Chapter 2 Study Guide

Contents1. Properties of Addition.....................................................................................................................1

2. Rounding.........................................................................................................................................2

3. Estimation........................................................................................................................................3

4. Adding Whole Numbers & Decimals................................................................................................4

5. Subtracting Whole Numbers & Decimals.........................................................................................5

6. Word Problems................................................................................................................................5

1. Properties of Addition

Identity Property: Any number plus zero is that same number.o Example: 8 + 0 = 8o Hint: Identity is who you are – the number keeps its identity.

Commutative Property: If you change the order of the addends, the sum stays the same.o Example: 45 + 15 = 15 + 45o Hint: Commute = back and forth

Associative Property: If you group the addends differently in parentheses, the sum stays the same

o Example: 3 + (9 + 6) = (3 + 9) + 6o Hint: Association = a group of people

Sample test questions:

1) Fill in the blank from the word bank: Any number plus is that same number.

Word Bank

sum parentheses zero

2) Multiple choice: The equation 2 + 1 = 1 + 2 is an example of theo Identity Propertyo Commutative Propertyo Associative Property

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2. RoundingWhen you round a number, you replace it with a number that’s around the same, but with fewer digits.

1) Find the place that you are rounding to and underline it.2) Check the number to the RIGHT of that digit3) Do you change the underlined digit?

If the digit to the right is 0, 1, 2, 3 or 4: the underlined digit stays the same If the digit to the right 5, 6, 7, 8, or 9: the underlined digit is increased by one

If the underlined digit is a 9, then it turns into a 0 and the next digit to the left is increased by one.

4) All the numbers to the RIGHT of the underlined digit get changed to zeroes.

Example:

Round to the nearest dollar (one)

$841.29

1) Underline the digit in the ones place2) Check the number to the RIGHT of that digit

It’s a 23) Since 2 is smaller than 5, the underlined 1

stays the same4) All the digits to the right of the underlined

digit turn into zeroes

Answer: $841.00Round to the nearest tenth

3.963

1) Underline the digit in the tenths place2) Check the number to the RIGHT of that digit

It’s a 63) Since 6 is bigger than 5, the 9 should be

increased by one. But 9 + 1 = 10! So put a 0 where the 9 is and add one

to the digit to the left of it4) All the digits to the right of the underlined

digit turn into zeroes

Answer: 4.00 or just plain 4

Sample test questions:

Round to the place of the underlined digit

9,725.8_____________

6.081_______________

749,322________________

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3. EstimationTo estimate, you simply round the numbers before adding or subtracting them. This gives you an answer that’s around the real one, but quicker to calculate.

Estimate the sum by rounding to the nearest hundred:

5 ,834+3,229≈ ?_____

+ _______________

_____

1) Round each number to the nearest hundred(see previous page for how to round)

5,800 + 3,200 ≈ ?

2) Find the sum.

5,800+ 3,200

__________9,000

Sample test question:

Estimate the difference by rounding to the nearest dollar (one):

$6.65−$ 4.73≈ ?_____

- _______________

_____

<< write what $6.65 rounds to

<< write what $4.73 rounds to

<< subtract and write the difference here

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4. Adding Whole Numbers & Decimals

Important reminders:

When setting up your problem, make sure to line up the decimal points and place value columns properly.

o Example: 74.5 + 2.38 =

7 4 . 5 +

2 . 3 87 6 . 8 8

o Remember, you can add “imaginary zeroes” at the right end of the decimal part so that there are the same number of digits after the decimal point

If the digits in a column add up to more than ten, “carry” the tens-place digit to the next column to the left

o Example: 30.87 + 6.14 =

1 13 0 . 8 7

+6 . 1 4

3 7 . 0 1

Sample test questions:

0 . 9 7 9+

0 . 0 8 4

6 0 . 4 3 0 1+

7 . 0 5 2 7

2 7 , 3 4 8 . 5+

1 , 9 3 1 . 6 2

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5. Subtracting Whole Numbers & Decimals

Important reminders:

When subtracting, the bigger number goes on top.o Example: What is the difference between 45 and 32?

4 5-

3 21 5

When setting up your problem, make sure to line up the decimal points and place value columns properly.

o Example: 69.66 - 14.3 =

6 9 . 6 6-

1 4 . 3 5 5 . 3 6

o Remember to add “imaginary zeroes” at the right end of the decimal part so that there are the same number of digits after the decimal point

If the top digit is smaller than the digit underneath it, “borrow” from the next column to the lefto If the column to the left is a zero, move on to the next column to the lefto Example: 2.168 – 0.4531 =

1 11

7 10

2 . 1 6 8 -

0 . 4 5 3 11 . 7 1 4 9

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Sample test questions:

9 . 2 0 9-

5 . 0 8 3

1 6 8 . 5-

5 0 . 3 1 2

1 . 0 8 8 7 5 2-

0 . 0 7 9 2 6

6. Word Problems

Take it one step at a time:

1) Read the problem carefully.2) What information is important? (circle or underline it!)3) Is there anything there that you don’t need? (cross it out!)4) Will you be adding or subtracting?

o Look for hint words:

Addition Subtractionsum difference

combine more thanincreased by less thanall together take away

in all left overand fewertotal change

NOTE: The list above doesn’t contain every single possible hint word – you may have to think about the situation described in the word problem and figure it out. Maybe drawing a picture or chart could be helpful.

5) Solve the problem, and make sure to show your work!6) Check your answer, to make sure it makes sense.

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Example:

Shira Devora buys one cupcake and one sandwich cookie.

If she has $3.00 in her purse, how much will be left over after she pays?

a) Shira Devora buys one cupcake and one sandwich cookie

How much did Shira Devora spend?

_______$2 . 25________

b) If she gives the cashier $3.00, what will her change be?(Hint: change = difference)

_______$0 . 75________

Use this area to write out & solve the problem. Make sure to copy your final answer to the column on the

left.

<< Think: Hint word “and” means I should add the price of the cupcake and the price of the sandwich cookie

Do the problem and show your work:

$ 1 . 5 9+

$ 0 . 6 6

$ 2 . 2 5

<< Think: Hint word “difference” means I need to subtract

$ 3 . 0 0+

$ 2 . 2 5

$ 0 . 7 5

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Sample test questions:

Use the space in this column to write out & solve each problem. Make sure to copy your final answer to the column on the left.

1) Batsheva put a 64 ounce carton of orange juice on the table.

Her brother bumped into the table and knocked over the juice.

Now Batsheva only has 17 ounces of orange juice left in the carton.

How many ounces are on the floor?

___________________________

1)

2) Rivky flew 1,853.7 miles from Chicago, Illinois to San Francisco, California.

Then she flew 2,394.6 miles from San Francisco to Honolulu, Hawaii.

a) From Chicago to Honolulu, how far did she travel in all?

________________________________

b) The distance from Honolulu to Tokyo, Japan is 3,855.8 miles.

How much farther is it from Honolulu to Tokyo than from Chicago to Honolulu?

_____________________________

a)

b)

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