PROPORTION - YOUR SUPERHERO SIDEKICK

Hello, Grade 6 friends! Today, we're going to dive into the exciting world of proportions—a magical concept in mathematics that helps us compare and relate different quantities in a balanced way. Imagine you have a delicious recipe for making cookies, and you want to adjust the ingredients to make more or fewer cookies while keeping the same tasty flavor.

 Proportions are like your recipe's secret code, ensuring that the right balance is maintained. As we explore proportions, think of them as the superhero sidekicks that help us keep things in harmony and maintain the perfect balance between different values. Get ready to embark on a proportional adventure in the world of math!

A proportion is a name which we give to any statement that two ratios are equal. It can be written in two ways, two equal fractions, or, using a colon, a: b = c: d or a/b : c/d.

It is obvious that if the two ratios are not equal then they are definitely not in proportion.

In any proportion the first and fourth term are called as extreme terms and the second and third as mean terms.

Example 1: Are the terms 20, 30, 40, 60 in proportion?

Solution: The ratio of first two terms is 20:30 = 2:3.

The ratio of the next two terms is 40:30 = 4:6= 2:3.

Since both the ratios are equal and hence the terms are in proportion.

                                                         Unitary Method

The method in which we first find out the value of one unit and then the value of required number of units is called as Unitary method.

10 apples = $40

1 apple = 40/10 = $4

 6 apples = 4 x 6 = $24

Example 2: If the cost of 6 notebooks is $72. Then what will be the cost of 4 notebooks?

Solution: Cost of 6 notebooks = $72

Hence the cost of one notebook will be = $72/6 = $12

Hence the cost of 4 notebooks =

Cost of one notebook x 4 = $12 x 4 = $48

Practice Questions

Q1)      Udanie made 63 runs in 7 overs and Tahir made 72 runs in 8 overs. Who made more run per over?

Q2)    The cost of 4kg wheat is $48. Find the cost of 10 kg of wheat.

Q3)    State True or False

           a) $40: $200 = 80kg : 400kg

           b) 23 litre : 69 litre = 12g:36g

Q4)    Determine the proportion

           a)      30, 40, 90, 360.

           b)      1,2,4,8

           c)       4,6,8,12

Q5)  The cost of 5 dozen bananas is $60.Find how many dozens of bananas one will get for $40.

Recap

1. For comparison by ratio, the two quantities must be in the same unit. If they are not, they should be expressed in the same unit before the ratio is taken.
2. The order in which quantities are taken to express their ratio is important.
3. Two ratios are equivalent, if the fractions corresponding to them are equivalent. Thus, 3 : 2 is equivalent to 6 : 4 or 12:8.
4. The method in which we first find the value of one unit and then the value of the required number of units is known as the unitary method.
5. In ratio and proportion the order is very important because as the order changes the ratio also changes.
                                                   Wrap-up with this video on proportion

CHECK BACK TOMORROW FOR YOUR QUIZ ON PROPORTION!!!