7th Grade 10/7 Sub Day Review

7th Grade 10/7 Sub Day Review

by Kellany Bennett

​

​WATCH THE VIDEOS AND READ THE NOTES SLIDES. SERIOUSLY.

A ratio that compares two quantities with different units.

A rate is NOT 

Multiple Select

Which is not a RATE

• $$\frac{2\ miles}{4\ hours}$$

• 60 hours in every 2 hours

• 30 miles per mile

• $$\frac{55\ sq\ ft}{\frac{1}{2}hour}$$

UNIT RATE

A rate in which the second quantity is one.

Examples of Unit Rate

Multiple Select

Which one is NOT a unit rate

• 4 miles per hour

• 4 miles in 3 hours

• $$\frac{30\ miles}{1\ hour\ }$$

• $$\frac{69\ gallons}{5\ hours}$$

Is a fraction that has a fraction in the numerator, denominator or both.

Speed is a unit rate

The speed limit is 35 "miles per hour".

At that speed, you can travel 35 miles in 1 hour.

El límite de velocidad es de 35 "millas por hora".

A esa velocidad, el taxi recorre 35 millas en 1 hora.

Heart Rate is a unit rate

How many times does YOUR heart beat per minute?

¿Cuántas veces SU corazón late por minuto?

Multiple Choice

If your heart beats 40 times in 30 seconds, how many times does it beat in 1 minute?

• 40

• 70

• 50

• 80

Multiple Choice

I can buy 4 candy bars for $2. What is the unit rate? (How many candy bars can I buy with $1?

• 4

• 2

• 3

• 1

Multiple Choice

Find the cost per apple if 10 apples costs $4.00

• $0.25

• $0.50

• $0.40

• $2.00

Multiple Select

Choose all the Complex Fractions.

• $$\frac{1}{4}$$

• $$\frac{\frac{1}{3}}{5}$$

• $$\frac{3}{\frac{2}{3}}$$

• $$4$$

Multiple Select

Which are NOT a complex fraction

• $$\frac{1}{4}$$

• $$\frac{2}{\frac{2}{3}}$$

• $$4$$

• $$2.4$$

Multiple Choice

If 5 gallons of gas costs $10.25, how much is one gallon of gas?

• $2.50

• $2.05

• $2.25

• $2.00

Multiple Choice

$$\frac{8\ pizzas}{3\ people}=\frac{?}{9\ people}$$  What number should go where the question mark is?

• 24

• 32

• 2

Multiple Choice

$$\frac{90\ dollars}{12\ hours\ of\ work}=\frac{30\ dollars}{?\ hours\ of\ work}$$  What number should go where the question mark is?

• 3

• 36

• 4

Multiple Choice

$$\frac{5\ daisies}{2\ roses}=\frac{?\ daisies}{24\ roses}$$  

What number should go where the question mark is?

• 12

• 60

• 27

Multiple Choice

$$\frac{240\ hamburgers}{36\ ta\cos}=\frac{20\ hamburgers}{?\ ta\cos}$$  

What number should go where the question mark is?

• 3

• 8

• 2

Multiple Choice

Which example is proportional?

• $$\ \frac{2\ grams}{1\ cup}=\ \frac{1\ gram}{\frac{1}{2}cup}$$

• $$\ \frac{3\ dollars}{6\ tickets}=\ \frac{9\ dollars}{10\ tickets}$$

• $$\ \frac{2\ red\ cars}{5\ total\ cars}=\ \frac{4\ red\ cars}{11\ total\ cars}$$

​Complex Fractions and Complex Ratios

• ​Of course, it can't all be whole numbers and decimals! Eventually, there have to be some fractions!!

• ​If one or both parts of the ratio contain a fraction, it's a complex ratio

• ​You will still look for multiplicative or division-based relationships!

  • ​In the bottom picture, see how they divide the 2 hours by 2 to get 1 hour, and do the same to 5 ²/₃

​Quickest Possible Route

1. Choose a unit to be tops and a unit to be bottoms

2. ​Fill in the numbers you know

3. ​To get the answer, look at the row that becomes a 1

4. ​Multiply the number by its reciprocal (flipped version)

5. ​Multiply the other row by the SAME number

6. ​Remember that you get the multiplication from the row you KNOW, not the "answer" row.

Multiple Choice

Write the fractional rate as a unit rate:

$$\frac{1}{2\ }$$  cup for 3 batches

• $$\frac{3}{2}$$  cup for 1 batch

• $$\frac{1}{6}$$  cup for 1 batch

• $$\frac{3}{4}$$  cup for 1 batch

• 1 cup for 3 batches

Multiple Choice

Write the fractional rate as a unit rate:

6 pages every  $$\frac{1}{5}$$  hour

• $$\frac{6}{5}$$  pages every  $$\frac{1}{5}$$  hour

• $$\frac{6}{5}$$  pages every 1 hour

• 30 pages every 1 hour

• 180 pages every 1 hour

Multiple Choice

Mur reads  $$\frac{5}{8}$$  page in  $$\frac{2}{3}$$  minute. What is the unit rate of page per minute? 

• 0.55 cakes

• 11.7 cakes

• 13.75 cakes

• 102.75 cakes

Multiple Choice

Sal walks   $$3\frac{1}{2}$$  miles in  $$1\ \frac{1}{4}$$  hours. Find the unit rate of miles per hour. 

• $$4\ \frac{3}{8}miles\ per\ hour$$  

• $$2\ \frac{4}{5}miles\ per\ hour$$  

• $$\frac{5}{14}miles\ per\ hour$$  

• $$4\ \frac{1}{6}miles\ per\ hour$$  

​What is a Proportion?

• A proportion is an equation that states two ratios are equal

• If something is proportional, it means that all its ratios are EQUAL.

• ​If asked if two ratios form a proportion (or are they proportional?), check to see if they are EQUAL by...

  • ​simplifying the ratios

  • ​looking for multiplicative or division-based relationships across

  • ​using a calculator to divide the ratios and see their decimal forms

​Checking for Proportionality

• ​You may not like the methods from before

  • ​dividing the ratios into decimals

  • ​simplifying to see if both simplify to the same ratio

  • ​looking for relationships

• ​There's more! Remember cross products, or means and extremes? If two ratios are proportional, their cross products or means and extremes have to be equal.

Multiple Choice

Do the ratios form a proportion?

• Yes, they form a proportion.
• No, they do not form a proportion.

Multiple Choice

Do these ratios form a proportion?

$$\frac{6}{8}\ ,\ \frac{27}{36}$$  

• Yes, they form a proportion.

• No, they do not form a proportion.

Multiple Choice

Determine whether each pair of ratios forms a proportion

• Proportion

• Not a Proportion

Multiple Choice

Determine whether each pair of ratios forms a proportion

• Proportion

• Not a Proportion

What we know...

• Tables have a constant multiplier/unit rate and have ratios that are equivalent.

• Graphs have a straight line and pass through the origin (0,0).

• Equations are in the form y=rx, where "r" is the unit rate.

• Situations are when one quantity is zero the other one is also zero. They have a constant multiplier/unit rate and the ratios are equivalent.

Multiple Choice

Is this table proportional?

The table is proportional

Because the table has a constant multiplier/unit rate of 5 and the ratios are equivalent.

This is the graph that is proportional.

Because the line is linear (straight line) and passes through the origin (0,0).

Multiple Choice

The equation y=5x is proportional. What is the unit rate?

• 2

• 6

• x

• 5

5 is the unit rate

Because 5 is in the position of "r" in the equation y=rx.

Multiple Select

Are both of these situations proportional?

• No, the Potato Sale and Ride Tickets are not proportional

• Yes, the Potato Sale and Ride Tickets are both proportional.

The situation is proportional because both the Potato Sale and the Ride Tickets are proportional.

Both will start at (0,0) and have constant multipliers. (Potato constant multiplier is 1.19 and the constant multiplier for the Ride Tickets is 4)

Multiple Choice

Which best describes the equation?
y = 75x

• Proportional
• Nonproportional

Multiple Choice

Does this graph represent a proportional relationship?

• Yes, because the line is pretty.
• No, because the line goes through the origin.
• Yes because the line goes through the origin.
• No, because the graph is non-proportional.

Multiple Choice

Which best describes the table?

• proportional
• non-proportional

Multiple Choice

Is the graph proportional or non proportional?

• proportional
• non proportional

Multiple Choice

What is the constant of proportionality?

• 8
• 16
• 24
• 2

Multiple Choice

Proportional or Non-Proportional?

• Proportional

• Non-Proportional

Multiple Choice

Proportional or Non-Proportional?

• Proportional

• Non-Proportional

Multiple Choice

Proportional or Non-Proportional?

• Proportional

• Non-Proportional

Multiple Choice

Is the graph proportional?

• yes
• no

Multiple Choice

What is the constant of proportionality?

• $3
• $4
• $2
• $9

Multiple Choice

Is the given table a proportional relationship? If so, what is the constant?

• Yes; 1/3
• Yes; 3
• Yes; 5
• No

Multiple Choice

Identify the constant of proportionality.

• k = 2

• k = 3

• k = 1.50

• k = 2/3

• none (not proportional)

Multiple Choice

What is the constant of proportionality for the following graph?

• 80
• 20
• 40
• 160

Multiple Choice

The graph shows the distance a train travels over time. How fast is the train traveling?

• 25 miles per hour

• 90 miles per hour

• 50 miles per hour

• 45 miles per hour

Multiple Select

Select ALL equations that are proportional.

• y = 3x

• y = 25x

• y = 7x

• y = 2x - 1

• y = 4000x

Multiple Choice

The constant of proportionality can be found by finding the __________  _____________.

• unit rate
• ratio rate
• proportion answer
• rational number

Multiple Choice

Which statement below accurately represents the graph?

• $100 is earned for each hour worked
• $200 earned for every 2 hours worked
  is the unit rate
• $500 is earned for every 8 hours worked
• $300 is earned after working 4 hours

What is a percent?

1. Percent just means part of 100.
2. Percent is a ratio that compares a number to 100.
3. Percent can be expressed as a decimal and as a fraction.

Multiple Choice

What does the word percent mean?

• part out of 10

• part out of 100

• part out of 1

• part out of 1000

Multiple Choice

25% is what fraction in simplest form?

• 1/2

• 1/4

• 1/3

• 1/5

Multiple Choice

Convert 20% to a decimal.

• .20

• 20

• .002

• 200

Multiple Choice

Convert 31% to a decimal.

• 3.1
• 0.031
• 0.31
• 310

Multiple Choice

Mrs. Patrick bought a package of 15 expo markers. 20% of them were blue the others were black. How many expo markers were blue?

• 3

• 5

• 7

• 9

Multiple Choice

Jack had to purchase a book for college.  The book cost $280 at the campus store.  Jack found it online for 15% off.  How much can he save if he purchases it online?

• $420
• $322.00
• $238
• $42.00

Multiple Choice

A video game costs $40 to make. To make a profit, a manufacturer marks it up by 20%. What is the markup amount?

• $49

• $47

• $48

• $46