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**Lesson 6-1Ratios**Lesson 6-2 Rates Lesson 6-3 Measurement: Changing Customary Units Lesson 6-4 Measurement: Changing Metric Units Lesson 6-5 Algebra: Solving Proportions Lesson 6-6 Problem-Solving Investigation: Draw a Diagram Lesson 6-7 Scale Drawings Lesson 6-8 Fractions, Decimals, and Percents Lesson 6-9 Percents Greater Than 100% and Percents Less Than 1% Chapter Menu**Five-Minute Check (over Chapter 5)**Main Idea and Vocabulary California Standards Key Concept: Ratios Example 1: Write Ratios in Simplest Form Example 2: Identify Equivalent Ratios Example 3: Real-World Example Lesson 1 Menu**Write ratios as fractions in simplest form and determine**whether two ratios are equivalent. • ratio • equivalent ratios Lesson 1 MI/Vocab**Ratio – comparison of two numbers by division.**3 to 4 3:4 a to b a:b**Equivalent Ratios: Two ratios that have the same value.**= = =**Write the ratio 8 yards to 64 yards as a fraction in**simplest form. = Write the ratio 3 pounds to 10 pounds as a fraction in simplest form. Write the ratio 192 crayons to 8 crayons as a fraction in simplest form. =**Answer: The ratio of Red Delicious apples to GrannySmith**apples is Write Ratios in Simplest Form APPLESMr. Gale bought a basket of apples. Using the table below, write a ratio comparing the Red Delicious to the Granny Smith apples as a fraction in simplest form. Mr. Gale’s Apples 12 Fuji 9 Granny Smith30 Red Delicious Red DeliciousGranny Smith Lesson 1 Ex1**FLOWERS A garden has 18 roses and 24 tulips. Write a ratio**comparing roses to tulips as a fraction in simplest form. • A • B • C • D A. B. C. D. Lesson 1 CYP1**Answer:**So, 12:15 and 32:40 are equivalent ratios. Identify Equivalent Ratios Determine whether the ratios 12 onions to 15 potatoes and 32 onions to 40 potatoes are equivalent. Write each ratio as a fraction in simplest form. The GCF of 12 and 15 is 3. The GCF of 32 and 40 is 8. Lesson 1 Ex2**Determine whether the ratios 3 cups vinegar to 8 cups water**and 5 cups vinegar to 12 cups of water are equivalent. • A • B • C • D A. yes B. no C. maybe D. not enough information Lesson 1 CYP2**POOLSIt is recommended that no more than one person be**allowed into the shallow end of an outdoor public pool for every 15 square feet of surface area. If a local pool’s shallow end has a surface area of 1,800 square feet can 120 people swim into that part of the pool? Recommended ratio Actual ratio Answer: Since the ratios simplify to the same fraction, the lifeguards are correct to allow 120 people into the shallow end of the pool. Lesson 1 Ex3**SCHOOL A district claims that they have 1 teacher for every**15 students. If they actually have 2,700 students and 135 teachers, is their claim correct? • A • B • C • D A. yes B. no C. maybe D. not enough information Lesson 1 CYP3**Five-Minute Check (over Lesson 6-1)**Main Idea and Vocabulary California Standards Example 1: Find Unit Rates Example 2: Find Unit Rates Example 3: Standards Example: Compare UsingUnit Rates Example 4: Real-World Example: Use a Unit Rate Lesson 2 Menu**Determine units rates.**• rate • unit rate Lesson 2 MI/Vocab**Ratio:comparison of two numbers by division.**Rate:A ratio that compares two numbers with different kinds of units. 128 pounds of dog food for 16 dogs. 1 gallon of milk for $2.59.**Unit Rate: A rate that is simplified so that it has a**denominator of 1 unit. 140 meters running in 28seconds. = 96 pages of a book read in 3 hours. = $6 for 24 cookies. =**Find Unit Rates**READINGJulia read 52 pages in 2 hours. What is the average number of pages she read per hour? Write the rate as a fraction. Then find an equivalent rate with a denominator of 1. Write the rate as a fraction. Divide the numerator and denominator by 2. Simplify. Lesson 2 Ex1**Find the unit rate. 16 laps in 4 minutes**• A • B • C • D A. 4 laps per minute B. 12 laps per minute C. 20 laps per minute D. 64 laps per minute Lesson 2 CYP1**Find Unit Rates**SODAFind the unit price per can if it costs $3 for 6 cans of soda. Round to the nearest hundredth if necessary. Write the rate as a fraction. Divide the numerator and the denominator by 6. Simplify. Answer: The unit price is $0.50 per can. Lesson 2 Ex2**Find the unit rate. $3 for one dozen cookies**• A • B • C • D A. $0.18 per cookie B. $0.21 per cookie C. $0.25 per cookie D. $3.60 per cookie Lesson 2 CYP2**Compare Using Unit Rates**The costs of 4 different sizes of orange juice are shown in the table. Which container costs the least per ounce? A 96-oz containerB 64-oz containerC 32-oz containerD 16-oz container Read the ItemFind the unit price, or the cost per ounce, of each size of orange juice. Divide the price by the number of ounces. Lesson 2 Ex3**Compare Using Unit Rates**Solve the Item 16-ounce container $1.28 ÷ 16 ounces = $0.08 per ounce 32-ounce container $1.92 ÷ 32 ounces = $0.06 per ounce 64-ounce container $2.56 ÷ 64 ounces = $0.04 per ounce 96-ounce container $3.36 ÷ 96 ounces = $0.035 per ounce Lesson 2 Ex3**The costs of different sizes of bottles of laundry detergent**are shown below. Which bottle costs the least per ounce? • A • B • C • D A. 96-oz container B. 64-oz container C. 32-oz container D. 16-oz container Lesson 2 CYP3**Use a Unit Rate**POTATOES An assistant cook peeled 18 potatoes in 6 minutes. At this rate, how many potatoes can he peel in 50 minutes? Find the unit rate. Then multiply this unit rate by 50 to find the number of potatoes he can peel in 50 minutes. Answer: The assistant cook can peel 150 potatoes in 50 minutes. Lesson 2 Ex4**Sarah can paint 21 beads in 7 minutes. At this rate, how**many beads can she paint in one hour? • A • B • C • D A. 21 B. 63 C. 120 D. 180 Lesson 2 CYP4**Five-Minute Check (over Lesson 6-2)**Main Idea and Vocabulary California Standards Key Concept: Equality Relationships for CustomaryUnits Example 1: Convert Larger Units to Smaller Units Example 2: Convert Larger Units to Smaller Units Example 3: Convert Smaller Units to Larger Units Example 4: Convert Smaller Units to Larger Units Example 5: Real-World Example Lesson 3 Menu**Change units in the customary system.**• unit ratio Lesson 3 MI/Vocab**Standard 6AF2.1 Convert one unit of measurement to another**(e.g., from feet to miles,from centimeters to inches). Lesson 3 CA**Multiply by**Convert Larger Units to Smaller Units Convert 2 miles into feet. Divide out common units. = 2 ● 5,280 ft or 10,560 ft Multiply. Answer: 10,560 ft Lesson 3 Ex1**A.**B.11 ft C.24 ft D.32 ft Convert 8 yards into feet. • A • B • C • D Lesson 3 CYP1**Since 1 ton = 2,000**pounds, multiply by . Then divide out common units. Convert Larger Units to Smaller Units ELEVATORThe elevator in an office building has a weight limit posted of one and a half tons. How many pounds can the elevator safely hold? Multiply. Answer: So, the elevator can safely hold 3,000 pounds. Lesson 3 Ex2**Complete .**• A • B • C • D A. 8,000 B. 8,500 C. 9,000 D. 9,500 Lesson 3 CYP2**Convert Smaller Units to Larger Units**Convert 11 cups into pints. Multiply and divide out common units. Multiply. Answer: 5.5 pints Lesson 3 Ex3**Convert 21 quarts into gallons.**• A • B • C • D A. 4.75 gal B. 5.25 gal C. 6.5 gal D. 7 gal Lesson 3 CYP3**Convert Smaller Units to Larger Units**SOCCERTracy kicked a soccer ball 1,000 inches. How many feet did she kick the ball? Lesson 3 Ex4**?**Complete 78 oz = ___ lb. • A • B • C • D A. B. C. D. Lesson 3 CYP4**LEMONADEPaul made 6 pints of lemonade and poured it into 10**glasses equally. How many cups of lemonade did each glass contain? Begin by converting 6 pints to cups. = 6 ● 2 cups or 12 cups Find the unit rate which gives the number of cups per glass. Lesson 3 Ex5**Answer:**Lesson 3 Ex5**CANDY Tom has 3 pounds of candy he plans to divide evenly**among himself and his 3 best friends. How many ounces of candy will each of them get? • A • B • C • D A. 1 oz B. 12 oz C. 15 oz D. 24 oz Lesson 3 CYP5**Five-Minute Check (over Lesson 6-3)**Main Idea and Vocabulary Targeted TEKS Example 1: Convert Units in the Metric System Example 2: Convert Units in the Metric System Example 3: Real-World Example Key Concept: Customary and Metric Relationships Example 4: Convert Between Measurement Systems Example 5: Convert Between Measurement Systems Example 6: Real-World Example Lesson 4 Menu**Change metric units of length, capacity, and mass.**• metric system • meter • liter • gram • kilogram Lesson 4 Ideas/Vocabulary**Standard 6AF2.1 Convert one unit of measurement to another**(e.g.,from feet to miles, from centimeters to inches). Lesson 4 TEKS**Convert Units in the Metric System**Complete 7.2 m = ? mm. To convert from meters to millimeters, use the relationship 1 m = 1,000 mm. 1 m = 1,000 mm Write the relationship. 7.2×1 m = 7.2× 1,000 mm Multiply each side by 7.2. 7.2 m = 7,200 mm To multiply 7.2 × 1000, move the decimal point 3 places to the right. Answer: 7,200 mm Lesson 4 Example 1**Complete 7.5 m = ? cm.**• A • B • C • D A. 0.75 B. 75 C. 750 D. 7,500 Lesson 4 Example 1 CYP