Directions: Solve the word problem. Write your answer in ratio, fraction, decimal and percent. Show your answer using models.
A class of sixty (60) students is comprised of thirty-six (36) females and twenty-four (24) males. We can see that thirty-six out of sixty (36/60) students are females and twenty-four out of sixty (24/60) are males. The two fractions can be read 60 as thirty-six sixtieths and twenty-four sixtieths. Represent this part-whole concept in a model with ratio, percent, decimal, and fraction.
Females / Males = 36 / 24 = 12 ∙ 3 / 12 ∙ 2 = 3 / 2
Females:
36 / 60
36 / 60 = ( 36 ∙ 5 / 3 ) / ( 60 ∙ 5 / 3 ) =
( 180 / 3 ) / ( 300 / 3 ) = 60 / 100 = 60% = 0.6
Males:
24 / 60
24 / 60 = ( 24 ∙ 5 / 3 ) / ( 60 ∙ 5 / 3 ) =
( 120 / 3 ) / ( 300 / 3 ) = 40 / 100 = 40% = 0.4
Dude
Pak u.
Sure, here's how we can represent the part-whole concept in different forms:
Ratio: The ratio of females to the total number of students can be expressed as 36:60. This means that for every 36 females, there are 60 students in total.
Percent: To express this as a percentage, we calculate the proportion of female students out of the total number of students. So, (36/60) * 100 = 60%. This means that 60% of the class is comprised of female students.
Decimal: To express this as a decimal, we divide the number of female students (36) by the total number of students (60). So, 36/60 = 0.6. This means that 0.6 (or 0.60) of the class is comprised of female students.
Fraction: As mentioned, the fraction representing the number of female students is 36/60. We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 12. This gives us 3/5. So, 3/5 of the class is comprised of female students.
Model: To represent this visually, we can use a bar or pie chart. A bar chart can have one section that represents the 36 female students (3/5 of the total length) and another section that represents the 24 male students (2/5 of the total length). A pie chart can have 60 equally divided sections, with 36 sections colored to represent female students and 24 sections colored to represent male students. These models visually show the proportion of females and males in the class.
To solve this word problem and represent the part-whole concept in different forms, we need to follow these steps:
Step 1: Determine the ratio.
The ratio is the relationship between the two quantities. In this case, we have 36 females out of 60 students and 24 males out of 60 students.
The ratio of females to students is 36:60, and the ratio of males to students is 24:60.
Step 2: Convert the ratio to fraction form.
To convert the ratio to fraction form, we can simplify the ratio by dividing both parts of the ratio by their greatest common divisor (GCD).
The GCD of 36 and 60 is 12, so dividing both parts by 12 gives us a simplified fraction of 3:5. This means that 3/5 of the students are females and 2/5 of the students are males.
Step 3: Represent the ratio in decimal form.
To convert the fraction to a decimal, divide the numerator (3) by the denominator (5). The result is 0.6. Therefore, 0.6 of the students are females and 0.4 of the students are males.
Step 4: Represent the ratio in percent form.
To convert the decimal to a percent, multiply it by 100. So, 0.6 * 100 = 60%. This means that 60% of the students are females, and similarly, 40% are males.
Step 5: Create a model.
To represent the part-whole concept using a model, draw a rectangle or a circle. Divide it into 5 equal parts, representing the total of 60 students. Shade or label 3 parts out of the 5 to represent the females and label the remaining 2 parts for the males.
In summary:
- Ratio: 3:5
- Fraction: 3/5
- Decimal: 0.6
- Percent: 60%
- Model: A rectangle or circle divided into 5 equal parts, with 3 parts shaded/labelled as female and 2 parts shaded/labelled as male.