Compatible Number - Numbers That Are Easily Multiplied Or Divided Mentally

Q1 Recap

(Chapters 1-4)

Vocabulary:

Compatible number - numbers that are easily multiplied or divided mentally.
Decimal - a representation of a real number using the base ten and decimal notation, such as 201.4, 3.89, or 0.0006.
Equivalent Ratio – ratios the express the same relationship between two quantities.
Estimate – a reasonable guess
Fraction- a number that represents part of a whole or part of a set
Greatest Common Factor- the greatest of the common factors of two or more numbers
Improper Fraction- a fraction with a numerator that is greater than or equal to the denominator
Mixed Number- a number that has a whole number part and a fraction part
Number Line - a line on which numbers are marked at intervals, used to illustrate simple numerical operations
Percent - a ratio that compares a number to 100.
Power of 10 – numbers such as 10; 100; 1,000; 10,000 and so on.
Product - the number or quantity obtained by multiplying two or more numbers together
Proportion - an equation that’s shows two ratios are equivalent.
Rate – A ratio comparing two quantities with different kinds of units
Ratio – A comparison of two quantities by division.
Ratio Table – a table with columns filled with pairs of numbers that have the same ratio
Rational Number - a number that can be written as a fraction
Reciprocal – two numbers with a product of 1
Scaling – to multiply or divide two related quantities by the same number
Simplest Form- a fraction in which the GCF of the numerator and denominator is 1
Unit Rate – a rate that is simplified so that it has a denominator of one.

Topic 1: Multiplying Decimals

Essential Understandings:

To estimate the product of decimals, round to the nearest whole number or compatible number before multiplying or dividing. Remember- “5 or above, give it a shove. 4 or below, let it go.”
Use the basic rules of multiplication when multiplying a decimal by a whole number or other decimal. To place the decimal in the product, find the sum of decimals places in each factor. Then place the decimal the same number of places in the product.

Examples: If the cost of flour is $4.25 per pound, how much does 3.4 pounds cost, rounded to the nearest cent?

Topic 2: Dividing Decimals

Essential Understandings:

Use the basic rules of division. To divide by decimals, change the divisor into a whole number by multiplying it by some power of 10 (take the decimal to the front door). Then multiply the quotient by the same power of 10. Finally, bring the decimal up and divide as usual.

Remember – “What you do to one side you must do to the other.”

Example: Eva worked 37.5 hours last week and earned $324.48.How much did she make per hour, rounded to the nearest cent?

Topic 3: Multiplying Fractions by Fractions

Essential Understandings:

To multiply fractions, you simply multiply the numerators, then the denominators. Write the product in simplest form.

Example:

Topic 4: Multiplying Fractions by Whole Numbers

Essential Understandings:

To multiply a fractions and whole numbers, write the whole number as an improper fraction. Then multiply the numerators, then the denominators. Write the product in simplest form

Example:

Topic 5: Multiplying Fractions by Mixed Numbers

Essential Understandings:

To find the product of fractions and mixed numbers, change the mixed numbers to and improper fractions before multiplying numerator by numerator and denominator by denominator.

Example:

Topic 6: Writing Ratios

Essential Understandings:

A ratio compares two quantities. It can compare a part to a part, part to whole, or whole to part.
Ratios can be written 3 different ways 1:2, 1 to 2, or ½
Ratios can be written in simplest form by dividing each quantity by the greatest common factor. Example: can be reduced to ½ by dividing both qualities by 2. (Scaling down)

“What is the ratio”, “Write the ratio”, “Find the ratio”

Example:

Topic 7: Equivalent Ratios

Essential Understandings:

• To create equivalent ratios, multiply or divide each quantity by the same number.

• To determine if two ratios are equivalent, first write the ratios in fraction form. Then find their cross products by multiplying the numerator of one ratio by the denominator of the other ratio. If the cross products are equivalent then the ratios are equivalent. This is called a proportion.

“Are these rates equivalent?”, “Which is an equivalent…?”, “Which is not equivalent?”

Example:

Topic 8: Rates

Essential Understandings:

• A rate is a ratio that compares two quantities with different kinds of units. For example: 120 miles in two hours.

• Because rates compare quantities with different units, the units must be included when writing or solving rates.

• Just like before we must be careful to write the units in the order they are given.

“At this rate…..”

Example:

Topic 9: Unit Rates

Essential Understandings:

• To determine a unit rate, you simply divide the numerator by the denominator and place the quotient over a denominator of 1.

“How many/much per….?” “Which is a better buy?” “Who pays better?”

Example:

Topic 10: Proportions

Essential Understandings:

A proportion can be used to find missing variable, convert measurements, and to find a unit rate.
You can set up a proportion by cross multiplying the given ratio by the desired ratio.

“When the problem gives you 3 numbers and asks you to find the 4th.”

Example:

Topic 11: Converting Measurements

Essential Understandings:

To convert measurements from one unit to another, you can use your knowledge of ratios to create a proportion.

“These problems typically involve map scales, temperature conversions, or cooking conversions”

Example:

Mrs. E’s desk is 4 ft. long. How many inches is it?

Topic 12: Converting Fractions to Decimals

Essential Understandings:

• To convert a fraction to a decimal you simply divide the numerator by the denominator.

Example:

Topic 13: Converting decimals to fractions

Essential Understandings:

To convert a decimal to a fraction you simply identify the place value of the last decimal place and use it as the denominator of the fraction. Simplify when possible.

“Write it like you read it”

Example:

Topic 14: Converting decimals to percent

Essential Understandings:

• To convert a decimal to a percent, you simply multiply the decimal by 100 and add a percent sign (%).

• The easiest way to do this, is to use you knowledge of Powers of 10 (move the decimal to the right two places)

“Draw a butt”

Example:

Topic 15: Converting percent to a decimal

Essential Understandings:

• To convert a percent to a decimal, you simply divide by 100 and remove the percent sign (%).

• The easiest way to do this, is to use you knowledge of Powers of 10 (move the decimal to the left two places)

“Draw a backwards butt”

Example:

Topic 16: Compare and Order Rational Numbers

Essential Understandings:

To compare and order fractions, decimals, and percent, first express all numbers in the same form. (decimal is easiest)
Use your knowledge of place value or common denominators to list the numbers in the order they are asked.
Remember to add zeros as needed.

“Least to Greatest” or “Greatest to Least”

Example:

Topic 17: Finding the Percent (%) of a Number

Essential Understandings:

To find the percent of a number, write the percent as a decimal, and then multiply it by the number. This is the part the given number is the whole.

Example:

Topic 18: Finding the Whole when given the part and percent

Essential Understandings:

To find the whole when given the part and percent, you simply change the percent to a decimal and divide the "part" by the percent.

Example:

Topic 19: Word Problems

Essential Understandings:

Follow these easy steps when solving word problems

Read carefully.
Identify any clue words that identify your standards. Such as; ratio, rate, better buy, percent, etc….
Identify clue words that identify the proper operation. Such as; altogether, how much more or less, of, shared, divided, reduced, increased, etc.…..
Reread the problem and eliminate useless information.
Draw an illustration (if needed).
Think “am I putting things together or taking them apart?” Or “should my answer be larger or smaller than the original numbers?”
Think “am I doing it once or the same thing over and over again?”
Solve the problem using the operation you have determined.
Think “does my answer make sense?”
If yes move on, if no rework the problem beginning at step 1.

Examples:

The ratio of adults to children at a movie is 3:4. If there are 196 people at the movie, how many of them are children?
In cooking class, the instructor divided 3/4 of an ounce of salt evenly to make 2 servings of a dish. How much salt did she put in each serving?
Which is the better buy, a 5-pack of marbles for $0.90 or 7-pack of marbles for $1.54?
Alana brought chocolate and vanilla cupcakes to school for her birthday. 44 students decided to take a cupcake, and 11 of them picked vanilla. What percentage of the students picked a vanilla cupcake?
The ratio of red cars to blue cars in a parking lot is 1:6. If there are 36 blue cars, how many red cars are in the lot?
David bought 0.7 pounds of peanuts and 0.59 pounds of raisins. How many pounds of snacks did she buy in all?
Marta's bird feeder holds 1/2 of a cup of birdseed. Marta is filling the bird feeder with a scoop that holds 1/10 of a cup. How many scoops of birdseed will Marta put into the feeder?
Sam bought 8 ball caps, one for each of her eight friends, for $8.95 each. The cashier charged her an additional $12.07 in sales tax. She left the store with a measly $6.28. How much money did Sam start with?
At a water park, 21 out of 28 tickets sold were child tickets. What percentage of the tickets were child tickets?
A 6-foot roll of yellow fabric costs $9.36. What is the unit price?
Edgar can read a total of 16 books in 4 months. At this rate how long will it take Edgar to read 20 books?
Lia has 8 3/4 pounds of bird seed left to share equally between 2 bird cages in her pet shop. How many pounds can she put in each bird cage?
Yesterday, Wayne's Snack Shack went through 9 5/6 bottles of ketchup. If they used 1/2 as much mustard as ketchup, how many bottles of mustard did they go through?
Karen spends $4,656.56 on 8 snowboards. The snowboards all cost the same amount. What is the cost of each snowboard?
Cheeseburgers cost $4.40 each. Ethan buys 8 cheeseburgers. How much does Ethan spend?