Steemkids math lesson for the week: Ratio and proportion| 10% payout to @steemkidss

Hello dear lovely kids. It's another week and another exciting mathematics class.
Please pay attention and learn from this week's lesson.
At the end of this lesson you should be able to solve problems relating to the topic of this week.
Guess what the topic is...

Ratio and proportion

Ratio is used when comparing two things.
It can be used to describe the relationship between one part to the other part.
It can either be written as a fraction or using the : symbol.
For example:

As you see in the picture above there are 5 oranges, 6 bananas and 4 pineapples.

(a) What is the ratio of oranges to the bananas?
(b) What is the ratio of pineapples to bananas

For (a) we are comparing the oranges to the bananas
The ratio of oranges to bananas = no. of oranges divided by the no. of bananas
=4/6 or 4:6.
The ratio of oranges to bananas is 4:6. _{(four is to six in words)}

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Ratio can also be used to describe the relationship between a part of a whole.

Example: Find the ratio of the shaded part to the whole shape in figure below

Ratio of rectangle = 4:10
Ratio of triangle = 1:2
Ratio = 1:3

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Solving problems on ratio and proportion

In a classroom, there are 100 boys and 50 girls.
(a)Solve for the ratio of boys to girls

(b) Find the ratio of boys compared to the total number of students/pupils in the class

(c) Solve for the ratio of girls compared to the total number of students in the class

Solutions

(a) number of boys = 100
Number of girls = 50
Ratio of boys to girls = number of girls divided by number of boys
That is: 100/50 (reduce to lowest term) = 50/25 = 2/1 = 2:1
The ratio of boys to girls = 2:1

Note: the ratio of girls to boys will be 1:2

(b) The ratio of boys compared to the total number of students in the classroom.
Step 1: determine the total number of students in the class by adding the number of boys to girls

Number of boys + number of girls = 100 + 50 = 150
Total number of students/pupils in the class = 150

Step 2: number of boys divided by the number of students

100/150 = 50/75 = 10/15 = 2/3 or 2:3
Therefore ratio of boys to the total number of students = 2:3

(c) Ratio of girls to the total number of students
Number of girls divided by the total number students
50/150 = 5/15 = 1/3 = 1:3
Therefore ratio of girls to the total number of students = 1: 3

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What is the ratio of 1 hour to to 25 mins?

Solution

In the question there are two quantities of the same kind which is time bit different units.
Since hour is greater than minute, it should be expressed in the smaller unit, that is in minute.

First step: Change 1hr to minute to minute.
To change hour to minute we multiply by 60.
That is: 1 ✖ 60 = 60 min.

The ratio of 1hr to 25 minutes is :
60/25 = 12/5 or 12:5

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Word problems on ratio and proportion

Three friends are given a sum of 400 steem. They are asked to share in the ratio of 1: 4 : 5. How much steem will each of them get?

Solution

Step 1: Find the total number of ratio by adding them up
1 : 4 : 5 = 1 + 4 + 5 = 10

Step 2: Find out the total amount each of them will receive.
For friend a his share is 1 so he will recieve
1/10 ✖ 400 = 400/10 = 40
He will receive 40 steem

For friend (b) his share is 4 so he will receive
4/10 ✖ 400 = 1600/10 = 160
He will receive 160 steem

For friend (c) his share is 5 so he will receive
5/10 ✖ 400 = 2000/10 = 200
He will receive 200 steem

Example 2
@madilyn02 and @benson6 are to share a certain amount of Sbd given by @steemkidss. They are asked to share in the ratio of 3:5. If @madilyn02 receive 180 sbd, how many sbd will @benson6 receive?

Solution

Step 1:Sum up the ratio
3:5 = 3 + 5 = 8

Step 2: Represent total amount of sbd shared with the letter d.

Step 3: multiply the ratio of @madilyn02 by the total amount of sbd, d shared and equate it to her her share.
Her ratio = 3 : 8
3/8 ✖ d = 180

Solve the equation
3/8 ✖ d =180
3d/8 = 180 (cross multiply)
3d = 8 ✖ 180 = 1440 =
3d = 1440

divide both sides by 3
3d/3 = 1440/3 = 480

The total amount of Sbd is 480.

Step 4: @benson6 share will be 480-180 = 300
His share of the sbd will be 300.

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Proportion

Proportion is a name given to a statement which shows that two ratios are equal. It is written in two ways:
I. Two equal fractions a/b = c/d
II. Using a colon a:b = c:d

When two ratios are equal, then the cross products of the ratio are equal.
a:b = c:d

a/b = c/d (cross products)
a ✖ d = b ✖ c

Assignment

• In a community there are 550 subscribers and 450 active. Find the ratio of the subscribers to active users

• Tara is 24 years old. Her brother veerat is 18 years old. What is the ratio Tara's age to veerat's age.

• David has 14 eggs. He uses 8 of them for cooking. What is the ratio of the number of eggs used to the original number of eggs David has.

• Sarah, glory and Arouhi are to share 400 Apples in the ratio of 1:4:5 respectively. How much does each receive?

Remember your entry should be as a comment under this post.

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@steemkidss will share 5 steem among all participants in the assignments.

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