(rational numbers)€¦ · (rational numbers) as you go through the unit, check off the concepts...

(Rational Numbers)As you go through the unit, check off the concepts that you have mastered. Leave the other ones unchecked so that you know which concepts you need to study before a test!

The following unit includes:

□ Adding/Subtracting Integers on a Number Line

□ Adding/Subtracting Integers with Rules

□ Multiplying/Dividing Integers

□ Adding/Subtracting Decimals

□ Multiplying Decimals

□ Dividing Decimals

□ Adding/Subtracting Fractions

□ Multiplying Fractions

□ Dividing Fractions

©2016 Math in Demand


(Rational Numbers)

Concepts(s):

Essential Questions:

Vocabulary:

Important Dates: Pre-Test: Post-Test: Vocabulary Quiz:

Scores: Pre-Test: Post-Test: Vocabulary Quiz:

· Rationals · Integers · Decimals · Fractions · Operations

· Numerator · Denominator · Reciprocal · Quotient

· How are adding and subtracting integers similar? · Why is it important to understand operations on rational

numbers? · How can number lines be used to interpret real world

problems?

· Adding/Subtracting Integers on a Number Line · Adding/Subtracting Integers with Rules · Multiplying/Dividing Integers · Adding/Subtracting Decimals · Multiplying Decimals · Dividing Decimals · Adding/Subtracting Fractions

This overview shows you important information that you will be learning throughout the

unit. Make sure to fill out important dates and scores!

· Multiplying Fractions · Dividing Fractions

(Adding/Subtracting Integers on a Number Line)

Follow these steps to add or subtract integers:


I can ___________________

_______________________

For example, 5 – (-4) becomes ____________

and

-8 – 7 becomes ______________

Numbers get bigger!

Step 1:

Step 2:

Place a dot on the number line for the first given number

Move from the dot either left or right according to the other given number.

Move right when adding a positive integer

Move left when adding a negative integer

Your stopping point is your answer!

Example:

-30 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6

What is -26 – (-9)? -26 + 9

Numbers get smaller! A number line is a great tool to use when

adding or subtracting integers!

5 + 4

-8 + -7

-17

add and subtract integers

on a number line.

(Adding/Subtracting Integers on a Number Line)

1.) 1 – 7 = -6

2.) -2 – (-3) = 1

3.) -2 – 9 = -11

Reflection: I learned…


On a rating of 1-5, how comfortable are you with this concept?

(5 is the highest)

1 2 3 4 5

-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1

-6

1

-11

(Adding/Subtracting Integers with Rules)

I can ___________________

_______________________


Change the following to addition:

1.) -9 – 2 = 2.) 7 – (-12) =

We can add integers by using rules

Addition Rules

Positive + Negative (Different Signs)

Subtract the two numbers. Keep the sign of the largest absolute value number.

Negative + Negative OR Positive + Positive (Same Signs)

Add the two numbers. Keep the sign.

Examples:

We can also add or subtract integers by using counters:

-8 + 5

-3

-9 + -2 7 + 12

1.) -4 – (-7) = 3

-4 + 7 = 3

2.) 3 – 8 = -5

3 + -8 = -5

add and subtract integers

using the addition rules.

(Adding/Subtracting Integers with Rules)




(5 is the highest)

1 2 3 4 5

1

2

3

4

5

6

-10 8 = -2

-15 – 7 = -22

19 – (-6) = 25

-21 – (-3) = -18

-12 – (-4) – 6 = -14

45 – 47 – (-21) = 19

(Multiplying/Dividing Integers)

I can ___________________

_______________________


Multiplying Integers Dividing Integers

Neg x Pos = Neg

Pos x Neg = Neg

Neg x Neg = Pos

Pos x Pos = Pos

Neg Pos = Neg

Pos Neg = Neg

Neg Neg = Pos

Pos Pos = Pos

Another Way to Think About Signs:

What do you notice about the table?

There is a pattern!

# of Negatives Outcome

1 Negative

2 Positive

3 Negative

4 Positive

If you have an odd number of negatives, then your answer is negative!

If you have an even number of negatives, then your answer is positive!

Examples: 1.) -12 4 = -48 2.)

−��

−� = 5

multiply and divide integers.

(Multiplying/Dividing Integers)




(5 is the highest)

1 2 3 4 5

1

2

3

4

5

6

-11 -5 = 55

-200 -5 = 40

-19 6 = 114

21 -3 = -7

-2 -5 3 = 30

-1 -1 -1 -2 -1 -1 = 2

(Adding/Subtracting Decimals)

I can ___________________

_______________________


What is a decimal?

Step 1:

Step 2:

Step 3:

Follow these steps to add decimals:

Why are decimals important?

Examples:

add and subtract decimals.

1.) 0.078 + 1.5 =

0.078 + 1.500 1.578

2.) 8.98 – 4.781 =

8.980 -4.781 4.199

A decimal is written in our base-ten number system. There are ten single-digit numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

Decimals are important in our everyday life. We use decimals every day when we are purchasing items at

the store, counting money or making change, and reading an odometer.

Write down the numbers with one underneath the other so that the decimals are lined up.

If necessary, add in any zeros that are needed to fill in any empty “spots”.

Add the numbers using column addition. Make sure to bring down the decimal.

(Adding/Subtracting Decimals)


1.) 0.089 + 31.356 = 31.445

2.) 93.4 – 0.0761 = 93.3239

3.) -0.456 – (-23.41) = 22.954



(5 is the highest)

1 2 3 4 5

31.445

93.3239

22.954

(Multiplying Decimals)

Example:

0.345 x 2.45 = 0.84525


I can ___________________

_______________________

Step 1:

Step 2:

Step 3:

Follow these steps to multiply decimals:

Multiplication Signs Negative x Positive = Negative Positive x Negative = Negative Negative x Negative = Positive Positive x Positive = Positive

multiply decimals.

Ignore the decimal and multiply as usual.

Count the total number of digits behind the decimal point(s).

Place the decimal according to the same number of digits you counted.

(Multiplying Decimals)


1.) 6.7 x 3.45 = 23.115

2.) -0.8 x 0.346 = -0.2768

3.) -2.13 x -0.78 = 1.6614



(5 is the highest)

1 2 3 4 5

23.115

-0.2768

1.6614

(Dividing Decimals)

Step 1:

Step 2:

Step 3:

Follow these steps to divide decimals:

Example:


I can ___________________

_______________________

Division Signs Negative Positive = Negative Positive Negative = Negative Negative Negative = Positive Positive Positive = Positive

5.50 0.50

5.50 0.50 = ?

550 50

50 550 11

-50 50 -50 0

11

divide decimals.

If divisor is not a whole number, move the decimal point to the right to make a whole number. Move the decimal in the dividend by the same number of places.

Divide as usual (long division).

Place the decimal point above the decimal point in the dividend.

(Dividing Decimals)


1.) -85.5 5 = -17.1

2.) -20.4 -6.4 = 3.1875

3.) 140 -5.5 = -25.4545…



(5 is the highest)

1 2 3 4 5

-17.1

3.1875

-25.45

(Adding/Subtracting Fractions)


I can ___________________

_______________________

What is a fraction?

Step 1:

Step 2:

Step 3:

Follow these steps to add or subtract fractions:

Before we can add or subtract fractions,

we must have:

Example:

Common Denominators

If denominators are different, find the least common denominator.

Multiply the numerators AND denominators by a number to get the LCM.

Add the numerators. Keep the denominators the same. If possible, reduce.

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add and subtract fractions.

A fraction is a ratio of two numbers. In other words, an integer divided by an integer.

1.) 28 – 5x + 2 + 4x a.) The expression has ____ terms. b.) Underline the variables c.) Box the coefficients d.) Circle the constants

(Adding/Subtracting Fractions)


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(Multiplying Fractions)


I can ___________________

_______________________

Multiplication Signs Negative x Positive = Negative Positive x Negative = Negative Negative x Negative = Postive Positive x Positive = Positive

How do we multiply fractions?

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Multiply the numerators together

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“Multiplying across” is not the same thing as “cross multiplication”.

Examples:

Make sure to SIMPLIFY your answers!

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(Dividing Fractions)


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_______________________

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How do we divide fractions?

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(rational numbers)€¦ · (rational numbers) as you go through the unit, check off the concepts...

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