Learning Target: I can… Convert rational numbers

A __________________ is a number that can be written as ________ where a and b are integers and b ≠ 0.

Types of Rational Numbers: Fractions can be converted into 1) Terminating Decimals (a decimal that ___) 2) Repeating Decimals

Types of Decimals Terminating Decimal: a terminating decimal ends! Examples: 1.42 3.7134 921.0089 Repeating Decimal: a repeating decimal repeats a number or pattern 6.77777… 1.921921921921…

Type of Decimal T = Terminating I = Irrational (neither) R = Repeating 8.79 3.231… 0.9191919191… 4.21 0.009 1.235… 4.691 2.183183183183…

To Convert From Fraction to Decimal: 1. Top number ____________________by bottom number 2. Use _____________________________

Example 1: Write as a decimal.

Example 2: Write as a decimal.

Example 3: Write as a decimal.

Example 4: Write as a decimal.

Converting Decimals to Fractions Write the digits after the decimal point in the __________________. Write the place value in the ________________________________. _________________________.

Example 1: Write -0.26 as a fraction.

Example 2: Write -0.7 as a fraction.

Example 3: Write 0.125 as a fraction.

Example 4: Write –3.1 as a fraction.

Example 5: Write 10.25 as a fraction.

Word problem  of the students completed their homework. What decimal of students completed their work? a. .67 b. .75 c. .875 d. .905

Exit: Convert the fractions to decimals and the decimals to fractions 1) 2) .32 3)

Learning Target: I can… Convert and order rational numbers

Comparing Fractions, Decimals, Percents To compare numbers that are in a different form, you must convert all numbers to the same form! Example: put the numbers in order from least to greatest - , .25, 0.05, 

Emily ate  of her dinner, John ate 78% of his dinner, Michael ate 0 Emily ate  of her dinner, John ate 78% of his dinner, Michael ate 0.81 of his dinner and Lucy ate  of her dinner. Who ate the most? Emily John Michael Lucy

Comparing Decimals Example: 0.342, 0.34, 0.4, 0.39, 0.312 Remember: Compare the place values starting at the tenths place!

You try it!

And again!

EXIT The table shows the position of each runner relative to when the first place finisher (Andre) crossed the finish line. Order the other four to see who crossed second, third, fourth and fifth. Jack Serena Andre Steffie Pete -2.5 -1.099 -0.283

Fraction Decimal Percent Top ÷ Bottom Use place values Decimal ∙ 100 Put it over 100 and reduce Use >% Percent ÷ 100 Percent

Change the following to fractions! REMEMBER TO REDUCE! 60% .25 90% .3 12% .05

Change the following to decimals! 57% 8% 2_ 25 1_ 8 5. 2/11

Change the following to percents!  0.24  0.39 1.74 

Review Richard got 19 out of 20 problems correct on his math test. What percentage did he get right?

The seventh graders set a goal to collect 250 cans for their school’s food drive. They collected 275 cans. What percent of their goal did they collect? 75% 91% 110% 125%

Brad earned a 92% on his social studies test Brad earned a 92% on his social studies test. Which fractional portion of the test did he answer INCORRECTLY?

EXIT 3

Fractions, Decimals, Percents (Day 2)

Review

Review

Review

Review – Learning Series Questions

Learning Target: I can… Find the percent OF a number

To find the percent of a number Use the % key and multiply! Example: Find 25% of 120.

You try it!

During a quality control check, a factory found that 5% of the parts it produces are defective. The factory recently completed an order for 144,000 parts. How many of the parts are NOT defective?

An airline has 400 flights a day. Of these, 80% leave in the morning An airline has 400 flights a day. Of these, 80% leave in the morning. Flights leaving in the morning depart on time ¾ of the time. How many flights leaving in the morning depart on time every day? 155 240 300 320

An airline has 200 flights a day. Of these, 70% leave in the morning An airline has 200 flights a day. Of these, 70% leave in the morning. Flights leaving in the morning depart on time ¼ of the time. How many flights leaving in the morning depart on time every day? 35 140 240 14000

Jackson has a board that is 6½ feet long Jackson has a board that is 6½ feet long. He needs a board that is ¼ of this length. What is the length of the board that Jackson needs? 1 5/8 2 1/6 2½ 6¼

EXIT

You try it! The sales tax is 7%. If you spent $60 on items, how much is your sales tax? $4.20 Including tax, how much did you spend? $64.20

You can also find how much to tip! A good tipping rate is 20%. This should be added to the bill! Example: Your bill at Bob Evans is $25.00. How much should you leave for a tip? $5.00 What will be the total amount that you spent? $25.00

Discounts Example: A shirt costs $35. There is a 16% discount. How much do you pay for the shirt? Step 1: Multiply the percent by your price 16% x 35 = 5.6 or 5.60 Step 2: Subtract the discount from the original price 35 – 5.60 = 29.40 New Price

You try it! The original price of a DVD is $20.00. If it is discounted 15%, what is the new price of the DVD? 17

Problem of the Day (Friday)

After grading the history exam, Mr After grading the history exam, Mr. Parsons discovered that  of the students who had taken the exam earned A’s or B’s. Of those students,  had earned 100% on the exam. If Mr. Parsons has 180 students, how many students earned 100% on the exam? 12 24 36 75

Review – discount, tax, tip 1. Find the new price of a $10,000 car that is discounted 35% 2. Find the total amount spent at a restaurant if the bill is $145 and you tip 20% 3. Find the total amount spent if you buy an item for $50 that is 20% off with 7% tax.

Review - Discounts A game cost $80.00. If it had a sale of 20% off, how much would you pay for the game? $16.00 $64.00 $60.00 $78.40

Sales Tax The sales tax is 6.5%. If you buy a television for $500, what will your total price be? Step 1: Multiply the percent by your price (to get your tax) 6.5% x 500 = 32.5 or 32.50 Step 2: Add tax to the original amount to get the total! 500 + 32.50 = $532.50 Total Price

Review Find the total cost of an $8.75 item with a 5.75% sales tax.

Multiple discounts and what is the better deal?

What is the sale price of the CD? Andrea needs to add 7% sales tax to the sale price of the CD. What should Andrea charge the customer for the CD, including tax? 3. The customer told Andrea that she could save time by just taking 8% off the regular price of the CD, because 15% – 7% is 8%. Is the customer right? Explain your reasoning.  

Exit Find the total amount spent if you buy an item for $50 that is 20% off with 7% tax.

Remember! Once you find sales tax, you ___________ it to the original price to get the total amount spent. a. Add b. Subtract c. Multiply d. Divide

And again! Once you find the discount, you _________ it from the original price to find the total spent a. Add b. Subtract c. Multiply d. Divide

Review Find the cost of a $9.00 shirt with a 10% discount.

Learning Series Questions

Review A total of 24 students tried out for the school baseball team. Of those who tried out, 75% made the team. How many students did not make the team? a. 6 b. 8 c. 16 d. 18

Fraction of a Number Multiply the fraction by the number! Example:  of 250 students attended the dance  ∙ 250 =

You try  of the 49 volleyball players went to volleyball camp. How many players went to camp?  ∙ 49 = 14

Review

Review

Solving Problems Involving Percents Use proportions!

Quick Check!

You try it!

Answer numerically!

You try it!

Jacqueline spent 40% of the money she earned babysitting last year Jacqueline spent 40% of the money she earned babysitting last year. If she spent $20, how much money did she earn babysitting last year?

The total cost for Betty’s lunch was $19. 00, including tip The total cost for Betty’s lunch was $19.00, including tip. If she left a 20% tip, what was the amount of her meal?

Percent of Change: When an amount increases or decreases Use: amount of change original amount *To find amount of change subtract the new amount from the old amount

Step 1: Find the amount of change (new – old) Step 2: Divide by the original amount Step 3: Change to a percent

Percent of Change Last year 600 kids went to Sherman. This year, 700 kids go to Sherman. What is the percent of change? Step 1: Find the amount of change (new – old) Step 2: Divide by the original amount Step 3: Change to a percent

Step 1: Find the amount of change Step 2: Divide by the original amount Step 3: Change to a percent

A girl was 4 ft 9 in. tall last year. This year she is 5 ft tall A girl was 4 ft 9 in. tall last year. This year she is 5 ft tall. Find the percent of increase in her height. Round to the nearest tenth of a percent. 2.0% 5.3% 5.0% 153.0%

Practice Problems Learning Series!

Problem of the Day! (Friday) What is the decimal equivalent of the fraction ? 3 5 0.2 0.6 0.25 60

Review! Find the total cost of a $10.00 item with a 4% sales tax