# + 4 ~ You divided 24 by 6 which equals x = 41. 5th Grade Math Notes. **Hint: Zero can NEVER be a denominator.**

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1 Basic Fraction numerator - (the # of pieces shaded or unshaded) denominator - (the total number of pieces) 5th Grade Math Notes Mixed Numbers and Improper Fractions When converting a mixed number into an improper fraction you multiply the denominator by the whole number then add the numerator. Example: Example: 5 x **Hint: The denominator does NOT change.** When converting an improper fraction into a mixed number you divide the numerator by the denominator. **Hint: Zero can NEVER be a denominator.** R The rule when converting fractions is that what ever ~ If your denominator is and it changes to you have to determine which operation was used. + ~ You divided by which equals. ~ you do to the top you must also do to the bottom. Since you divided by you also have to divide by. Equivalent Fraction ~ divided by equals **Hint: The dividend becomes the whole number and the remainder becomes the numerator and Ex. Ex. your denominator does NOT change.** ~ For the numerators add straight across. ~ The denominator does not change. Adding Fractions + 5 * Hint: Make sure you have a common denominator before you add.

2 Adding & Subtracting with UNLIKE Denominators Multiplying Fractions ~ Multiply the numerator by the numerator. + ~ Multiply the denominator by the denominator.. Find the least common multiple (LCM) by listing the multiples of each denominator in the problem. Circle Ex. x the least common multiple and use it as your common denominator. (Ex: the LCM of and is. Use as your common denominator.) : :. Rename the fractions using the new common denominator.. Perform the operation & keep the new denominator. 7 + *HINT: remember to simplify your answer.. Write the answer in simplest form. Ex. 7 Dividing Fractions Sled Method ~ Invert the fraction ~ multiply the fractions ~ The method will help you find the simplest form of a fraction AND the GCF and LCM for the numerator and denominator x ~ Draw a picture to represent the first fraction and draw a picture beneath that to represent the second fraction. ~ Draw a line where the second fraction ends and that fraction has a new denominator. ~ See how many squares on the bottom picture match the top picture and that is the new fraction. ~ Draw a sled and write the fraction in it. ~ Divide by the lowest prime number. ~ Continue dividing by the lowest prime number until the numbers under the sled cannot be divided by any number other than ~ The two numbers under the last sled shows the fraction in simplest form. ~ To find the GCF multiply the numbers to the left of the sled. (ex. x ) GCF ~ To find the LCM multiply the numbers to the left of the sled and below the sled (ex. x x x ) LCM

3 . Drag the decimal straight down. Subtracting Decimals:. Line up the decimal points and subtract as usual.. Drag the decimal point straight down.. Multiply as usual. Multiplying Decimals:. Count the digits behind the decimals.. Place your decimal point in the product (answer). Make sure the product and the original problem have the same number of digits behind the decimal.. Divide as usual. Operations With Decimals Adding Decimals:. Line up the decimal points and add as usual. Dividing Decimals:. Move the decimal in the divisor so it is a whole number. Move the decimal in the dividend the same number of spaces.. In your answer place the decimal directly above the decimal in the dividend. Fraction Decimal and Percent % ~ To find the decimal divide the numerator by the denominator decimal inches foot feet yard 70 yard mile 580 feet mile kilometer 000 meters gallon quarts quart pints pint cups cup 8 ounces oz. lb. 8 oz. oz. lb. lb. Measurement Conversions Rounding Rap distance capacity weight Yo find that place value Circle that digit Move to the right underline get it. 0- circle stays the same 5-9 add one is the game Now flex your muscles like a hero Digits to the right change to zero All the other digits stay the same Yo! You re the winner of the rounding game! ~ The percentage is the first two numbers behind the decimal point. (decimal %) ~ To determine a fraction from a decimal put the decimal in fraction form and simplify. Ex

4 hundred thousands ten thousands thousands hundreds tens ones hundredths tens hundred millions ten millions millions ten thousands thousands tenths hundreds thousandths hundred thousands ones Place Value 5th Grade Math Notes If the last digit is divisible by then the original number is divisible by. Divisibility Rules -5 Example: 8 (Since 8 is divisible by two then 8 is divisible by.) If the sum of the digits is divisible by three then the by. Example: (Since 8 is divisible by then 95 is divisible by.) Whole Numbers If the last two digits are divisible by four then the by. Example: 8 (Since 8 is divisible by four then 8 is divisible by.) If the last digit is a five or a zero then the number is divisible by 5. Example: 95 (Since the last digit is a 5 then 95 is divisible by 5.) Whole Numbers Long Division Divide 7 R Multiply 7 Subtract - Bring down Parts of a Whole If the number is divisible by two and three then the number is divisible by. If the last three digits are divisible by eight then the by 8. Divisibility Rules -0 Example: 5 Is it divisible by? yes because is divisible by Is it divisible by? yes because 5++ and is divisible by so 5 is divisible by Example 78 (Since 8 is divisible by eight then 78 is divisible by 8.) ~ Divide into 7 one time so goes above the 7. ~ Multiply by which equals and subtract from 7 which equals. ~ Then bring down the and the process begins again until every number has been divided. ~ The final answer is 7 remainder. **Hint: If you have to bring a number down then you start back over with divide. If the sum of the digits is divisible by nine then the by 9. If the last digit is a zero then the number is divisible by 0. Example: (Since 8 is divisible by 9 then 95 is divisible by 9.) Example: 50 (Since the last digit is a 0 then 50 is divisible by 0.)

5 triangle: P s + s + s A A bh A "(5") 5 in. b x h quadrilateral: P s + s + s + s A bh Geometry Formulas P "+"+" 8" P 7" + 7" 5" + 5" " A x 7 in. P " + " + " + " 0" A x in. Geometry Formulas P perimeter (The distance around a figure.) A area (The measure in square units of the inside of a plane figure.) V volume (The number of cubic units a space of a solid figure takes up.) in. in. in. ft. 0 ft. circle: C r (.) A r V l x w x h V x x V in. C r A r Mean Median Mode and Range Mean (average): Data: ~ Add the numbers together ~ Count up how many numbers you added together Median: ~ Put the numbers in numerical order and the Range: Mean 5 number in the middle is the median. Mode: C ( )(") C Median 5 ~ The number that occurs most often. Mode: A ( ) A 9 C 8.8" A 8. in. and divide the sum by that number. Ex ~ The largest number subtract the lowest number. Ex. 9-7 Range 7 Line Graph Shows changes over time Double-Bar Graph Compares similar Data Data Analysis ft. V l x w x h V x x 0 V 0 ft. Circle Graph Shows data that is part of a whole Line Plot Shows frequency of data along a number

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