It was Mazie’s birthday. She was excited because she got a beautiful pink and white cake and eighteen (18) popsicles. Mazie gave four (4) of the popsicles to her friends. Her mother told her to share more of the popsicle but Mazie was reluctant. She wanted to keep half the amount of the popsicles for herself. Her mother insisted that she share more popsicles. Mazie started crying because she did not know how many of the popsicles to keep. Can you help Mazie? How many more popsicles should Mazie share?

Like Mazie, we sometimes don’t know how much of our food to share and how much to keep for ourselves. It is always a good idea to keep some of your food so you can have it at another time or on another day. But how do you how much of your food to keep and how much to eat? Let’s find out. Let us use the following objects to represent Mazie’s popsicle.

Question

1. How many popsicles do you see?
2. How many popsicles did Mazie share?
3. How many popsicles represents half of the total popsicles?
4. How many more popsicles should Mazie share?

Answer

1. 18 popsicles
2. Mazie shared 4 popsicles
3. 9 represents half of the total popsicles
4. Mazie should share 5 more popsicles

Writing Fractions

Do you know what portion of food you consume daily?
Do you know the number of times you eat per day?
Before you give an answer, remember that all foods go into the stomach; and since the stomach has to work hard to get the food out of its walls, every food is counted except water. So, let us help you with the counting.

Lets’ say you go to bed around 10 pm. You sleep for 10 hours and open your eyes almost the same time each morning which is 8am.
That means you only have 14 hours left out of the 24 hours.
Your first meal is around 8:15 am and you eat every time you get the chance which is about 10:15am, 12:15pm, 2:15pm, 4:15pm 6:15pm, 8:15pm and around 9:30pm and even around 2am.
That’s a total of 9 hours out of the 14 day-time-hours.
Can you represent the total number of hours that you eat as a fraction of the total day-time hours?
You are correct. This is: = 9/14 This is called a fraction.

A Fractions is part of a whole. It can be written as the amount that is shared over the whole (total amount). That is: 9/14
Two numbers are used to represent a fraction. The top number is called the numerator, the line is called the fraction bar or the division bar and the bottom number is called the denominator.
A fraction = number of selected items / total number of items

Remember that you cannot share what you do not have.
if you have 4 donuts you cannot eat 7 donuts.
You can eat 1 out of the 4 donuts = ¼
You can eat 2 out of the 4 donuts = 2/4.
You can eat 3 out of the 4 donuts = ¾
You can eat all 4 donuts = 4/4 = the whole or the total amount

Example 1:

There are five (5) gummies on a plate. Four (4) of the gummies were eaten.

1. What fraction of the gummies were eaten?
2. What fraction of the gummies remained?
Look at the illustration bellow: hearts are used to represent the gummies. There is one (1) blue gummy and four (4) red gummies which give a total of five (5) gummies.




Solving Fractions

1. Four (4) red gummies were eaten = the numerator.
2. Five (5) gummies = whole = the denominator.
3. The portion that was eaten is =4/5 which is read four-fifths.
4. One (1) blue gummy remains =1/5 which is read one-fifths.

From the example above, did you notice that you ate more than half of the gummies? Do you know that working with fractions can help you keep tract of the amount of food you eat daily? Do you know that you can use fractions to calculate the number of meals you want to eat? You can decide to wait 5-hours before you have your first meal or you can decide to have a 4-hour break between meals. Whatsoever you decide, fractions can help.



Like and Unlike fractions

The top number is known as the numerator. It represents the portion that is taken out of the whole. The bottom number is known as the denominator. It represents the number of equal parts the whole is split into or the total amount the whole is shared into.

Like and unlike fractions examine the denominator (bottom number). Fractions with the same denominators are called like fractions. For example: 1/7 , 3/7 , 5/7
Fractions with different denominators are called unlike fractions. For example: 2/7 , 1/5

You can use like fractions to keep track of the amount of food that you eat daily, such as pizzas or juices. You can use the result to examine the amount or portion of the same food items the you eat as well as to decide on eating smaller portion at less intervals.



Example 2:

Suppose you ordered 3 pizzas in one day at different times. Each pizza is cut into 8 equal slices.

You ate 5 slices from the first pizza that is: =5/8
You ate 7 slices from the second pizza that is: =7/8
You ate 4 slices from the third pizza that is: =4/8

Can you see that the denominator (the bottom number) is the same? These are called like fractions. You can add these fractions in order to know the number of slices of pizza you have for the day.
=5/8 + 7/8 + 4/8 =(5+7+4)/8 =16/8
You ate a total of 16 slices of pizza.



How many groups of 8 can you get out of 16? Yes, you are correct it is 2 groups. Therefore, you ate 2 whole pizzas. Next time, try to eat less slices. You could actually save some money and save you stomach.



Example 3:

Do you drink juices throughout the day? Lets’ say you drank from a 2 liter bottle, 1 liter bottle or 600ml bottle. Lets’ write the drinks in ml which is 20ml, 10ml and 6ml respectively.
Lets assume you drank 12ml of the 20 ml bottle, 7ml of the 10ml bottle and 5ml of the 6ml bottle. The fractions are: 12/20 , 7/10 , 5/6
Can you see that the denominator (the bottom number) is different for all fractions? These are called unlike fractions.



Activity 1:

Look at the fractions below. Can you identify the number of like and unlike fractions?
1. How many are like fractions?
2. How many are unlike fractions?

1/8 , 4/5 , 2/7 , 3/5 , 4/7 , 5/12 , 6/13 , 6/7

Learn more about like and unlike fraction here

Types of Fractions

1. Proper Fractions

Proper fractions are fractions in which the value of the numerator is less than the value of the denominator. For example: 3/8 represents a proper fraction. The numeral 3 is less than the numeral 8.



Example 4:

There are eight (8) oranges in a bag. The oranges are placed on a tray in the center of a table. Three (3) of these oranges are green.



Question

1. Count the number of oranges on the tray
2. What word is used to represent the total number of oranges?
3. how many oranges are green?
4. Write the portion of green oranges as a fraction.



O O O O O O O O




Answer

1. Total number of oranges is 8.
2. whole is used to represent the total number of.
3. There are 3 green oranges.
4. This can be written as 3/8

You were already introduced to proper fractions from the beginning of the lesson. A proper fraction is where the numerator is less than the denominator. This can be illustrated with a pot of rice. If a pot of rice holds 15 servings and you shared 2 servings of rice on a plate. Can you represent the 2 servings as a fraction? This can be written as a proper fraction, since 2 is less than 15. That is: 2/15



2. Improper Fractions

Improper fractions are fractions in which the value of the numerator is greater than the value of the denominator. For example: 13/5 represents an improper fraction since, 13 is greater than 5.



Example 5:

Your mother bought three bags of oranges form the supermarket. Each bag contains twelve oranges. When your mom checked the bags, five of the twelve oranges in one of the bags were spoilt.
Can you count the number of oranges that were good?
You are correct. Seven oranges were good.
Can you count the total number of oranges that were good from the three bags?
You are correct 31 oranges were good all together.

1. All oranges from the first bag were good. That is 12 out of 12 oranges were good. =12/12
2. All oranges from the second bag were good. That is 12 out of 12 oranges were good =12/12
3. Seven oranges from the third bag were good. That is 7 out of 12 oranges were good =7/12
4. What do you notice about these fractions? You are correct. The denominator is the same.
5. What is the name of fractions with the same denominator? You are correct. They are called like fractions.
6. What is the easiest way to add like fractions? You are correct. Add the top number of each of the fractions.

=12/12 + 12/12 + 7/12 =(12+12+7)/12 =31/12
Since 31 is greater than 12 and 31 is the numerator then, this it is considered an improper fraction.



Example 6:

Lets’ say, you have a certain bowl that you use to eat your cereal. That bowl holds approximately 500 grains of cereals. You eat 450 grains at 8am, then 350 grains at 2pm and 410 grains at 8pm. The fractions are written bellow:

450/500+ 350/500 + 410/500= 1210/500

Remember that you use the same bowl each time to eat your cereal. Can you see the total number of grains you eat daily? 1210 grains. All these add up and contribute to your overeating. This is nearly 2 ½ bowls of grains.

If you continue to learn fractions you will be better able to calculate your total consumption as well as your total calory intake. By keeping track of the amount of food you eat and the number of times you eat per day will help you to eat less.

Learn more about improper fractions here



3. Mixed Number

A mixed number is the sum of a whole number and a proper fraction. A whole number is a set of natural numbers or counting numbers. For example {1, 2, 3, 4, 5, ….}. Proper fractions are fractions in which the value of the numerator is less than the value of the denominator. Example: 2/5. Therefore, a mixed number is written as follows: 2 3/5
Remember that the whole number is added to the proper fraction as follows: 2+3/5 but it is written as 2 3/5 .



Example 7

Your mother bought three bags of oranges form the supermarket. Each bag contains twelve oranges. When your mom checked the bags, five of the twelve oranges in one of the bags were spoilt.
Can you count the number of oranges that were good?
You are correct. Seven oranges were good.
Can you count the total number of oranges that were good from the three bags?
Let us count the oranges in each bag.


1. All oranges from the first bag were good. That is 12 out of 12 oranges were good. =12/12 = 1 bag
2. All oranges from the second bag were good. That is 12 out of 12 oranges were good =12/12 = 1 bag
3. Seven oranges from the third bag were good. That is 7 out of 12 oranges were good =7/12
4. How many bags of oranges were good? You are correct. Two (2) bags of oranges were good.
5. What is the fraction for the number of oranges that were good in the bag with the spoilt oranges? You are correct. =7/12.

The mixed number for good oranges is two bags of oranges + the proper fraction. This is written 2+7/12 =2 7/12



Example 8:

There are three (3) trays of eggs on a table. Each tray contains twelve (12) eggs. By the end of the week 2 eggs remain in the first tray, 1 egg remains in the second tray and 5 eggs remain in the third tray.


1. How many eggs were eaten from each tray?
First tray: 10 eggs were eaten from the first tray. Fraction =10/12.
Second tray: 11 eggs were eaten from the second tray. Fraction =11/12.
Third tray: 7 eggs were eaten from the third tray. Fractions =7/12.

2. How many eggs were eaten for the week?
What do you remember about like fractions? You are correct. Like fractions have the same denominator. To find the total add its numerator as shown below.
10/12+ 11/12 + 7/12= (10+11+7)/12 =28/12

3. Why is the answer given above represents an improper fraction?
You are correct. The numerator is greater than the denominator.

4. How many groups of 12 can you get from 28?
Use the sticks below to help you.
| | | | | | | | | | | | | | | | | | | | | | | | | | | | .

There are 2 groups of 12 sticks and 4 single sticks remaining. This can be written as a mixed number: =2+4/12 =2 4/12

Keep tracking the amount of food you consume. You are doing a good job. You ate over 2 trays of eggs for the week. What can you do to limit the number of eggs you eat per week?
Learn more about mixed fractions here



4. Equivalent Fractions

Equivalent fractions are fractions that looks different but are the same in value. It is best to simplify fractions to its lowest term in order to know if they are the same.

In the example above with the eggs. Remember that you ate 28 eggs in one week. You represented 28/12 as an improper fraction.
28/12 as a mixed number =2 4/12.
4/12 is the same as 1/3.
The answer should have been written as 2 1/3 in its lowest form.

You may be wondering how we arrived at 1/3. Look at the illustration below:
4/12 = (4÷4)/(12÷4) =1/3.
Remember, sticks are an excellent tool for grouping.
1. How many groups of 4 can you get out of 4 sticks?
|||| = 1 group of 4.
2. How many groups of 4 can you get out of 12 sticks?
|||| |||| |||| = 3 groups of 4. This proves that 4/12 is the same as 1/3 they are called equivalent fractions.



Example 9:

You decide to have two (2) eggs, four (4) slices of bread and six (6) ham slices for lunch. There are 12 egg, 10 slices of bread and 12 ham slices. What fraction of food did you take for lunch?


1. eggs =2/12
2. bread =4/10
3. ham =6/12

These fractions can be written in their lowest terms. You must find a number that can be divided exactly into the numerator and denominator of the fraction.

1. Eggs =2/12= (2÷2)/(12÷2)= 1/6 say one-sixth.
2. Bread =4/10= (4÷2)/(10÷2)= 2/5 say two-fifth.
3. Ham =6/12= (6÷3)/(12÷3)= 2/4 = (2÷2)/(4÷2)= 1/2 say half.

These are equivalent fractions: 2/12 is the same as 1/6 and 4/10 is the same as 2/5 and 6/12 is the same as 2/4 which is the same as 1/2 . Can you see that you ate 1/6 of eggs, 2/5 slices of bread and ½ pack of ham slices. This proves that you are eating too many ham slices.

Fraction are very tricky but if you practice using them, they become quite easy. You can also teach your children the same.
Learn more about equivalent fractions here