Decimal and Fractions

Review Unit

Class Notes

Date Adding and Subtracting Decimals

Learning Targets

  1. I can add decimals.
  2. I can subtract decimals.

Steps

  1. Write the problem vertically, lining up the decimals.
  2. Fill in any empty spaces with zeros (0).
  3. Add or subtract from right and left to get your answer.
  4. Bring the decimal straight down.
  5. Simplify by erasing any unnecessary zeros. These are the zeros that appear at the very end of the answer, to the right of the decimal.

Examples

1)  9.8 + 9.7 + 9.425 +9.85 2) 10 – 9.85

3) Logan wants to buy a new bike that costs $135.00. He started with $14.83 in his savings account. Last week, he deposited $15.35 into his account. Today, he deposited $32.40. How much more money does he need to buy the bike?

Solution

Determine the total amount of money Logan has by adding.

14.83

15.35

+ 32.40

$62.58

Determine how much more Logan needs by subtracting what he has from the total cost.

135.00

- 62.58

$72.42

Try This

1) 8.3 + 2.7 2) 9.7 – 4 3) 13.009 + 12.83 4) 7.435 – 3.0042

5) 0.0679 + 3.75 6) 9.67 – 0.635 7) 7.03 + 33.8 + 12.006 8) 5.35 – 4.7612

9) Brad works afterschool at a local grocery store. How much did he earn in all for the month of October?

10) The highest career batting average ever achieved by a professional baseball player is 0.366. Bill Bergen finished with a career 0.170 average. How much lower is Bergen’s career average that the highest career average?

Date Multiplying Decimals

Learning Target

I can multiply decimals using the standard algorithm.

Important Information

·  There are three ways to show multiplication

ü  4 × 2 traditional symbol (this symbol disappears in Algebra)

ü  4(2) parentheses around one or both numbers

ü  4 • 2 dot in the middle of two numbers, not to be confused with a decimal

Steps

  1. Line up the digits to the right, ignore the decimals for now. DO NOT LINE UP THE DECIMALS!
  2. Starting at the far right side, multiply the ones digit on the bottom row by each number of the top row.
  3. Place a zero as a place holder in the second line of your answer in the ones column.
  4. Multiply the tens digit by each number in the top row.
  5. Continue to use a zero as a place holder and multiply until there are no numbers left.
  6. Add each of your columns up.
  7. Count up all the decimal places from both numbers that you multiplied and place that many decimals in your final answer.
  8. Simplify by erasing any unnecessary zeros. These are the zeros that appear at the very end of the answer, to the right of the decimal.

Examples

1)  3.062 × 5 2) 3.25 × 4.8

3) Apples are on sale for $0.49 per pound. What is the price for 6 pounds of apples?

0.49 2 decimal places

× 6 + 0 decimal places

$2.94 2 decimal places

Try This

1) 0.06 × 1.02 2) 0.66 • 2.52 3) 1.4(0.21)

4) 12.6 • 2.1 5) 0.005 × 0.003 6) 6.017(2)

7) (1.54)(3.05)(2.6) 8) 0.2 • 0.94 • 1.3

9) Jill walks her dog every morning. If she walks 0.37 kilometers each morning, how many kilometers did she walk during the month of January?

10) A deli charges $4.56 for a pound of turkey. If Tim wants 3.8 pounds, how much will it cost him?

Date Dividing Decimals by Whole Numbers

Learning Target: I can divide decimals by whole numbers.

Important Information

·  Parts to a Division Problem

ü  Dividend ÷ Divisor = Quotient

ü  Dividend: The number being divided. It goes on the inside of the house when working the problem out.

ü  Divisor: The number you are dividing by. It goes on the outside of the house.

ü  Quotient: The answer to a division problem. It goes on top of the house.

Flashback: Dividing Whole Numbers

Now the dividend becomes a decimal…

Steps

1)  Place the decimal point in the quotient (answer) directly about where it appears in the dividend.

2)  Divide

3)  Multiply

4)  Subtract

5)  Check

6)  Bring down

7)  Repeat steps 2-7, as needed

Examples

1) 2.52 ÷ 3 2) 0.435 ÷ 15

3) Ethan and two of his friend are making a sculpture using balloons, strips of paper and paint. The materials cost $11.61. If they share the cost equally, how much should each person pay?

Try This

1) 10,626 ÷ 21 2) 4905 ÷ 45 3) 2109 ÷ 111

4) 0.91 ÷ 7 5) 0.684 ÷ 9 6) 57.484 ÷ 4

7) The tennis team is having three tennis rackets restrung. The total cost is $54.75. What is the average cost per racket?

Date Dividing Decimals by Decimals

Learning Target: I can divide decimals by decimals.

Steps

1)  Move the decimal in the divisor to the very end, make it a whole number.

2)  Count how many places it had to be moved.

3)  Move the decimal in the dividend the same number of spots. Ignore the old decimal.

4)  Place the decimal point in the quotient (answer) directly about where it appears in the dividend.

5)  Divide

6)  Multiply

7)  Subtract

8)  Check

9)  Bring down

10)  Repeat steps 5-10, as needed until it either terminates (ends) or becomes a repeating decimal. You may need to add additional zeros (0) before one of these two things happen.

Examples

Try This

1) 51.2 ÷ 0.24 2) 10.875 ÷ 1.2 3) 18.4 ÷ 2.3

4) 12.586 ÷ 0.35 5) 50.9 ÷ 4.5 6) 8.43 ÷ 0.12

7) Kyle’s family drove 329.44 miles. Kyle calculates that the car averages 28.4 miles per gallon of gas. How many gallons of gas did the car use?

8) Jan spends $5.98 on ribbon. Ribbon costs $0.92 per meter. How many meters of ribbon does Jen buy?

9) Anna is saving $6.36 a week to buy a computer game that costs $57.15. How many weeks will she have to save to buy the game?

Date Simplify Fractions and Equivalent Fractions

Learning Targets

  1. I can simplify fractions.
  2. I can create equivalent fractions.

Important Terms

·  Simplify: To write a fraction or expression in simplest form. To reduce or put in lowest terms.

·  Equivalent Fraction: Fractions that name the same amount or part, they are equal.

Examples:

Part A: Simply Fractions

Write the fraction 18/24 in simplest form.

-  Method 1: Use a ladder diagram. - Method 2: Use the Greatest Common Factor

Part B: Equivalent Fractions

-  Create two equivalent fractions for each given faction.

§  To do this, multiply or divide both the numerator (top number) and denominator (bottom number) by the same number.

-  Fill in for the missing number.

Try This:

Write each fraction in simplest form.

1)  6/8 2) 4/20

3) 10/35 4) 12/72

Find two equivalent fractions for each fraction.

1)  2/3 2) 6/8

3) 4/10 4) ¼

Find the missing numbers that make the fractions equivalent.

1) 4/36 = x/18 2) 2/7 = 40/x

3) 70/100 = 7/x 4) 56/8 = x/2

Date Mixed Numbers and Improper Fractions

Learning Targets

  1. I can convert improper fractions into mixed numbers.
  2. I can convert mixed numbers into improper fractions.

Important Terms:

  1. Numerator: The top number of a fraction and tells how many parts are being used.
  2. Denominator: The bottom number of a fraction and tells how many parts make up the whole.
  3. Improper Fraction: A fraction where the numerator is greater than or equal to the denominator. Example: 9/7
  4. Proper Fraction: A fraction where the numerator is less than the denominator. Example: ¾
  5. Mixed Number: A number made up of a whole number and a fractional part. Example: 3 ½

Examples:

Converting Improper Fractions to Mixed Numbers

·  Write 15/2 as a mixed number.

Converting Mixed Numbers to Improper Fractions

·  Write 2 1/5 as an improper fraction.

Try This:

Write each improper fraction as a mixed number.

1) 19/5 2) 43/5

3) 108/9 4) 98/11

Write each mixed number as an improper fraction.

5) 9 ¼ 6) 4 9/11

7) 18 3/5 8) 11 4/9

Date Adding & Subtracting Fractions with Unlike Denominators

Learning Targets

  1. I can add fractions with unlike denominators.
  2. I can subtract fractions with unlike denominators.

Flashback: Adding and Subtracting with Like Denominators

1)

2)

Now we have unlike denominators…

Steps:

·  Find a common denominator (find the LCM of the denominators or multiply the denominators).

·  Write equivalent fractions using the common denominator.

·  Keep the denominator the same.

·  Add or subtract the numerators.

·  Make sure your answer is in simplest form.

ü  Don’t forget to ask yourself the following questions before moving on to the next problem. If you answer YES to either of these questions you MUST fix that before moving on!!!

o  Is this an improper fraction?

o  Can it be reduced?

Something to Remember

·  When the numerator and the denominator are the same number, the fraction is equal to 1.

Examples:

1) 2)

Try This:

1) 10/33 + 4/33 2) 13/18 – 7/18 3) 9/26 + 2/26 – 5/26

4) 3/10 + 1/2 5) 1/6 + 2/9 6) 7/8 + 3/4

7) 2/9 + 1/6 + 1/3 8) 7/8 – 2/3 9) ¾ - 3/5

10) 3/50 – 1/25 11) 2/3 + ¼ + 1/6 12) 5/6 – 2/3 + 7/12

13) Bailey spent 2/3 of his monthly allowance at the movies and 1/5 of it on baseball cards. What fraction of Bailey’s allowance is left?

14) Carlos has 7 cups of chocolate chips. He used 1 2/3 cups to make a chocolate sauce and 3 1/3 cups to make cookies. How many cups of chocolate chips does he have now?

Date Adding & Subtracting Mixed Numbers with Regrouping

Learning Targets

  1. I can add mixed numbers.
  2. I can subtract mixed numbers.
  3. I can subtract mixed numbers using regrouping.

Steps:

·  Find a common denominator (find the LCM of the denominators or multiply the denominators).

·  Write equivalent fractions using the common denominator.

·  Keep the denominator the same.

·  Add or subtract the numerators.

·  Add or subtract the whole numbers.

·  Make sure your answer is in simplest form.

ü  Don’t forget to ask yourself the following questions before moving on to the next problem. If you answer YES to either of these questions you MUST fix that before moving on!!!

o  Is this an improper fraction?

o  Can it be reduced?

ü  Don’t forget to pay special attention for the answers that show up as an improper fraction within a mixed number. Example: 3 7/6 These must be converted to just a mixed number. 3 + 1 1/6 = 4 1/6

Examples:

1)

2)

3)

Sometimes you must regroup/borrow before subtracting mixed numbers…

Two Methods

·  Method 1: Borrowing

  1. Create equivalent mixed numbers with common denominators (same as before).
  2. Bring down the denominator (same as before).
  3. Borrow one from the whole number in the first mixed number.
  4. Rewrite the numerator in the first mixed number. The new numerator is the sum of the numerator and the denominator.
  5. Subtract numerators.
  6. Subtract whole numbers.
  7. Make sure your answer is in simplest form.

Examples: 1)

2)

·  Method 2: Changing to Improper Fractions

  1. Create equivalent mixed numbers with common denominators (same as before).
  2. Change both mixed numbers into improper fractions.
  3. Bring down the denominator.
  4. Subtract the numerators.
  5. Make sure your answer in is simplest form.

Examples:

1) 6 5/12 – 2 7/12 2) 8 – 5 ¾

77/12 – 31/12 change to improper fractions 8/1 – 23/4 change to improper fractions

46/12 subtract numerators 32/4 – 23/4 create like denominators

3 10/12 change to a mixed number 9/4 subtract numerators

3 5/6 simplify 2 ¼ change to mixed number

Try This:

1) 2 ¾ + 3 ⅚ 2) 2 2/3 + 1 ¾ 3) 23 ½ + 35 ¼

4) 25 1/7 + 25 2/5 5) 4 7/8 – 2 2/9 6) 10 4/5 – 6 3/10

7) 7 11/12 – 4 2/3 8) 32 4/7 – 14 1/3 9) 28 11/12 – 8 5/9

10) A sea turtle traveled 7 ¾ hours in two days. It traveled 3 ½ hours on the first day. How many hours did it travel on the second day?

11) Tasha’s cat weighs 15 5/12 lb. Naomi’s cat weighs 11 1/3 lb. Can they bring both of their cats to the vet in a carrier that can hold up to 27 pounds? Explain.

Try This: Regrouping

1) 10 ½ - 2 5/8 2) 8 – 4 5/6 3) 2 ½ - 1 ¾

Date Multiplying Fractions and Mixed Numbers

Learning Targets:

  1. I can multiply fractions by fractions.
  2. I can multiply fractions by whole numbers.
  3. I can multiply fractions by mixed numbers.

Important Information

·  You DO NOT need common denominators.

·  To make any whole number a fraction, put it over 1.

Ex. 8 = 8/1 15 = 15/1 100 = 100/1

·  To change any mixed number to a fraction, make it an improper fraction.