Hun. Thousands

5 th Grade Midterm Review Notes

Place Value

Value – product of digits times place Standard form - number written using digits Word form- number written using words (written as you would read it) Expanded form- written as addition of the multiplication statements of each digit times place Rounding - “5 or more raise the score; 4 or less let it rest .”

1. Keep all digits before the place being rounded2. Keep or change place based on digit on the right of the place you are rounding.3. Everything after the place you are rounding becomes zeroes.

Comparing and Ordering- to compare and order numbers, line up your numbers by the place value and then starting on the right , look for the biggest/smallest place, if two digits are in the same place , compare the digits, if the digits are the same then move to the next place to the left and continue.*Sometimes placeholders are needed and can help when comparing.

Powers of Ten

100 = 1 10−1 = 1

10 or 0.1

101 = 10 10−2 = 1

100 or 0.01

102 = 10 x 10 = 100103 = 10 x 10 x 10 = 1,000¿ soon…*Exponents that are on a base of 10 tell you how many zeroes come after the 1

*Exponent tells you how many times you are multiplying 10 by itself

*When multiplying something by a power or 10, shortcut is to move decimal # of zeroes/ exponent to the right

*Sometimes you need place holders

*Decimals are at the end of whole numbers

Billions

,

Hun. MillionsTen Millions

Millions

,

Ten ThousandsThousands

,

Hundreds

Tens

Ones

.

Tenths

HundredthsThousandths

FACTOR

x FACTOR

PRODUCT

*A number/place is 10 times as much as the place to the right and 110 times as much as the place

to the left.

Multiplying Multi-digit Numbers When multiplying multi-digit #’s, place values are important and place holders

need to be used. When multiplying regularly place holders are added to the partial products to make sure to line up the

first part of the product under the digit you are multiplying by.

*When multiplying regularly, line up your digits left to right—it helps to have the number with the more digits on top.

- Then multiply one digit at a time from the bottom right to left by all digits on top one by one right to left, carrying when necessary.

-Next, put a place holder(s) to line up and continue.

-After all digits on the bottom are multiplied by all the digits on top; add all partial products for final product.

**EXPANDED FORM: Break each number up by place and use the box method to multiply and then add all the partial products for the final product.

DIVISION

“Does McDonald’s Sell CheeseBurgers?”

Divide, Multiply, Subtract, Check and Bring down

1. Divide - Divide the divisor into the partial dividend.2. Multiply - multiply the partial quotient by the divisor.3. Subtract – subtract the partial dividend by the product.4. Check - check that your difference is smaller than your divisor.5. Bring down - bring down your next digit and continue until there is no remainder.

Properties of Addition and MultiplicationAssociative Property- When two or more numbers are being added or multiplying the GROUPING of the numbers can change but the sum or product will be the same.

Commutative Property- When two or more numbers are being added or multiplying the ORDER of the numbers can change but the sum or product will be the same.

Identity Property- When adding a number with 0 or multiplying it by 1, the sum or product will be that number.

FACTOR x FACTOR = PRODUCT

DIVIDEND ÷ DIVISOR = QUOTIENT

Distributive Property- When a number outside the parenthesis of two digits being added is applied to everything inside the parenthesis—multiply the number outside by each number inside and keep the operation between the two.

Operations with Decimals

ADDING/SUBTRACTING

When adding or subtracting decimals make sure to line up the digits by the decimalo Remember if there is no decimal, the decimal is at the end of the whole number

After you line up your decimals, bring your decimal straight down to your answer and add or subtract normally

*To estimate with decimals –estimate/round the numbers to whole numbers and then add or subtract mentally, this will help you make sure you place your decimal correctly in your answer

MULTIPLYING

When multiplying decimals, line up your digits right to left (ignoring your decimal). Multiply normally Count the total number of digits after each decimal point Then starting at the end of your product count that same number of places/digits to the left to place

your decimal point correctly in your answer.

*To estimate with decimals –estimate/round the numbers to whole numbers and then add or subtract mentally, this will help you make sure you place your decimal correctly in your answer