Multiplying & Dividing Rational Numbers

Multiplying & Dividing Rational Numbers Recall: A number in the form 𝑚 𝑛 where m and n are integers and n is different from zero, is called a rational number. Proper Fractions: A proper fraction is a fraction where the numerater is smaller than the denominator. Ex: 2/3, 7/9. etc Improper Fractions: An improper fraction is a fraction where the numerator is greater or equal to the denominator. Ex: 3/2,9/7,5/7, etc. Mixed Numbers: A mixed number is a combination of a whole number and a proper fraction. Ex: 1 2/3, 3 2/5, etc. To multiply fractions, you multiply the numerators together and the denominators together. , provided and . 𝑎𝑏 × 𝑐 𝑑 = 𝑎 ×𝑐 𝑏 ×𝑑 𝑏 ≠ 0 𝑑 ≠ 0 You can simplify fractions before you multiply (reduce to lowest terms). To reduce a fraction to lowest terms, divide the numerator and the denominator by the greatest factor. Common factor means a number that divides evenly into the numerator and denominator. Example 1: Evaluate the following. a) − 23 × 6 −7 = −2 ×6 3 × −7 ( ) =− 12 −21 = 1221 = 47

b) – −5 12 × 36 −5 =− −5 ( )×36 12 ×−5 =− −180 −60 =− 180 60 =− 3 c) 34 × 35 × 2 13 = 35 × 35 × 73 = 34 × 15 × 71 = 3 ×1 ×74 ×5 ×1 = 2120 Homework: Pg. 37: #3 Reduce to lowest terms. a) 5/(-10)=-5/10=1/2 e) –(-6)/11=-(-6/11)=6/11 i) – (-15)/(-35)=-15/35=-3/7 Pg. 44 #1: Write those numbers to 8 decimal places rounding where necessary. a) 3. 23 = 3. 23232323 b) 42. 307 = 42. 307307307 = 402. 30730731 d) 690. 045 = 690. 045454545 =690.04545455

e)-2.6513=-2.6513513513 =-2.65135135 #2 Write the repeating decimals, using a dot or a bar over the repeating digits a) 6. 3333… = 6. 3 b) 0. 17171717… = 0. 17 d) 0. 0363636… = 0. 036 f) − 46. 23333… =− 46. 23 Pg. 203: #1 Write each ratio as a percent. a) 7:100=7/100=7% d)0.8 : 1000=0.8/100=0.8% #2 Express each decimal as a percent. a) 0. 38 = 0. 38 ×100% = 38% e) 0. 035 = 0. 035 ×100% = 3. 5% m) 3. 06 = 3. 06 ×100% = 306% Either multiply by 100% OR move the decimal place two digits to the right. #3 Express each percent as a decimal. i)137% a)24%=24%/100%=0.24 d)3%=3%/100%=0.03 Divide by 100% OR move the decimal place two digits to the left

The reciprocal of any rational number m/n, where m and n are integers anddifferent from zero, is defined to be the rational number n/m. Example 2: What is the reciprocal of a)4=4/1 The reciprocal of 4 is 1/4. b) 2/3 The reciprocal of 2/3 is 3/2. To divide rational numbers, multiply the numerator by the reciprocal of thedenominator. 𝑎𝑏 ÷ 𝑐 𝑑 = 𝑎𝑏 × 𝑑 𝑐 , provided , and . = 𝑎 ×𝑑 𝑏 ×𝑐 𝑏 ≠ 0, 𝑐 ≠ 0 𝑑 ≠ 0 Example 3: Evaluate the following a) − 7 10 ÷ 4 −9 =− 7 10 × −9 4 ⎡ ⎣ ⎤ ⎦ =− 7 × −9 ( ) 10 ×4 ⎡ ⎣ ⎤ ⎦ =− −63 40 ( ) = 6340 b) − 75 3 ÷ − 15 4 =− 25 1 ÷ − 15 4 =− 25 1 × 4 −15 =− 51 × 4 −3

= −5 ×4 1 × −3 ( ) =− 20 −3 = 20 3 c) 12 −39 ÷ − 10 −9 ÷ 18 −5 = 12 −39 × −9 −10 × −5 18 = 6 × −3 ( )× −1 ( ) −13 ( ) −1 ( )×18 = 18 13 ×18 = 1 13