Using fractions in everyday life

Fractions are all around us every day. For example, you may encounter fractions when you read a number that is less than one whole, like a decimal, or when you use a recipe to make a cake. Brainstorm when and where you might use fractions in your life.

Fractions

Fractions with the same bottom number or denominator can be added or subtracted together. This is because only parts of the same whole can be added together. For example, you can add $\frac{3}{8}+\frac{2}{8}$   by counting the total number of “eighths”:

When fractions have a different denominator, we need to find a common denominator. A common denominator is a shared multiple of the denominators of several fractions. In the following example, we express how to do this: $\frac{1}{2}+\frac{2}{3}$

We divide each part of the $\frac{1}{2}$ into three equal parts and we divide each part of the $\frac{2}{3}$ into 2 equal parts. That's why in the following image the $\frac{1}{2}$ is multiplied on top and bottom by 3 and the $\frac{2}{3}$ is multiplied on top and bottom by 2.

Now our fraction problem is presented a bit different:

$\frac{1}{2}+\frac{2}{3}=\frac{3}{6}+\frac{4}{6}$

Since we added two of the same things – in this case we are adding sixths – we can add these together:

$\frac{3}{6}+\frac{4}{6}=\frac{3+4}{6}=\frac{7}{6}$

Finding the common denominator

Consider the following fraction problem:

$\frac{19}{24}-\frac{1}{6}$

Create a list of possible common denominators that we could use to solve this problem. When you finish your list, compare with a partner or a family member and consider the following:

• How many common denominators were you able to find?
• What patterns do you find in the list?
• Which common denominator would be the most reasonable to use for this problem? Why?

There is always a guaranteed method of finding a common denominator: by multiplying the two denominators together. In our example previous, we would get:

$24 \times 6 = 144$

However, as you may have noticed, this is not the smallest common denominator we could have used. For practical purposes, it is generally ideal to search for the least common denominator (or perhaps you know it as the least common multiple – the LCM) when solving an addition or subtraction fraction problem.

Task 1

Solve the following problems. For each one, be mindful of your choice of common denominator.

Applications

When do we add or subtract fractions in real life? Construct a list of examples and compare with others, if possible, to expand your list.

When tackling a real problem involving fractions, consider the following:

• Are the fractions mixed numbers or improper?
• Will I be adding or subtracting fractions?
• What do I know? What do I need to solve for?

Task 2

If you would like, you can complete the next series of word problems using TVO Mathify. You can also use your notebook or the following fillable documents.

1. Florence was measuring out their bedroom perimeter using measuring tape that measured in inches. They found the following measurements for each wall:

Side 1: $89\frac{1}{4} inches$

Side 2: $65\frac{7}{16} inches$

Side 3: $80\frac{7}{8} inches$

Side 4: $62\frac{1}{2} inches$

What was the total perimeter of the room?

2. Kel was baking a giant cake for their mom’s birthday. The recipe called for $6\frac{1}{2}$ cups of flour in a large mixing bowl. However, without realizing, Kel accidentally added $9\frac{1}{4}$ cups of flour instead of the $6\frac{1}{2}$ cups.

How much flour does Kel need to remove to get the recipe right?

If Kel uses a $\frac{1}{4}$ cup measuring cup to remove the flour, how many scoops will he need to use?

If you would like, you can complete this activity using TVO Mathify. You can also use your notebook or the fillable document.

Fraction questions

The following table has a collection of various fractions. Your task is to create five different addition/subtraction problems whose answer is one of the fractions from the table.

• You can choose from any of the following fractions as your answers, but each of your problems must use a different fraction.
• Try to create a variety of problems. Use more than two fractions, use different fractions with unique denominators, or write a word problem.
• Write a full solution for each problem you create.

Reflection questions

• What is a real-life situation where using a fraction is more effective than using a decimal number?
• How might you explain the concept of equivalent fractions to someone who is new to fractions? Explain what strategy you would use and/or what tools or pictures would be helpful.
• Can you have a common denominator of 0? How about 1? If yes for either, provide an example.

Reflection

As you read the following descriptions, select the one that best describes your current understanding of the learning in this activity. Press the corresponding button once you have made your choice.

Now, expand on your ideas by recording your thoughts using a voice recorder, speech-to-text, or writing tool.

When you review your notes on this learning activity later, reflect on whether you would select a different description based on your further review of the material in this learning activity.

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