A Fraction as a Percent

A Fraction as a Percent exercise

• Understanding the importance of fractions and percent.

  Hints

  Remember that fractions show how many parts of a whole there is.

  The same is true with percentages.

  $\frac{3}{5}$ and $\frac{60}{100}$, or 60%, are linked. With this information, how many parts out of 5 does 60% represent?

  Solution

  A percent represents a part of something out of 100. When converting a fraction to a percent, it tells us how many parts out of 100 the fraction represents.

  For example, $\frac{3}{5}$ as 60% means that 3 out of every 5 parts make up 60% of the whole. This helps us understand the fraction's relationship to a whole hundred.

• What is the correct order of steps to convert a fraction to a percent?

  Hints

  We always start off by setting up our tape diagram with 0%, 100% and the total parts that make up 100%.

  How many parts do we need to divide the diagram into?

  How many parts do we need to shade?

  What does the shaded part represent?

  Solution

  Set up a tape diagram, or bar model, marking 0%, 100% at the top, and 0 and the whole underneath. In this example, the whole would be 2.

  Now divide the tape diagram by the number of the whole provided. Here, we would divide it into two parts. We notice this is halfway, so mark 50% at the top.

  Next, shade in how many parts of the whole the fraction has. The fraction in the example has one part of the whole, so shade in one part.

  Finally, write the percent as shown by the number of parts shaded in. In this example, 1 part of 2 is equal to 50%. This means $\frac{1}{2}$ = 50%.

• Which answer shows $\frac{2}{8}$ as a percentage?

  Hints

  Remember, set up a tape diagram to help.

  Find what 25%, 50% and 75% would be on the tape diagram.

  Solution

  If we shade in one part of the tape diagram up to $\frac{2}{8}$, we see that it is equal to 25%.

  This means $\bf{\frac{2}{8}}$ as a percent is 25%.

• What percentage are these fractions equal to?

  Hints

  Remember to set up tape diagrams like this one for $\frac{1}{2}$ to help you.

  Then shade in 1 part. $\frac{1}{2}$ is equal to 50%.

  Solution

  Here we can see the correct pairs.

• Which answer represents the displayed fraction as a percent?

  Hints

  Set up a tape diagram like this to help you.

  Divide 100 by 10, to get 10. Each block is worth 10%.

  Now shade in the total parts of the fire Olivia put out, which is 8.

  Solution

  With the tape diagram set up, shade in 8 parts, since each block represents 1 part.

  Now look at the matching % at the top.

  We can see that $\bf{\frac{8}{10}}$ is equal to 80%.

• Enter the values that make this step by step solution true.

  Hints

  Remember that the numerator represents the parts of the whole, and the denominator represents total parts that make up the whole.

  What must you multiply the denominator, 20, by to get 100? You need to multiply the numerator by the same value.

  Solution

  First, we find out how much of the fire remains. 5 parts of the fire remain, so this is our numerator. The denominator is represented by how many parts in the whole. Here, it is 20, so our fraction is $\frac{5}{20}$.

  Next, we need to create a fraction with 100 as the denominator. To do this, we multiply 20 by 5 to get 100. We must multiply the numerator by the same value; 5 multiplied by 5 is 25. The new fraction is $\frac{25}{100}$.

  Finally, we can convert $\frac{25}{100}$ to a percent. A percent represents out of 100, so $\frac{25}{100}$ as a percent is 25%. This means that 25% of the fire remains.