Mathematics 5 - Quarter 2 - Week 8

​MATHEMATICS 5

Quarter 2 - Week 8

​Lesson 1

​Ratio Using Either the Colon (:) or Fraction

​Lesson 2

Equivalent Ratios

​Lesson 3

Definition and Description of a Proportion

Give the ratio of ​chicks to hens.

4:2

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​RATIO

A ​RATIO is a comparison between the quantities of two things.

Give the ratio of DOGS to CATS.​

​4:5

​We can express ratios in different ways:

1)​ by using COLON ( : )

2) by ​using FRACTION

3) ​in words ("to") -> sa module ay ang colon at fraction lamang ang naka-title, pero babanggitin pa rin ngayon itong "in words" :)

Balikan natin ang example kanina: 4:5​

Ito ay nakasulat sa colon form. Kung isusulat o ie-express ito sa fraction form, ang magiging numerator ay ang unang value o bilang (4), at ang denominator naman ay ang ikalawa (5).​

Sa fraction, ito ay isusulat na 4/5 o .

(In words, four dogs is to five cats / four dogs to five cats / four is to five / four to five / 4 is to 5 / 4 to 5.)

Maaari ring i-simplify ang ratio.

Halimbawa ay mayroon kang 6/12 na ratio.

What will you do to simplify it?​

​We can use the greatest common factor (GCF) in simplifying the given ratios or fractions.

Simplify the following ratios.​

1) ​3:6 ->

2) ​2:4 ->

3) ​4:6 ->

4) ​6/4 ->

5) ​2/6 ->

​

EQUIVALENT ​RATIOs

Let us take a look at this.​

1) ​3:6 = 1:2

2) ​2:4 = 1:2

3) ​4:6 = 2:3

4) ​6/4 = 3:2

5) ​2/6 = 1:3​

​Naka-simplify ang bawat ratio. Ibig sabihin, ang mga nasa kaliwa (itim) ay pareho lamang sa kanan (pula). Since simplified ito, ang mga nakapula ay pinaliit lamang na form ng original given ratio. Kapag ini-lowest term ang mga naka-itim, ang lalabas na value ay ganoon din sa mga nasa pula. Therefore, equivalent ratios ang mga ito.​

The equivalent ratios can also be larger numbers than the given ratios.​

1) ​3:6 = 6:12

2) ​2:4 = 4:8

3) ​4:6 = 12:18

4) ​6/4 = 24:16

5) ​2/6 = 10:30​

ang mga naunang halimbawa ay naka-simplify. dito naman, naka-multiply ang bawat set sa iisang number. Halimbawa sa 3:6. sa 2 ini-multiply ang bawat term. (3 x 2 = 6; 6 x 2 = 12)

kaya naging 6:12 ang 3:6.

(which are still equivalent ratios)

How to check if the ratios are equivalent?​

​To check if the ratios are equivalent,

the product of the means should be equal with the product of the extremes.

What are these "means" and "extremes'?

​3 : 7 and 6 : 14

​extremes

(terms na nasa loob, 2nd at 3rd terms)

(terms na nasa dalawang gilid, 1st at 4th terms)

MEANS

​3 : 7 and 6 : 14

​muLTIPLY THE extremes (3 x 14 = 42)

multiply the means (7 x 6 = 42)

Kailangang equal o pareho ang means sa extremes para masabing equivalent ratios ang bawat set. Kapag hindi pareho ang product na lumabas, hindi equivalent ratios ang mga ito.

Parehong 42 ang lumabas na product. Therefore, equivalent ratios ang 3:7 at 6:14.​

complete the missing term to make the ratios equivalent.

​15 : 25 and 3 : _

complete the missing term to make the ratios equivalent.

​15 : 25 and 3 : 5

complete the missing term to make the ratios equivalent.

​20 : 16 and _ : 4

complete the missing term to make the ratios equivalent.

​20 : 16 and 5 : 4

complete the missing term to make the ratios equivalent.

​1 : 3 and 3 : _

complete the missing term to make the ratios equivalent.

​1 : 3 and 3 : 9

identify whether the ratios are equivalent or not.

​8 : 10 and 16 : 20

identify whether the ratios are equivalent or not.

​8 : 10 and 16 : 20

EQUIVALENT RATIOS

identify whether the ratios are equivalent or not.

​18 : 5 and 54 : 15

identify whether the ratios are equivalent or not.

​18 : 5 and 54 : 15

EQUIVALENT RATIOS

identify whether the ratios are equivalent or not.

​12 : 16 and 4 : 3

identify whether the ratios are equivalent or not.

​12 : 16 and 4 : 3

NOT EQUIVALENT RATIOS

Definition and Description of a Proportion

​HOW DO WE DEFINE/DESCRIBE A PROPORTION?

A proportion is an equality of two ratios.

a:b = C:D​​

Hence, EQUIVALENT RATIOS are PROPORTIONS.

1:2 = 3:6​ ​

a/b = C/D​

1/2 = 3/6​

The examples show ratios that are equivalent to the other ratios.

You can also use cross multiplication to check proportions. Express first the ratio to its fraction form.

​6

​6

Both products are 6.

Therefore, the ratios show a proportion.

​Let's solve some problems on proportion.

1) Two numbers are in the ratio 2 : 3. If the bigger number is 6, what is the smaller number?

2) Juliana saves ₱60.00 in 4 weeks. At this rate, how long will it take to generate ₱300.00?

Two numbers are in the ratio 2 : 3. If the bigger number is 6, what is the smaller number?

​In this problem, the missing value is the 3rd term.

​

​Solution 1: (i-multiply ang term na may ka-partner, tapos i-divide ito sa term na walang ka-partner)

2:3 = _:6

2 x 6 = 12

12 ​÷ 3 = 4

The answer is 4.​

​

​Solution 2: (i-express sa fraction ang ratio. Ang magiging partners na kapag fraction form ay numerator to numerator, at denominator to denominator. I-divide ang may ka-partner, at i-multiply ang quotient sa naiwang term)

2:3 =_:6 --> 2/3 =_/6

​6 ​÷ 3 = 2

2 x 2 = 4​

The answer is 4.​​

Dito ay denominator ang may ka-partner kay iyon ang kukuhanan ng quotient.

​

​Let's solve some problems on proportion.

1) Two numbers are in the ratio 2 : 3. If the bigger number is 6, what is the smaller number?

2) Juliana saves ₱60.00 in 4 weeks. At this rate, how long will it take to generate ₱300.00?