Operations With Fractions. Chapter 4 Math 7

Transcription

1 Operations With Fractions Chapter 4 Math 7

2 Estimating With Fractions and Mixed Numbers Lesson 4-1

3 Using Benchmarks With Fractions A benchmark is a convenient number used to replace fractions that are less than 1.

4 Estimating Sums and Differences Using Benchmarks Estimate as O when the numerator is very small compared to the denominator Estimate as ½ when the numerator is about half the denominator Estimate as 1 when the numerator and the denominator are nearly equal

5 Estimate to add Estimate ⅞ + ⅗ using benchmarks ⅞ 1 ⅗ ½ 1 + ½ = 1 ½ Use benchmarks to estimate each fraction and then add

6 Estimating with Mixed Numbers When a sum or difference involves mixed numbers, you can make a reasonable estimate by rounding to the nearest whole number 8 ⅕ - 4 ¾ 8 5 = 3 Round each mixed number and then subtract

7 Estimating Products To estimate a product of mixed numbers, round each mixed number to the nearest whole number, then multiply 2 ⅖ x 6 ⅟₉ 2 x 6 = 12 round each number then multiply

8 Estimating with Compatible Numbers To estimate a quotient of mixed numbers, you can use compatible numbers 43 ⅟₄ 5 ⁷ ₈ 42 6 = 7

9 practice Work with a partner to complete odds or evens workbook p. 62

10 Adding and Subtracting Fractions Lesson 4-2

11 Adding Fractions If the denominators are the same, add the numerators and keep the denominator ⅖ + ⅕ = ⅗

12 Adding Fractions If the denominators are different, find LCD, make equivalent fractions, add the numerators and keep the denominator ⅘ + ⅔ Find LCD and make equivalent fractions ¹² ₁₅ + ¹⁰ ₁₅ = ²² ₁₅ = 1 ⁷ ₁₅

13 Subtracting Fractions If the denominators are the same, subtract the numerators and keep the denominator ⅖ - ⅕ = ⅕

14 Subtracting Fractions If the denominators are different, find LCD, make equivalent fractions, subtract the numerators and keep the denominator ⅘ - ⅔ Find LCD and make equivalent fractions ¹² ₁₅ - ¹⁰ ₁₅ = ² ₁₅

15 practice Work with a partner to complete odds or evens workbook p. 64

16 Adding and Subtracting Mixed Numbers Lesson 4-3

17 Adding Mixed Numbers Mentally Mental Math Find 10¹ ₅ + 6⅖ Add the whole numbers = 16 Add the fractions ¹ ₅ + ⅖ = ⅗ Combine the two parts 16 + ⅗ = 16 ⅗

18 Adding Mixed Numbers With Unlike Denominators Find 8 ⅓ + 6 ½ Estimate = 15 Find the LCD: for ⅓ and ½ is 6 Add 8 ² ₆ + 6 ³ ₆ = 14 ⁵ ₆ Simplify 14 ⁵ ₆ is in simplest form

19 Adding Mixed Numbers with Renaming Find 15⁵ ₆ + 3 ½ Stack: 15⁵ ₆ = 15⁵ ₆ Find LCD + 3 ½ = 3³ ₆ 18⁸ ₆ Rename ⁸ ₆ as 1² ₆ Add ² ₆ = 19² ₆ Simplify 19⅓

20 Add mixed numbers Practice

21 Subtracting Mixed Numbers With Unlike Denominators Find 8 ½ - 6 ⅓ Estimate 9-6 = 3 Find the LCD: for ⅓ and ½ is 6 Add 8 ³ ₆ - 6 ² ₆ = 2 ⅟₆ Simplify 2 ⅟₆ is in simplest form

22 Subtracting Mixed Numbers with Find 7 2 ⁵ ₈ Renaming Write 7 as a mixed number Stack the problem Subtract Simplify if needed 7 ⁸ ₈ 2 ⁵ ₈ 5 ³ ₈

23 Another Example 11 ⅟₆ - 5 ⅔ Find LCD and stack it up Rename Simplify 5 ³ ₆ = 5 ½ 11 ⅟₆ = 10 ⁷ ₆ - 5 ⁴ ₆ = 5 ⁴ ₆ 5 ³ ₆

24 Subtract, simplify Practice Time

25 Multiplying Fractions and Mixed Numbers Lesson 4-4

26 Three Easy Steps Find ⁵ ₆ x ⅔ Step 1: multiply numerators: 5 x 2 = 10 Step 2: multiply denominators: 6 x 3 = 18 Step 3: simplify: ¹⁰ ₁₈ = ⁵ ₉

27 Multiply x Whole Number What is ² ₇ of 28? Rewrite as: ² ₇ x ²⁸ ₁ Simplify before multiplying: ² ₁ x ⁴ ₁ Multiply numerators: 2 x 4 = 8 Multiply denominators: 1 x 1 = 1 Simplify: ⁸ ₁ = 8

28 Mixed Number x Mixed Number Find 2 ³ ₅ x 4 ½ Step 1: rewrite as improper fraction: ¹³ ₅ x ⁹ ₂ Step 2: multiply numerators: 13 x 9 = 117 Step 3: multiply denominators: 5 x 2 = 10 Step 4: simplify and write as a mixed number: ¹¹⁷ ₁₀ = 11 ⁷ ₁₀

29 multiply Partner Practice

30 Dividing Fractions and Mixed Numbers Lesson 4-5

31 Definition Two numbers that when multiplied their product is 1 Facts/Characteristics to find the reciprocal of a fraction interchange, or flip the numerator and denominator Vocabulary Word ⅔ and ³ ₂ Reciprocals ⅔ = ⁴ ₆ are reciprocals of each other Examples Non-Examples

32 Find ⅔ ⁵ ₆ Fraction Fraction ⅔ ⁵ ₆ = ⅔ ⁶ ₅ Step 1: rewrite and multiply by the reciprocal of the divisor = 2 6 = 12 Step 2: multiply = 4 Step 3: simplify 5 * did you cancel?

33 Dividing Mixed Numbers Rewrite the mixed numbers as improper fractions and then follow the steps 9½ 2³ ₄ = ¹⁹ ₂ ¹¹ ₄ rewrite as improper fractions = ¹⁹ ₂ x ⁴ ₁₁ multiply by reciprocal of = ⁷⁶ ₂₂ divisor = ³⁸ ₁₁ = 3 ⁵ ₁₁ simplify

34 Partner Practice Divide Mixed Numbers

35 Divide Fractions and Whole Numbers Remember all whole numbers can be written with a denominator of 1 Find : ³ ₄ 5 Find: 5 ³ ₄ = ³ ₄ ⁵ ₁ = ⁵ ₁ ³ ₄ = ³ ₄ x ¹ ₅ = ⁵ ₁ x ⁴ ₃ = ³ ₂₀ = ²⁰ ₃ = 6 ⅔

36 Divide Practice

37 Solving Equations With Fractions Lesson 4-6

38 Solving equations with fractions Use inverse operations to get the variable alone on one side of the equation Ex: x- ⅓ = ⁵ ₆ + ⅓ = ⁵ ₆ + ⅓ add ⅓ to each side x = ⁵ ₆ + ⅓ find common denominator x = ⁵ ₆ + ² ₆ x = ⁷ ₆ = 1¹ ₆ simplify

39 Solve these equations Partner Practice