Unit 7 Review: Practical Problems, Proportions, & Similar Figure

Unit 7 - Review

Practical Problems, Proportions, & Similar Figures

Let's go over a few things that will be on your test!

Practical Problems with Rational Numbers

Read practical problems carefully! Careful with fractions & percents!

• Look for KEY WORDS that tell you what operation you are doing.

• To convert a fraction to a percent, DIVIDE & then multiply by 100 (or move the decimal two places).

• To find part of the whole: MULTIPLY the fraction by the total.

• To divide a whole into equal parts: DIVIDE total by the part.

• To compare values: Write the values in the SAME FORMAT, then compare.

Unit 7: Practical Problems, Proportions, & Similar Figures

Multiple Choice

The Pizza Shop offers more than just pizza! The shop's menu is 3/5 pizza and 1/6 subs. What percentage of their menu is neither pizza or subs?

• 76.7%

• 23.3%

• 60%

• 16.7%

Fill in the Blank

There are 150 students in the 7th grade. 2/3 of the grade went to the dance. Of the students who went to the dance, only 1/4 bought snacks while they were there. How many students went to the dance and spent money?

Multiple Choice

Mrs. Watson ordered nachos. She quickly ate 1/4 of the order. She gave 1/2 of what was left to Mrs. Brooks. What percent of the original order did Mrs. Brooks get to enjoy?

• 75%

• 25%

• 50%

• 37.5%

Proportion Word Problems

We can use proportions to solve word problems. Remember to use W=K=U to set up the proportions: Words = Known = Unknown

• If you're given a scale factor, that is your KNOWN.

• Be CONSISTENT when you fill in the values.

• Remember, proportions can be written multiple ways -- if the cross products are the same, the proportions are equivalent!

Unit 7: Practical Problems, Proportions, & Similar Figures

Multiple Choice

How many inches long would the model train be?

• 5.5 in.

• 6.5 in.

• 7.5 in.

• 9.5 in.

Multiple Choice

The height of a telephone pole on a map is 6 cm. The scale is 2cm:20m. What is the actual height of the telephone pole?

• 6 m

• 10 m

• 18 m

• 60 m

Multiple Choice

If 3 pounds of apples costs $0.90, how much will 10 pounds cost?

• $3.00

• $2.50

• $3.50

• $2.25

Multiple Choice

James is making a scale model of the 18th hole of his favorite golf course. The actual yardage is 450 yards long and 15 yards wide. James wants his model to be 12 inches in length. Which could be used to find the width of his model if he uses the same ratio?

• $$\frac{12}{450}=\frac{15}{x}$$

• $$\frac{450}{12}=\frac{x}{15}$$

• $$\frac{450}{12}=\frac{15}{x}$$

• $$\frac{15}{12}=\frac{450}{x}$$

Similar Figures

Congruent figures are the same SHAPE and SIZE.

Similar figures are the same SHAPE, but not the same SIZE. Their sides are proportional.

• Use the congruency statement or the similarity statement to match up corresponding parts.

• Corresponding angles will be congruent (equal) in both congruent or similar figures.

• To find missing sides of similar figures, use a proportion!

Unit 7: Practical Problems, Proportions, & Similar Figures

Multiple Choice

What is true about the shape and size of similar figures?

• Same shape and same size

• Same shape and not the same size

• Different shape and same size

• Different shape and not the same size

Multiple Choice

What is true about the angles of similar figures?

• Corresponding angles are proportional.

• Complementary angles are proportional.

• Corresponding angles are congruent.

• Complementary angles are congruent.

Multiple Choice

What is true about the sides of similar figures?

• Corresponding sides are proportional.

• Corresponding sides are congruent.

• Opposite sides are proportional.

• Opposite sides are congruent.

Multiple Choice

The term "congruent" means ...

• matching

• similar

• corresponding

• equal

Multiple Choice

Two objects that are the same shape but not the same size are _______.

• Congruent

• Vertical

• Similar

• Complementary 

Multiple Choice

The pair of figures is similar. Find the missing side.

• x = 20

• x = 12

• x = 5

• x = 4

Multiple Choice

Pentagon JKLMN is similar to pentagon VWXYZ.
What is the measurement of angle X?

• 30 degrees

• 60 degrees

• 150 degrees

• 120 degrees

Multiple Choice

$$\Delta ABC\sim\Delta DEF$$

What side corresponds with AB? 

• BC

• FE

• DE

• FD