Grade Six Mathematics Answers to last week’s exercise
Greetings, boys and girls. Welcome back to our Math corner. I trust that you are having an awesome Sunday and are prepared to work diligently. In this week’s session, we will be looking at ratio, where we’ll be examining its concept, along with examples and solving problems. Let’s begin.
Ratio
What is a ratio?
Ratio, in math, is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another. In a ratio, two quantities are compared using division. Here the dividend is called the ‘antecedent’ and the divisor is called the ‘consequent’
Example 1
In a class of 40 students, 25 of them prefer Mathematics and 15 prefer English.
To represent this information as a ratio, we write it as 25: 15. Here, the symbol ‘: ‘ is read as “is to”. So, the ratio of students who prefer Mathematics to the students who prefer English is read as ‘25 is to 15’.
Calculation of Ratios
Boys and girls, let’s examine how the calculation of ratio is done. To calculate the ratio of two quantities, we apply the following steps.
(We will use an example to demonstrate each step).
If 20 cups of sugar and 40 cups of flour are needed to make a cake, let us calculate the ratio of flour and sugar used in the recipe.
Step 1:
Step 2: Step 3:
Step 4:
Find the quantities of both the scenarios for which we are determining the ratio. In this case, it is 20 and 40.
Write it in the fraction form a/b. So, we write it as.20/40. Simplify the fraction further, if possible. The simplified fraction will give the final ratio. Here, 20/40 can be simplified to 1/2.
Therefore, the ratio of sugar to flour can be expressed as 1: 2.
Boys and girls, let’s now apply what we have learned by completing the following exercise.
Exercise 1
1. In a class, there are 15 girls and 12 boys. What is the ratio of girls
to boys?
2. Anna has $75. Rashid has $100. What is the ratio of Rasid’s money
to Anna’s money?
3. In one season, a basketball team won 60 games and lost 20 games.
What is the ratio of games won to games lost?
4. A duck has 15 ducklings. Five of the ducklings are male. What is
the ratio of male to female ducklings?
5. Express the following ratios in their simplest form: (a) 2 : 10
(b) 80 : 20
(c) 6m : 30m
(d) 100cm : 25cm
Good job, boys and girls! Let’s move on.
How to Divide a Number by a Ratio
Let’s now examine how a number can be divided by a ratio using the example below:
Example 1
Joy and Karen have 200 buttons and they need to share them in the ratio 6:2. How many buttons does each of them receive?
Firstly, the buttons will be divided into 8 equal portions because when the quantities are added, we get: (6 + 2 = 8).
Secondly, as 8 is the total number of portions, we need to divide 200 by 8 – which gives us 25.
Our ratio was 6:2, so we need to multiply both parts by 25 to get our answer:
6 x 25 = 150
2 x 25 = 50
Therefore, Joy will receive 150 buttons, while Karen will receive 50 buttons.
Review the example above once more and complete the exercise below:
Exercise 2
Calculate the following shares:
1. Three numbers are in the ratio 5: 10 : 10, and the sum of the
numbers is 100. Find the numbers.
2. 3. 4.
Divide 500 into two parts which are in the ratio 30: 20.
A container contains 120 balloons, some pink and some blue. The ratio of pink balloons to blue ones is 8: 7. How many blue marbles are there?
If $5000 is divided among three people in the ratio 7:10:23, find the share of each.
Excellent work. Students!
Now, boys and girls, do you know we can also use ratios to find unknown quantities? Yes, we can! Let’s learn how!
Using ratios to find unknown quantities
Let’s examine how this is done. using the following example as a demon stration:
Example 1
The sweet company likes to put uneven numbers of sweets in their bags. They are currently creating a bag of blue and pink sweets in the ratio 4:6. If you get a bag with 12 blue sweets in it, how many will there be in total?
To work this out, it is necessary to divide the number of blue sweets by the ratio, to find the common denominator.
Hence; 12/4 = 3