Bellwork: We will do a Number Talk today. Monday

500-449

250-219

Multiplying and Dividing Fractions and Decimals

Fractions Review Common Denominator- a number with which both of the denominators share at least one factor that is not the number 1 For 4 and 7, then a common denominator is 28. Improper Fraction- the numerator is larger than the denominator 8 5 Mixed Number- whole number with a fraction 2 1 6 Simplify- reduce the numerator and the denominator by the same number 8 12 ÷4 ÷4 = 2 3

Multiplying Fractions Review Multiply straight across, then simplify numerator x numerator denominator x denominator 5 7 x 3 5 = 2 1 6 x 3 3 4 =

Dividing Fractions Review Change division to multiplication by taking the reciprocal (flipping numerator and denominator) Multiply straight across, then simplify numerator x numerator denominator x denominator 5 7 ÷ 3 5 = 3 1 6 ÷ 1 3 4 =

Multiply and divide with negatives Use the same rule for integers: Same signs are POSITIVE P x P = P N x N = P Different signs are NEGATIVE P x N = N N x P = N The negative sign could be… in front of the fraction - 1 2 On the numerator −1 2 On the denominator 1 −2 ***If there is a negative sign on both the numerator and the denominator, it is positive ( 2 negatives make a positive) −1 −2 = 1 2

Examples

Multiplying decimals Review Multiply (ignoring decimals) Count the total number of decimal places are in the problem Move your decimal that many places to the left 1.23(3.5) = 1.456 x 2.2 =

Dividing decimals Review The first number or the numerator goes inside The second number or denominator is on the outside If you have a decimal number on the outside: Move the decimal to the right until you have a whole number Move the decimal inside the same number of spaces as you did on the outside Put the decimal point directly above where it is inside Add zeroes as needed (you may not use a remainder) 4.16 ÷ 0.8= 18.29 3.1 =

Multiply and divide with negatives Use the same rule for integers: Same signs are POSITIVE P / P = P N / N = P Different signs are NEGATIVE P / N = N N / P = N

Examples

Practice Book Pg. 390

Bellwork: 1. 2. 3. Combine like terms using your integer rules. tUESDAY

Adding and subtracting fractions and decimals

Adding and subtracting Fractions Review Make sure you have common denominators Adjust your numerators if necessary Add/Subtract numerators straight across Use the same denominator Make mixed numbers (if necessary) How many times can the denominator go into the numerator? That’s the whole number What's leftover? That’s the numerator 5 7 - 3 5 = 2 1 6 + 3 2 3 =

Add and subtract with negatives Use the same rule for adding integers: Same signs, ADD P + P = P N + N = N Different signs, SUBTRACT N + P = depends P + N = depends The negative sign could be… in front of the fraction - 1 2 On the numerator −1 2 On the denominator 1 −2 Use the same rule for subtracting integers: BOX IT KEEP the 1st number the same Change subtraction to ADDITION Take the OPPOSITE of the second number Then follow addition rules ***If there is a negative sign on both the numerator and the denominator, it is positive ( 2 negatives make a positive) −1 −2 = 1 2

Examples

Adding and subtracting decimal Review Line up your decimals You may have to add zeroes after the decimal point Add/ Subtract like you normally would Bring down your decimal 1.23−0.5 = 1.456 + 2.2 =

Add and subtract with negatives Use the same rule for adding integers: Same signs, ADD P + P = P N + N = N Different signs, SUBTRACT N + P = depends P + N = depends Use the same rule for subtracting integers: BOX IT KEEP the 1st number the same Change subtraction to ADDITION Take the OPPOSITE of the second number Then follow addition rules

Examples

Practice Book Pg. 384

wEDNESDAY Bellwork: Angles- obtuse, acute, right Classify each triangle by its sides and angles. Equal sides and equal angles, if any, are indicated in each diagram. Sides- scalene, isosceles, equilateral   Angles- obtuse, acute, right wEDNESDAY

All Operations with rational Numbers

Individual Practice Work on a column at a time Get checked If correct: Try the next column for a chance to earn bonus points If incorrect: Fix your mistakes and try another column for an opportunity to get a 100%

Individual Practice: AC Work on half the sheet at a time Get checked If correct: Try the next half for a chance to earn bonus points If incorrect: Fix your mistakes and try the other half for an opportunity to get a 100%

Agenda: Worksheet due Tuesday for a grade if you did not finish Bellwork: David wants to fill his backyard swimming pool. His garden hose delivers 40 gallons in 5 minutes. How many gallons of water will be in the pool after 20 minutes? 1 hour?   Show Your Work 20 min. ______________ 1 hour _______________ Thursday Agenda: Worksheet due Tuesday for a grade if you did not finish

Terminating and Repeating Decimals

Step One - Divide Divide 3 into the first number in the dividend. 3 will go into 4 one time. Write a 1 above the 4 because that’s the current dividend. 1 3) 495

Step Two - Multiply Multiply the divisor times the first number in the quotient. Write the answer below the number you just divided into. 1 3) 495 3

1 3) 495 3 1 Step Three - Subtract Subtract. Be sure to line up your numbers carefully. 1 3) 495 3 1

Step Four – Bring Down Draw an arrow and bring the second digit in the dividend down. 1 3) 495 3 1 9

Step Five – Repeat Repeat the steps in the same manner as before, as shown in the next set of slides. 1 3) 495 3 1 9

Repeat Step One - Divide Divide 3 into the new number. 3 will go into 19 six times. Write a 6 above the 9 because that’s the current dividend. 1 6 3) 495 3 1 9

Repeat Step Two - Multiply Multiply the divisor into the new number in your quotient. 3 x 6 = 18 Write 18 below the number you just divided into. 1 6 3) 495 3 1 9 18

Repeat Step Three - Subtract 1 6 3) 495 3 1 9 18 1

Repeat Step Four – Bring Down 1 6 If there are more digits in the dividend, repeat the procedure. Bring the third digit in the dividend down. 3) 495 3 1 9 18 1 5

Repeat Step Five – Repeat 1 6 5 If there are more digits in the dividend, repeat the procedure. If there are no more digits in the dividend, write the final subtraction answer as a remainder. If there is no remainder, you’re finished! Pat yourself on the back for a job well done. 3) 495 3 1 9 18 1 5 15

When you have a fraction… Begin long division Add decimal and zeros as needed Align decimal and divide

Express as a decimal. Example: 3 7 5 Begin long division . 8 3 .00 3 7 5 Begin long division . 8 3 .00 Add decimal and zeros as needed -24 Align decimal and divide 6 -56 Answer will: 4 -40 * Terminate OR * Repeat

The top number ALWAYS gets “caught” in the division box. Example: = = .625 *Remember: The top number ALWAYS gets “caught” in the division box. Also: when dividing don’t forget your decimal, line up your answer, and add zeros as needed to bring down.

Express as a decimal. You try: 7 5 . 4 3 .00 -28 2 -20

A decimal that stops or “terminates” is a terminating decimal If the same block of digits in a decimal repeats without end, the decimal is a repeating decimal Show a repeating block by putting a bar over the repeating digits. = = Example:

Here is another example and a few to try Here is another example and a few to try. *remember- divide the numerator by the denominator. Example: Now you try a few: 1. 2. 3.

Repeating Decimals Try a few: 1) (.3333333…) = 2) = (.5833333…)

Whiteboard Practice! Change to decimal then determine whether its terminating or repeating 𝟓 𝟖

Whiteboard Practice! Change to decimal then determine whether its terminating or repeating 𝟐 𝟔

Whiteboard Practice! Change to decimal then determine whether its terminating or repeating 𝟒 𝟓

Whiteboard Practice! Change to decimal then determine whether its terminating or repeating 𝟕 𝟖

Whiteboard Practice! Change to decimal then determine whether its terminating or repeating 𝟓 𝟗

Whiteboard Practice! Change to decimal then determine whether its terminating or repeating 𝟑 𝟓

Whiteboard Practice! Change to decimal then determine whether its terminating or repeating 𝟓 𝟏𝟎

Accelerated: How to turn a repeating decimal into a fraction Write .33 as a fraction. x = .33 100x = 33 .33 - x = - x 99x = 33 = 99 X = 33 99 or 1 3

Accelerated: How to turn a repeating decimal into a fraction Write .89 as a fraction. x = .89

Accelerated: How to turn a repeating decimal into a fraction Write .6 as a fraction. x = .6

Accelerated: How to turn a repeating decimal into a fraction Write .724 as a fraction. x = .724

Agenda: Worksheet due Tuesday for a grade if you did not finish Bellwork: You have a Bellwork Quiz today. You may get out your bellwork 1- 4 to use for your quiz. fRIDAY Agenda: Worksheet due Tuesday for a grade if you did not finish

Terminating and Repeating Decimals

Challenge Questions Write a fraction that is equivalent to a terminating decimal between 0.5 and 0.75.

Challenge Questions The value of pi is 3.1415926… A mathematician, Archimedes, believed that pi was between 3 1 7 and 3 10 71 . Was he correct?

Challenge Questions A unit fraction is a fraction that has 1 as its numerator. Write the four greatest unit fractions that are repeating decimals.

Challenge Questions Fractions is simplest form that have denominators of 4, 8, 16, and 32 produce terminating decimals. Fractions is simplest form that have denominators of 6, 12, 18, and 24 produce repeating decimals. What causes the difference?

Start Practice sheet due Thursday

Bellwork: mONDAY

All Operations with rational Numbers

Bellwork: Tuesday

All Operations with rational Numbers-word problems

WEDNESDAY Review K z B GRAB SHEET FROM BACK TABLE Fill in MATH board with letters A-Z in the alphabet: Put letters in board randomly & only use once! MUST USE MARKER!!! Do not put letters in order Do not try to spell words  Have out a blank sheet of paper K z B WEDNESDAY Review

Rational Review

Fill in the blanks with the choices to the right by comparing the rationals. ___________ < ______________ < _____________ - 𝟖 𝟏𝟐 -0.59 -0.7

At 10 am, Jane began a shopping spree using her credit card At 10 am, Jane began a shopping spree using her credit card. By 3 pm, her bank account balance was -$45.50. If her balance changed by -$10.50 per hour, how much did Jane have at 10 am before she began shopping?

Solve: 12(-3)= -27 / -3= -18 – 20 = -11 + 3 =

Which situation can be described using this number line? The temperature decreases by 5 degrees and then increases by 7 degrees. John loses $3 then finds $4. On the first play, the football team lost 5 yards. On the next play, the football team gained 4 yards.

Label each fraction Terminating (T) or repeating (R) 25 99 18 48 2 9 9 80

On December 30th, the temperature was -11°F in the afternoon On December 30th, the temperature was -11°F in the afternoon. By the evening, the temperature dropped 6 degrees. The next day, on December 31st, the temperature rose 14 degrees. What was the temperature on December 31st?

Peggy has $200 in her piggy bank Peggy has $200 in her piggy bank. She take out 3 4 of the money in order to buy a new bike. Out of the money she took from her piggy bank, she only used 4 5 to purchase the bike. How much money does Peggy have leftover from her bike purchase that can be returned to her piggy bank?

Order least to greatest: 𝟐 𝟑 , 0.66, 𝟔 𝟏𝟎 , 0.06, 0.555

Choose all fractions that simplify to -10 -2 ¼(-4 ½) -66 ¼ ÷ 6 5 8 -10 1 6 – 1 6 -5 1 3 + (-4 2 3 )

In Bill’s family, both parents can eat ¾ of an 8-slice pizza on their own and all 3 children can eat ¼ of an 8-slice pizza on their own. Due to a mistake made by Pizza Plus, the family only received two 8-slice pizzas. How many MORE SLICES does the family need to fill up on pizza?

Have out cover sheet and pencil After the test: Thursday: Test

Test

After the Test Challenge: fRIDAy

Finish Test/ Challenge question