A percentage is another way of expressing a fraction that's used often in everyday situations. The word percent means "out of "
Let's take a look at the square below.
Notice that
the square has been divided into equal parts, and
of those parts are shaded.
Since out of parts are shaded, we say that " percent of the square is shaded."
We have a special symbol that we use instead of the word percent. This symbol is written as follows:
Using this symbol, we say that " of the square is shaded."
Which of the following models shows
Recall that is the same as out of
So, we need a model that shows shaded tiles out of The correct model is:
What percent of the square is shaded?
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a
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$40$ |
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b
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$42$ |
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c
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$22$ |
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d
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$32$ |
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e
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$30$ |
Which model shows $24\%?$
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a
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b
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c
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d
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e
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When more than pieces are shaded in a model where pieces represent a whole, the percentage will be greater than
Let's take a look at the model below, where one large square represents one whole:
In this model, tiles are shaded. Therefore, this model represents
Given that a large square represents a whole, draw a model that shows
First, recall that is the same as out of
So, we need a model where tiles represent one whole, and tiles are shaded. This model is as follows:
If a large square represents one whole, what percentage is illustrated in the model above?
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a
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$100\%$ |
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b
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$60\%$ |
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c
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$170\%$ |
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d
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$180\%$ |
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e
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$160\%$ |
If a large square represents one whole, which model shows $145\%?$
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a
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b
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c
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d
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e
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How do we find the percentage represented by a fraction model when the model isn't split into equal pieces?
The answer is to express the fraction as an equivalent fraction with a denominator of
As an example, let's consider the model below:
This model represents the following fraction:
To make an equivalent fraction with a denominator of we multiply both the numerator and the denominator by
Since is equivalent to we conclude that our fraction model represents
We can also use equivalent fractions to construct a simplified fraction model for a given percent. Let's see an example.
Which of the models below represents
First, recall that is the same as
We now need to simplify this fraction. Dividing the numerator and denominator by we get
Finally, we divide the numerator and denominator by once more:
The model that shows is:
Which model represents $75\%?$
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a
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b
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c
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d
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e
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What percentage of the shape above is shaded?
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a
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$50\%$ |
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b
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$60\%$ |
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c
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$70\%$ |
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d
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$30\%$ |
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e
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$40\%$ |
If a -sided polygon represents a whole, draw a model representing
First, recall that is the same as
Now, we simplify the fraction. Dividing the numerator and denominator by we get
Finally, we write as a mixed number:
Therefore, our model could be the following:
If one large shape represents a whole, which model shows $230\%?$
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a
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b
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c
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d
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e
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If one $10$-sided polygon represents a whole, which model shows $190\%?$
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a
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b
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c
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d
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e
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