7NS Review

Rational Numbers

​Apply and extend previous understandings of operations with fractions to add, subtract, multiply and divide rational numbers.

Multiple Select

Select all that are rational numbers

• 0.24

• -14.2

• $$2\ \frac{1}{5}$$

• $$-\frac{5}{6}$$

• $$0.\overline{3}$$

Rational numbers

• are ratios of two integers

• if you can convert a number into a fraction it is a rational number

• all positive and negative numbers

• decimals that terminate or have repeating patterns

Multiple Choice

$$-6,\ 0.\overline{5}\ ,\ and\ 3.75$$  are ALL examples of rational numbers

• True 

• False

Examples of Rational numbers

Multiple Select

Select all that are rational numbers

• 0.24

• -14.2

• $$2\ \frac{1}{5}$$

• $$-\frac{5}{6}$$

• $$0.\overline{3}$$

Square Roots: perfect squares

Multiple Select

Select ALL the Rational Numbers:

• -12.7

• $$\Pi$$

• $$-9\ \frac{1}{4}$$

• $$\sqrt{4}$$

• $$\sqrt{6}$$

Hierarchy of whole numbers

Dividing Decimals

Multiple Choice

If the decimal has a pattern and goes on forever it is called....

• terminating

• repeating

• infinity

• ending

Multiple Choice

2.07 ÷ 0.9

• .23

• 23

• 2.3

Multiple Choice

92.37 ÷ 0.5

• 184.74

• 18.474

• 1847

• 0.005

Multiple Choice

If the remainder is 0 we call the decimal ...

• Finished

• Terminating

• Repeating

• Cyclical

​MGSE7.NS.2d Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

Multiple Choice

Identify the repeating decimals. I.  –0. $$\overline{353}$$   II.  3.611 III   –1.35555... IV.  2.15 V.  7.7770

• I and III

• I, III, V

• II

• I

Multiple Choice

0.444444444... is a repeating decimal.

• True 

• False

Multiple Choice

Write   4/100  as a decimal

• .4

• .40

• .400

• .04

Multiple Choice

Is the fraction 1/12 a repeating or terminating decimal?

• Repeating

• Terminating

Multiple Choice

Write the decimal equivalent to 9/20

• $$\overline{.45}$$

• .45

• $$.4\overline{5}$$

• .5

Multiple Choice

Convert the fraction to a decimal: $$\frac{8}{11}$$  

• $$.\overline{16}$$  

• .72

• .16

• $$.\overline{72}$$  

Method 2

Divide the numerator by the denominator. If the decimal digit(s) repeat, put a bar over the repeating digit(s).

​Some text here about the topic of discussion.

Changing Fractions to Decimals Method #2

Draw

Convert 4/11 to a Decimal. Show your work.

Multiple Choice

Convert the fraction to a decimal:  $$-\frac{1}{40}$$  

• .025

• -.25

• -.025

• .25

Fill in the Blank

Write $$-6\frac{1}{2}$$ as a decimal

Fill in the Blank

Write $$\frac{3}{25}$$ as a decimal

Fill in the Blank

Write $$-\frac{7}{8}$$ as a decimal

Fill in the Blank

Write $$2\ \frac{1}{8}$$ as a decimal

​MGSE7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers.

Multiple Choice

Try this:

$$42.46\ +\ 10.44$$  

• 529

• 52.9

• 52.80

Adding Decimals

To add decimals start by writing the amounts out and lining them up by the decimal points.

Multiple Choice

-5.7 + 0.9

• 2.1

• -4.8

• -8.3

• -10.7

Multiple Choice

Find  -6.23 - 7.5

• 13.73

• 1.3

• -1.2

• -13.73

Multiple Choice

What is the sum of these fractions in lowest terms? Don't forget that you need a common denominator.

• 4/5

• 3/20

• 17/20

• 4/20

Remember that you need to find a common denominator. Whatever you multiply the denominator by to get a common denominaot, you also mutliply the bumerator byh the same number

​

​Some text here about the topic of discussion.

Adding and Subtracting Fractions

​

Multiple Choice

What is the difference? You need a common denominator.

• $$\frac{13}{24}$$

• $$\frac{5}{24}$$

• $$\frac{12}{48}$$

• $$\frac{6}{5}$$

Fill in the Blank

$$\ -1\frac{\ 1\ }{\ 8}\ -\ \frac{\ 3\ }{4}\ =\$$  

Fill in the Blank

$$\ \ -\frac{\ \ 3\ }{\ 4}\ +\ \frac{\ 1\ }{2}\ =\$$  

Fill in the Blank

$$\ -3\ \frac{\ 1}{3}\ -\ 2\ =\$$  

​MGSE7.NS.2c Apply properties of operations as strategies to multiply and divide rational numbers.

Multiple Select

$$-\frac{5}{6}\times\frac{2}{5}$$  

• $$-\frac{10}{30}$$  

• $$\frac{-7}{11}$$  

• $$-\frac{1}{3}$$  

• $$\frac{1}{3}$$  

Multiplying Rational Numbers

​Multiplying Rationals follows the same rules as multiplying integers.

If the signs are the same, the product will be positive.

​

If the signs are different, the product will be negative.​

Some text here about the topic of discussion

Multiple Choice

$$-\frac{3}{5}\times4\ \frac{1}{6}=$$  Simplify your answer when possible.

• $$-2\ \frac{1}{2}$$  

• $$-4\ \frac{3}{30}$$  

• $$-4\ \frac{4}{11}$$  

• $$2\ \frac{1}{2}$$  

Fill in the Blank

$$\frac{5}{7}\cdot-\frac{1}{10}$$  

Fill in the Blank

$$-\frac{1}{4}\div\frac{1}{2}$$  

Fill in the Blank

$$-2\div-\frac{1}{3}$$  

Fill in the Blank

Trying doing it yourself first. Use a calculator only if necessary.

Enter your answer as a fraction or decimal.

$$3\ \frac{1}{2}\ \div\ \left(-\frac{7}{3}\right)$$  

Thinking Process - If you used a calculator, show what you entered on a whiteboard. If you didn't use a calculator, show how you arrived at your answer on a whiteboard. Don't forget to upload your work.

Multiple Choice

Solve:  $$-2.36\times0.5$$  

• -1.18

• 1.18

• 4.72

• -4.72

Poll

Will the product be positive or negative?

$$-3.04\left(-5.6\right)$$  

• Positive

• Negative

Multiple Choice

(2.5)(-1.2)

• -3.7

• 3.7

• 3

• -3

Multiple Choice

81.9 x 0.5 =

• 40.95 

• 409.5

• 40.02

• 400.2

Fill in the Blank

$$-2.25\div-0.05$$  

Multiple Choice

19.32 ÷ 2.3

• 8.4

• 7.2

• 8.9

• 8.6

Multiple Choice

$$5.75\div\left(-0.25\right)=$$  

• $$23$$  

• $$-2.3$$  

• $$2.03$$  

• $$-23$$  

Multiple Select

Find the quotient of (-14.56) ÷ (-0.4)

• 36.4

• -36.4

• 3.64

• -3.64

​MGSE7.NS.3 Solve real‐world and mathematical problems involving the four operations with rational numbers.

Draw

Solve the following: -5/6 x 3/4

Draw

Solve the following: -6/7 + 4/8

Draw

Solve the following: -3/5 - 5/6

Draw

Solve the following: 5/8 divided by 3/4

Draw

Solve the following: -8.6 + 7.2

Draw

Solve the following: 3.2 - (-4.51)

Draw

Solve the following: 0.4 divided by 0.8

Draw

Solve the following: 13.9 x 7.12

​MGSE7.NS.3 Solve real‐world and mathematical problems involving the four operations with rational numbers.

You added 2.5 and 4.25 first to find the total number of hours worked.

Then you divided 54 by the sum to find the amount earned per hour.

Justify and Evaluate

Follow the order of operations.

(2.5 + 4.25) = 6.75 Add inside parentheses.

54 ÷ 6.75 = 8. Divide.

​Makana earned $8 per hour mowing lawns.

Solve

Makana earned $54 mowing lawns in two days. He worked 2.5 hours yesterday and 4.25 hours today. If Makana was paid the same amount for every hour he works, how much did he earn per hour?

WRITE IN NOTES

Multiple Select

Aolani overdrew her checking account by $10. She later wrote a check for $40. What does her bank account look like now? Check all that apply

• 10 - 40 = -30

• -10 - 40 = -50

• 10 + (-40) = -30

• -10 + (-40) = -50

We know that any subtraction can be turned into addition through KCC

-8 - 2 = -8 + (-2)

-10

Multiple Select

Daniel had $85. Later that day he withdrew $15. How much money does Daniel now have? Check all that apply

• -85 - 15 = -100

• 85 - 15 = 70

• 85 + (-15) = 70

• -85 + (-15) = -100

Multiple Choice

It was 50 degrees at noon but then dropped to 12 degrees below zero at midnight. What is the difference in temperature from noon to midnight?

• 50 - (-12) = 50 + 12 = 62

• 50 - 12 = 50 + (-12) = 38

• -50 - 12 = -50 + (-12) = -62

• -50 - (-12) = -50 + 12 = -38

Converting Fractions and Decimals to Solve Problems

Each part of a multipart question on a test is worth the same number of

points. The whole question is worth 37.5 points. Kai got 1/2 of the parts of a question correct. How many points did Kai receive?

Multiple Choice

Mrs. Borcherding can grade 5 ¼ tests in 30 minutes. She started grading tests at 5:30pm and finished at 9:30pm. How many tests did she grade in total?

• 32

• 20.5

• 21

• 42

Multiple Choice

The length of a kangaroo’s leap can be up to 6 ½ times its height. If a kangaroo is 7.5 feet tall, how far can it jump?

• 51.25 ft

• 48 ft

• 48.75

• 51.5 ft

Open Ended

Mark, Ryan, Christina and Emma all live on the same street as their school:

Mark lives 5 ½ blocks west of the school

Ryan lives 4 ¼ blocks east of the school

Christina lives 2 ¾ blocks west of the school

Emma lives 6 ½ blocks east of the school

Everyone met up at Ryan's house, and then went to Christina's house to eat pizza. How much did Emma walk in total?

• The total amount he earned divided by the total hours he worked

gives the amount he earns per hour.

• Use the expression 54 ÷ (2.5 + 4.25) to find the amount she earned

per hour.

Formulate a plan

Identify the important information.

• Makana made $54 mowing lawns.

• Makana worked 2.5 hours yesterday and 4.25 hours today.

• You are asked to find how much he earned per hour.

Analyze information

Makana earned $54 mowing lawns in two days. He worked 2.5 hours yesterday and 4.25 hours today. If Makana was paid the same amount for every hour he works, how much did he earn per hour?

WRITE IN NOTES

Multiple Choice

Anela earned $60 washing cars in two days. She worked 1.5 hours

yesterday and 3.25 hours today. Anela was paid the same amount for

every hour she works, how much did she earn per hour? Hint: Analyze, Plan, Solve, Justify and Evaluate.

• $12.63

• $13.00

• $11.11

• $8.00

Multiple Choice

To prepare for a race, Lloyd ran every day for two weeks. He wan a total of 67,592 meters. Lloyd ran the same distance everyday. He took a two-day rest and then started running again. The first day after his rest, he ran the same distance plus 1,607.87 meters more. How far did Lloyd run that day?

• 6,444.87 meters

• 6,435.78 meters

• 6,435.87 meters

• 6,453.87 meters

Comparing Rational Numbers

• Find a common denominator

• Rewrite each fraction with the same denominator

• Order the numerators

Multiple Choice

6/10 ____ 2/5

• >

• <

• =

Compare the Fractions

Find the common denominator, then compare the numerators.

Was your prediction correct?

Multiple Choice

Compare the two numbers:

7/8 ____ .9

• <

• >

• =

Compare Fractions with Decimals

• Turn the fraction into a decimal OR change the decimal to a fraction.

• To compare decimals, make sure you have the same place values.

Multiple Choice

Compare 2/5 to 0.2

• <

• >

• =

Fill in the Blank

Sam's bank account balance reads -$2.50. Hanks bank account balance reads -$1.75. Who has more money in his account? Who has a greater debt?