Worksheet on Multiplication of Rational Number

In worksheet on multiplication of rational number, the questions are based on multiplication of rational numbers; to find the multiplicative inverse and also to find the product. This exercise sheet on multiplication of rational numbers has different types of questions that can be practiced by the students to get more ideas to solve all types of questions in rational numbers for eighth grade math students.



1. Find each of the following products:

(i) 3/5 × (-7)/8

(ii) (-9)/2 × 5/4

(iii) (-6)/11 × 5/3

(iv) (-2)/3 × 6/7

(v) (-12)/5 × 10/-3

(vi) 25/-9 × 3/-10

(vii) 5/-18 × -9/20

(viii) (-13)/15 × (-25)/26

(ix) 16/-21 × 14/5

(x) (-7)/6 × 24

(xi) 7/24 × (-48)

(xii) (-13)/5 × (-10)



2. Verify each of the following:

(i) 3/7 × (-5)/9 = (-5)/9 × 3/7

(ii) (-8)/7 × 13/9 = 13/9 × (-8)/7

(iii) (-12)/5 × 7/(-36) = 7/-36 × (-12)/5

(iv) -8 × (-13)/12 = (-13)/12 × (-8)



3. Verify each of the following:

(i) (5/7 × 12/13) × 7/18 = 5/7 ×(12/13 × 7/8)

(ii) (-13)/24 × {(-12)/5 × 35/36} = {(-13)/24 × (-12)/5} × 35/36

(iii) {(-9)/5 × (-10)/3} × 21/-4 = (-9)/5 × {(-10)/3 × 21/-4}



4. Fill in the blanks:

(i) (-23)/17 × 18/35 = 18/35 × (_____)

(ii) -38 × (-7)/19 = (-7)/19 × (_____)

(iii) {15/7 × -21/10} × (-5)/6 = (_____) × {(-21)/10 × (-5)/6}

(iv) (-12)/5 × {4/15 × 25/-16} = {(-12)/5 × (4/15) × (_____)



5. Find the multiplicative inverse (i.e., reciprocal) of:

(i) 13/25

(ii) (-17)/12

(iii) (-7)/24

(iv) 18

(v) -16

(vi) -3/-5

(vii) -1

(viii) 0/2

(ix) 2/-5

(x) (-1)/8



6. Find the value of:

(i) (5/8)^-1

(ii) (-4/9)^-1

(iii) (-7)^-1

(iv) (1/-3)^-1



7. Verify the following:

(i) 3/7 × {5/6 + 12/13} = (3/7 × 5/6) + (3/7 × 12/13)

(ii) -15/4 × (3/7 + (-12)/5) = (-15/4 × 3/7) + (-15/4 × (-12)/5)

(iii) (-8/3 + -13/12) × 5/6 = (-8/3 × 5/6) + (-13/12 × 5/6)

(iv) -16/7 × {-8/9 + (-7)/6} = (-16/7 × (-8)/9) + ((-16)/7 × -7/6)



8. Name the property of multiplication illustrated by the following statements:

(i) -15/8 × -12/7 = -12/7 × -15/8

(ii) {(-2)/3 × 7/9} × (-9)/5 = (-2)/3 × {7/9 × (-9)/5}

(iii) (-3)/4 × {(-5)/6 + 7/8 = {(-3)/4 × (-5)/6} + {(-3)/4 × 7/8}

(iv) (-16)/9 × 1 = 1 × (-16)/9 = (-16)/9

(v) (-11)/15 × 15/-11 = 15/-11 × (-11)/15 = 1

(vi) -7/5 × 0 = 0



9. Fill in the blanks:

(i) The product of a rational number and its reciprocal is __________ .

(ii) Zero has __________ reciprocal.

(iii) The numbers __________ and __________ are their own reciprocals.

(iv) Zero is __________ the reciprocal of any number.

(v) The reciprocal of a, where a ≠ 0, is __________ .

(vi) The reciprocal of 1/a, where a ≠ 0, is __________ .

(vii) The reciprocal of a positive rational number is __________ .

(viii) The reciprocal of a negative rational number is __________ .


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