Grade Six Mathematics
Answers to last week’s exercises:
Calculate the missing quantity
Ratio Hello Boys and Girls!
Did you have an enjoyable week? Did you do lots of work? This week, we will learn about Ratio.
What is Ratio?
1. Ratio is a relationship between two quantities, normally expressed as the quotient of one divided by the other. For example, if a box contains six red marbles and four blue marbles, the ratio of red marbles to blue marbles is 6 to 4, also written 6:4.
2. We use ratios to make comparisons between two things.
3. When we express ratios in words, we use the word “to”—we say “the ratio of something to something else.”
4. Ratios can be written in several different ways: as a fraction, using the word “to”, or with a colon.
Let us use the following illustration of shapes to learn more about ratios. 5. How can we write the ratio of squares to circles, or 3 to 6? The most common way to write a ratio is as a fraction, 3/6. We could also write it using the word “to,” as “3 to 6.”
6. Finally, we could write this ratio using a colon between the two numbers, 3:6.
7. Be sure you understand that these are all ways to write the same number. Which way you choose will depend on the problem or the situation:
● ratio of squares to circles is 3/6 ● ratio of squares to circles is 3 to 6 ● ratio of squares to circles is 3:6
Let us try to answer the following questions.
Exercise 1
1. A math club has 25 members, of which 11 are males and the rest are females. What is the ratio of male members to all club members?
2. A group of preschoolers has 8 boys and 24 girls. What is the ratio of girls to all children?
3. A group of preschoolers has 15 boys and 12 girls. What is the ratio of girls to boys?
4. A pattern has 4 blue triangles to every 12 yellow triangles. What is the ratio of blue triangles to all triangles?
5. A gardening club has 21 members, of which 13 are males and the rest are females. What is the ratio of females to all club members?
6. Dylan drew 1 heart, 1 star, and 26 circles. What is the ratio of circles to hearts?
Let us now share objects using ratio.
Share 28 marbles between Sally and Sue, in the ratio 3:4. [This means that every time Sally gets 3 marbles, Sue gets 4 marbles.]
We can work this sum another way: Number of marbles to be shared = 28 Ratio of shares = 3:4
Sum of shares = 3+4 = 7
Sally gets 3/7 of 28 = 12
Sue gets 4/7 of 28 = 16
Exercise 2
Now work the following:
1. Share 12 marbles in the ratio 1:2
2. Share 30 pins in the ratio 1:4
3. Share 24 oranges in the ratio 1:3
4. Share 40 eggs in the ratio 2:3
5. Share 36 nuts in the ratio 1:2:3
Solve the following problems
6. Sophia and Isabella share a reward of $117 in a ratio of 1:8. What fraction of the total reward does Sophia get?
7. Jayden and Caden share a reward of $140 in a ratio of 2:5. What fraction of the total reward does Jayden get?
8. The ratio of girls to boys in a swimming club was 2:4. There were 14 girls. How many total members were there in the club?
9. A jar contains 550 beans. Of all the beans, 2/5 are white beans and the rest are navy beans. What is the ratio of white beans to navy beans?
Equivalent Ratio
Equivalent ratios (which are, in effect, equivalent fractions) are two ratios that express the same relationship between numbers. We can create equivalent ratios by multiplying or dividing both the numerator and denominator of a given ratio by the same number.
A list of some of the equivalent ratios is as follows: 1) 1:2, 2:4, 4:8, 8:16, 16:32, 32:64, 64:128, ... 2) 1:3, 2:6, 3:9, 4:12, 5:15, 6:18, 7:21, 8:24...
3) 1:4, 2:8, 3:12, 4:16, 5:20, 6:24, 7:28, ...
4) 1:5, 2:10, 3:15, 4:20, 5:25, 6:30, 7:35, ...
5) 1:6, 2:12, 3:18, 4:24, 5:30, 6:36, 7:42, ...
The example problems on equivalent ratios are given below:
Example 1: Find whether 8:18 and 12:27 are equivalent ratios?
Solution: The simplest form of 8:18 is obtained by dividing it by 2; i.e. 4:9. Also, the simplest form of 12:27 is obtained by dividing it by 3, i.e. 4:9. Since both have same simplest form, 8:18 and 12:27 are equivalent ratios.
Example 2: Find two ratios equivalent to16:20 by division method. Solution: 16:20
Dividing both by 2, we get 8:10
Dividing both by 4, we get = 4:5
Thus, 16:20 = 8:10 = 4:5
These are required equivalent ratios.
Example 3: Determine four ratios equivalent to the ratio 7:4. Solution: Given that 7: 4
Multiplying both numbers by 2, we get
7 x 2: 4 x 2
= 14:8
Multiplying both numbers by 3, we get
7 x 3:4 x 3
= 21:12
Multiplying both numbers by 4, we get
7 x 4:4 x 4
= 28:16
Multiplying both numbers by 5, we get
7 x 5:4 x 5
= 35:20
Thus, 14:8 = 21:12 = 28:16 = 35:20
These are ratios equivalent to 7:4.
Next week, we will work more examples. Goodbye Boys and Girls! BE SAFE!