Chapter 7.1, Problem 37PPS

(A)

To determine

To compare the shaded portion of figure & write as a fraction. Write fraction as a percent & then compare that which has the greatest shaded part.

Answer to Problem 37PPS

Hence, the fraction $=\frac{1}{4}$ as a percent $=25\%$

Explanation of Solution

Given:

Total parts of the triangle $=3$

Shaded parts of the triangle $=2$

Concept Used:

We use the concept of same whole fraction method.

For example,

If each of the square is a “whole”, the shaded area represents the fraction $\frac{3}{2}$ . If the entire rectangle is the whole, the shaded area represents $\frac{3}{4}$

Calculation:

As per given information,

The given figure represents $1$ shaded parts out of $4$ equal parts.

Fraction representing shaded region of triangle $=\frac{1}{4}$

Now, convert the fraction to a decimal,

  $\frac{1}{4}=0.25$

Then multiply by $100$ to convert the decimal into a percentage

  $=0.25\times 100=25\%$

Conclusion:

Thus, the fraction of given figure $=\frac{1}{4}$ &as a percent $=25\%$

(B)

To determine

To compare the shaded portion of figure & write as a fraction. Write fraction as a percent & then compare that which has the greatest shaded part

Answer to Problem 37PPS

Hence, the fraction is $\frac{6}{20}$ & as a percent is $30\%$

Explanation of Solution

Given:

Total parts of the square $=20$

Shaded parts of the square $=6$

Concept Used:

We use the concept of same whole fraction method.

For example,

If each of the square is a “whole”, the shaded area represents the fraction $\frac{3}{2}$ . If the entire rectangle is the whole, the shaded area represents $\frac{3}{4}$

Calculation:

As per given information,

The given figure represents $6$ shaded parts out of $20$ equal parts.

Fraction representing shaded region of triangle $=\frac{6}{20}$

First reduce this fraction by dividing both the numerator and denominator by the Greatest Common Factor of $6$ and $20$ using , we get

  $=\frac{3}{10}$

Then using long division method, $3$ divided by $10$ ,

  $=0.3$

To convert the decimal into a percentage, multiply by $100$

  $=0.3\times 100=30\%$

Conclusion:

Thus, the fraction of given figure is $\frac{6}{20}$ & as a percent is $30\%$

(C)

To determine

To compare the shaded portion of figure & write as a fraction. Write fraction as a percent & then compare that which has the greatest shaded part

Answer to Problem 37PPS

Hence, the fraction is $\frac{2}{8}$ as a percent $=25\%$

Explanation of Solution

Given:

Total parts of the rectangle $=8$

Shaded parts of the rectangle $=2$

Concept Used:

We use the concept of same whole fraction method.

For example,

If each of the square is a “whole”, the shaded area represents the fraction $\frac{3}{2}$ . If the entire rectangle is the whole, the shaded area represents $\frac{3}{4}$

Calculation:

The given figure represents $2$ shaded parts out of $8$ equal parts.

Fraction representing shaded region of triangle $=\frac{2}{8}$

First reduce this fraction by dividing both the numerator and denominator by the Greatest Common Factor of $2$ and $8$ using , we get

  $=\frac{1}{4}$

Then using long division method, $1$ divided by $4$ ,

  $=0.25$

To convert the decimal into a percentage, multiply by $100$

  $=0.25\times 100=25\%$

Conclusion:

Thus, the fraction of given figure is $\frac{2}{8}$ & as a percent $=25\%$ .