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Guided Practice

Sara has 300 trading cards in her collection. She sells 12% of her cards at the garage sale. How many cards does she sell?

Find 12% of 300.

A percent is a fraction with a denominator of 100.

12% of 300 is 36. Sara sells 36 of her cards at the garage sale.
What is 95% written as a fraction?

To write 95% as a fraction, write it with a denominator of 100.

Then you can simplify the fraction if possible.

95% written as a fraction is 19/20.

How many shoes are in 50% of a box?

50% of a box = shoes.

Write these percents as fractions in simplest form.

10%  = /

25% = /

50% = /

75% = /

You can also use mental math to solve some percent problems like these.

12% of 300 is the same as
10% of 300 + 1% of 300 + 1% of 300.

10% of 300 is 300 ÷ 10, or .

1% of 300 is 300 ÷ 100, or .

So, 12% of 300 is

+ + = 36.
Melissa spends 20% of her time at home during the week studying. She spends 8 hours at school and 16 hours at home, for a total of 24 hours.

How much time does Melissa spend studying? Write your answer as a decimal.

Melissa spends hours a week studying at home.

What is 83% of 1,400?
Use a comma in your answer.

83% of 1,400 is .

What is 5% of 100?

5% of 100 is .

What is 15% written as a fraction?

15% = /

What is 42% written as a fraction in simplest form?

42% = /

What is 250% written as a fraction in simplest form?

250% = /

What is 18% written as a fraction?

18% = /

To compute the percent of a number, you can multiply the percent by the number.

For example, 32% of 60 is 0.32 × 60, or

32/100 × 60 = 8/25 × 60.

To compute the whole, when you are given the percent and the part, you can divide.

For example, 64 is 80% of what number?

64 ÷ 80/100 = 64 × 100/80

You can also use equivalent ratios: 64/? = 80/100.

45 is 75% of what number?

45 is 75% of .

3 is 30% of what number?

3 is 30% of .

7 is 25% of what number?

7 is 25% of .

27 is 90% of what number?

27 is 90% of .

Multiply to determine 32% of 60.

32% of 60 is .

64 is 80% of what number?
Use any method to compute the answer.

64 is 80% of .

57.12 is 51% of what number?
Estimate first. Then compute the answer.

57.12 is 51% of .

9.45 is 15% of what number?
Estimate first. Then compute the answer.

9.45 is 15% of .

36 is 18% of what number?
Estimate first. Then compute the answer.

36 is 18% of .

11 is 20% of what number?
Estimate first. Then compute the answer.

11 is 20% of .

36 is 200% of what number?
Estimate first. Then compute the answer.

36 is 200% of .

90 is 125% of what number?
Estimate first. Then compute the answer.

90 is 125% of .

You can't learn math just by solving problems. But you need to get used to solving problems! Good problems are problems that challenge you and make you think—not problems that you can answer quickly. So, challenge yourself. Find challenging math problems to solve, and don't be afraid to get them wrong or not be sure of the answer. The process can be painful, but it's really worth it!

At the right are 5 percent problems that you might find challenging. Good luck! There are no answers in the Instructor's Guide for these!

Try out these challenge questions!

Jackson's little brother has 8 toy trucks that he brings with him to a sleepover. These trucks represent 40% of his truck collection.

Jackson's brother has a total of trucks in his collection.

The number of banana bread muffins a baker makes every day is 20% of the total number of muffins he makes.

On Wednesday, the baker made 29 banana bread muffins, so he made a total of muffins that day.

On Friday, the baker made 50 banana bread muffins, so he made a total of muffins that day.

Trisha answered 95% of the questions on her science test correctly. She answered 38 questions correctly.

So, there were a total of questions on her science test.

Seventy-five percent of a class answered the first question on a test correctly, 55% answered the second question correctly, and 20% answered neither of the questions correctly.

Thus, % of the class answered both questions correctly.

The original price of a suit is $200. The price increased by 30% of the original price, and after this increase, the store offered a 30%-off coupon for a one-day sale. Customers who used the coupon got 30% off the increased price. How much did these customers pay for the suit?

They each paid $ for the suit.

100%
100%
The area of a trapezoid is given by the formula 0.5 × h × (b1 + b2).

b1 b2 h

This is actually the formula for the area of a triangle and a parallelogram too! For a triangle, either b1 or b2 will be 0. For a parallelogram, b1 and b2 are equal.

Can you draw some examples to see how that works?

The areas of different shapes can be added together to determine the area of a more complex shape. Consider this square. It is made up of 4 trapezoids, each with the same height, and one square in the center.

You can multiply the large square's side length by itself to determine the total area. Or, you can determine the area of the 4 trapezoids, and then add that value to the area of the center square to determine the total area.

In a rectangle, the side that is to the base is the height.

If we the rectangle, the area stays the same.

The height is the distance from a base to the opposite side.

A has an area of one half times base times height.

What is the area of this triangle?

8.84 ft 12 ft

The area is square ft.

What is the area of this parallelogram?

18 cm 13.14 cm

The area is square centimeters.
What is the area of the right triangle?

14 cm 13.14 cm

The area is square centimeters.
What is the area of this trapezoid?

19 in. 29 in. 19 in.

The area is square inches.
What is the area of this trapezoid?

3.8 m 1.9 m 2.0 m

The area is square meters.

Determine each area exactly.

Area of 4 trapezoids:    square in.

Area of center square: square in.

Area of large square:   square in.

What is the total area of this complex shape?

The total area is square km.

The dashed lines divide the perimeter of the hexagon into 12 equal segments. And each distance from the center point to the side is the same. What is the total area of the hexagon?

The total area is square mm.

This solid figure has 2 square faces that are the same area and 4 other rectangular faces that have the same area. What is the total area of all the shapes that cover the outside of this solid figure?

The total area is square units.