Sarin’s family like to eat fruits. His mother prefers to buy from the supermarket as she can have more choices and cheaper in price. Orange, apple and pear are the family most liking and they eat them every day after their dinner. Sarin is a good helper for his mother in handling the fruits when his mother comes back from marketing.

After Sarin washes and sorts the fruits, he stores them in a big basket.

**What is a ratio?**

If Sarin has 5 apples and 6 oranges, Sarin can express the ratio of the number of apples to the number of oranges as **5 : 6**

The apples to oranges ratio = 5 : 6

If we normalized the ratio based on the number of oranges

The normalized apples to oranges ratio = 5/6 : 6/6 = 0.8333 : 1

This means that if Sarin adds one orange, he will need to add 0.8333 apples so that he can maintain the apples to oranges ratio as 5 : 6

If Sarin has 12 oranges

12 × 0.8333 = 10

Sarin will have 10 apples

Now, Sarin puts his 5 apples and 6 oranges into a basket, the ratio of the number of apples to the number of oranges in the basket is still 5 : 6. The total number of fruits in the basket is 11. The number of apples to the number of fruits in the basket is 5 : 11.

The number of fruits in the basket = 5 + 6 = 11

The apples to all fruits ratio = 5 : 11

The oranges to all fruit ratio = 6 : 11

The all fruit to apples ratio = 11 : 6

The all fruit to oranges ratio = 11 : 5

What will be the ratio of apples to oranges to all fruits ratio in the basket?

From the model

The ratio of apples to oranges to all fruits = 5 : 6 : 11

Apples : Oranges : All Fruits = 5 : 6 : 11

The normalized ratio based all fruits,

Apples : Oranges : All Fruits = 5/11 : 6/11 : 11/11 = 0.4545 : 0.5454 : 1

We can know from the normalized ratio that there are 45.45% of apples and 54.54% of oranges in the basket.

Apples are the favour fruits for his brother, Hairu. Hairu likes to use 9 pears to exchange with Sarin for 2 apples. Now Sarin has 3 apples, 6 oranges and 9 pears in the basket, the ratio of apples to oranges to pears now is 3 : 6 : 9 or 1 : 2 : 3.

**Sarin now have 18 fruits in total and Hairu happily ate the 2 apples.**

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