Reteach. Chapter 9. Grade 5

Transcription

1 Reteach Chapter 9 Grade

2 Lesson 1 Reteach Round Fractions Round Up If the numerator is almost as large as the denominator, round the number up to the next whole number Example: 1 9 rounds to 1 9 is almost as large as Round to If the numerator is about half of the denominator, round the fraction to Example: rounds to 1 is about half of 0 1 Round Down If the numerator is much smaller than the denominator, round the number down to the previous whole number Example: 1 rounds to 0 1 is much smaller than Round each fraction to 0, 1, or 1 Use a number line if needed 1 _ 9 _ 7 7 _ 1_ _ 6 1_ 1 9 _ 9 _ _ 1 7 _ Grade Chapter 9 Add and Subtract Fractions 69

3 Lesson Reteach Add Like Fractions Follow these steps to add fractions with like denominators Find _ + 1_ Step 1 Add the numerators Use the like denominator _ + _ 1 = _ So, _ + 1 _ = _ or 1 _ Step Write the sum in simplest form Divide the numerator and denominator by their greatest common factor _ = _ or _ 1 Add Write each sum in simplest form Draw a picture or use models to check 1 _ 7 + _ 7 = 1 _ + 1 _ = _ + 1 _ = 7 _ + _ = 11 _ _ 1 = 6 _ + _ = 7 1 _ + _ = 1 _ + 1 _ = 9 1 _ 9 + _ 9 = 1 _ 7 + _ 7 = 11 1_ + _ = 1 1 _ 6 + _ 6 = 70 Grade Chapter 9 Add and Subtract Fractions

4 Lesson Reteach Subtract Like Fractions Follow these steps to subtract fractions with like denominators Find _ 9 - _ 9 Step 1 Subtract the numerators Use the like denominator _ 9 - _ 9 = _ 6 9 Step Write the difference in simplest form Divide the numerator and denominator by their greatest common factor So, _ 9 - _ 9 = 6 _ 9 or _ 6_ 9 = _ 6 9 or _ Subtract Write each difference in simplest form Draw a picture or use models to check 1 _ 7 - _ 7 = _ - 1 _ = _ - 1 _ = 7 _ - _ = 11 _ 1-7 _ 1 = 6 _ - _ = 7 _ 6-1 _ 6 = _ - _ = 9 _ 9 - _ 9 = 1 _ 1 - _ 1 = 11 7 _ - 1 _ = 1 9_ - _ = Grade Chapter 9 Add and Subtract Fractions 71

5 Lesson Reteach Add Unlike Fractions When adding fractions with unlike denominators, it helps to write the problems in vertical form Find 7_ + _ Step 1 Step Find the least common denominator (LCD) Multiples of :, 6, 9, 1, 1, 1, 1,, Multiples of :,,, The LCD is Rename each fraction using the LCD 7_ = _ 1 _ = _ Step Write the problems vertically Add Add Write each sum in simplest form 1 _ + _ 6 _ _ Multiples of : Multiples of 1: Multiples of 6: Multiples of : LCD: LCD: So, _ + _ 6 7_ = 1_ + _ = + _ 7_ or 1 _ 1 = So, 11 _ 1 + _ = _ + _ = _ + 9 _ = 9_ + _ 6 = 6 7 _ + _ = 7 _ + _ = _ + _ 6 = 7 Grade Chapter 9 Add and Subtract Fractions

6 Lesson 7 Reteach Subtract Unlike Fractions You can _ draw 1_ models to help subtract fractions with unlike denominators Find - Show models for and Find the LCD of and 1 Use models to show how many twelfths are in, and how many twelfths are in 1 Take away models to subtract 1 So, - 1 = 1 Multiples of :,, 1, Multiples of :, 6, 9, 1, The LCD of and 1 is _ _ _ _ Use fraction models to subtract the fractions Write each difference in simplest form 1 _ _ _ 1 - _ 1 = Subtract Write each difference in simplest form 1 _ - _ = 7 _ - 1 _ = _ - _ = _ 6-7 _ 1 = 9 _ 0 - _ = _ _ 1 - _ 1 = _ 1 _ - _ = 6 11 _ 1-1 _ = 9 7 _ - 1 _ = _ 1 Grade Chapter 9 Add and Subtract Fractions 7

7 Lesson Reteach Problem Solving: Determine Reasonable Answers Linden buys 1 pounds of cashew nuts and 1 1 pounds of peanuts He mixes the nuts together About how many pounds of nuts are there altogether? Step 1 Understand Step Plan What do you know? You know the amount of cashew nuts and the amount of peanuts What do you need to find? You need to find about how many pounds of nuts there are altogether You can use estimation to find a reasonable answer Step Solve Step Check Round each amount to the nearest whole number Then add 1 _ 1 _ 1 1 Linden bought about + 1 or pounds of nuts Is the answer reasonable? Yes, because 1 _ + 1 _ 1 = _ Grade Chapter 9 Add and Subtract Fractions

8 Lesson Reteach Problem Solving: Determine Reasonable Answers (continued) Determine a reasonable answer to solve each problem 1 Renata bought 0 pound of pine nuts and 09 pound of macadamia nuts Is 1 pound, pounds, or pounds the most reasonable estimate for how many pounds of nuts she purchased altogether? One container has pounds of pineapple and another has 1 7 pounds of pineapple Sani buys both containers Which is the most reasonable estimate for how many pounds of pineapple he bought in all: pounds, pounds, or 6 pounds? From the beginning of a trail, Claire hiked miles to the lake Then she hiked miles to the nature center Is miles, 6 miles, or 7 miles the most reasonable estimate for how far Claire hiked altogether? In the morning, Kevin s cat eats 1 of a can of cat food In the afternoon, the cat eats 1 of a can of food In the evening, the cat eats of a can of food Which is the most reasonable estimate for the amount of food the cat eats throughout the day: 1 can, cans, or cans? At the beginning of the week there were pounds of jelly beans in a jar By the end of the week, there were 17 pounds of jelly beans in the jar Which is the most reasonable estimate for how many jelly beans were eaten during the week: 0 pound, 1 pound, or pounds? 6 A DVD player costs $19 A portable digital music player costs $179 Is $1, $0, or $ the most reasonable estimate for how much more the digital music player costs? Grade Chapter 9 Add and Subtract Fractions 7

9 Lesson 9 Reteach Estimate Sums and Differences You can round mixed numbers to the nearest whole number to estimate sums and differences of mixed numbers Use number lines to help you Estimate _ - 1 is closer to 6 than to 1 - _ = So, - 1 is about 1 is closer to than to Show each mixed number on a number line and round it to the nearest whole number Then estimate the sum 1 _ is closer to than to is closer to than to _ + _ 9 + = Estimate by rounding each mixed number to the nearest whole number 9_ - _ _ _ 7 9 _ _ - = + = - = 76 Grade Chapter 9 Add and Subtract Fractions

10 Lesson 11 Reteach Add Mixed Numbers Find _ 6 + _ 6 Step 1 Step Add the fractions _ 6 + _ 6 7_ 6 Add the whole numbers _ 6 + _ 6 6 _ 7 6 Step Simplify 6 _ 7 6 = 7 _ 1 6 So, _ 6 + _ 6 = 7 1 _ 6 Add Write each sum in simplest form Check your result for reasonableness 1 _ 9 + _ 9 7_ + _ = _ 1 + _ _ _ 9 = _ _ + _ 1 _ _ 7 = 9 _ + 1 _ = 9 1 _ + 7 _ = 7 _ 6 + _ 6 = Grade Chapter 9 Add and Subtract Fractions 77

11 Lesson 1 Reteach Subtract Mixed Numbers Find 6 _ - 1_ Step 1 Subtract the fractions 6 _ - 1 So, 6 _ - 1 _ = _ or 1 _ Step Subtract the whole numbers 6 _ - _ 1 _ Step Simplify _ = 1 _ Subtract Write each difference in simplest form Check your result for reasonableness _ - _ 1 1 _ - 1 _ = 1 11 _ 1-7 _ 1 = 11 7 _ - 1 _ = 1 _ - 1 _ 1 = _ - 1 _ 6 _ _ 6 = _ - _ = 6_ _ = 1 1 _ _ 6 = 9 _ - _ 1 _ _ 7 6 _ 0-1 _ = _ - _ = 1 6 _ - _ = _ _ = 7 Grade Chapter 9 Add and Subtract Fractions

12 Lesson 1 Reteach Subtract with Renaming Sometimes you need to rename fractions in order to subtract them Find 6 1_ - _ Step 1 Regroup 6 1 as _ - _ Step Subtract the whole numbers _ - Step Subtract the fractions _ - Step Simplify if possible _ in simplest form is 1 So, = 1 Subtract Write each difference in simplest form Check your result for reasonableness 1 7 _ _ 9 _ - _ 1 _ _ _ - _ = 6 1 _ 6-1 _ = _ - _ = 1 _ _ 1 = 9 70 _ - _ = _ 9-7 _ 9 = Grade Chapter 9 Add and Subtract Fractions 79