Chapter 1 - XYZ Custom Plus

20Chapter 1 The BasicsE Multiplication with FractionsThe last concept we want to cover in this section is the concept of reciprocals.Understanding reciprocals requires some knowledge of multiplication with fractions.To multiply two fractions, we simply multiply numerators and multiplydenominators._13. Multiply 2 3 ⋅ _ 7 9NoteIn past math classesyou may have writtenfractions like 7_ 3(improper fractions) as mixednumbers, such as 2 1_ 3. In algebrait is usually better to write themas improper fractions rather thanmixed numbers.14. Multiply 8 1 _5 .ExAmplE 13SOlutiON_Multiply 3 4 ⋅ _ 5 7 .The product of the numerators is 15, and the product of the denominatorsis 28:3_4 ⋅ _ 5 7 = _ 3 ⋅ 54 ⋅ 7 = _ 1528ExAmplE 14Multiply 7 _ 1 3 ._SOlutiON The number 7 can be thought of as the fraction 7 1 :7 1 _3 = 7 _1 1 __3 = 7 ⋅ 11 ⋅ 3 = _ 7 315. Expand and multiply 11 _12 2 .ExAmplE 15SOlutiONhaveExpand and multiply _ 2 3 3 .Using the definition of exponents from the previous section, we 2 _3 3 = 2 _3 ⋅ 2 _3 ⋅ 2 _3 = 8 _27fReciprocalsWe are now ready for the definition of reciprocals.DefinitionTwo numbers whose product is 1 are called reciprocals.ExAmplESGive the reciprocal of each number.Give the reciprocal of each number.16. 6Number16. 5Reciprocal1_5_Because 5 1 _=5 5 _1 1 _=5 5 5 = 117. 317. 21_2_Because 2 1 _=2 2 _1 1 _=2 2 2 = 118. 1 _218.1_3_3 Because 1 3 (3) = _ 1 _3 3 _=1 3 3 = 119. 2 _319.3_44_3Because 3 _4 4 __=3 1212 = 1Answers13. 14 _2714. 8 _515. 121 _14416. 1 _617. 1 _318. 2 19. 3 _2