8 km24B *2. Lanao del Sur 13, 4944.4 km2ARMM **3. Isabela 12, 414.9 km224. Bukidnon 10, 496.6 km2105. Agusan del Sur 9 ,989.5 km2136. Maguindanao 9, 729.0 km2ARMM7. Cagayan 9, 295.8 km2R28. Quezon 9, 069.6 km24A ***9. North Cotabato 9, 008.9 km21210. Negros Occidental 7, 965.2 km26www.census.gov.ph

Extend

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