Go Math! Middle School Grade 7 Practice Fluency Workbook 1st Edition Chapter 3 Rational Numbers
HMH Grade 7 Rational Numbers Exercise 3.5 solutions Page 23 Problem 1 Answer
An expression is given as, 1/2÷(−3).
It is required to find the quotient.
To find the quotient, first rewrite the problem and then multiply with the reciprocal.
Rewrite the problem to multiply by the reciprocal.
Hence, 1/2÷(−3)=1/2⋅(−1/3).
Multiply with the reciprocal.
1/2⋅(−1/3)=1⋅(−1)/2⋅3
1/2⋅(−1/3)=−1/6
Hence, 1/2⋅(−1/3)=−1/6.
Check the sign.
A positive divided by a negative is negative.
So, 1/2÷(−3)=−1/6.
The quotient of 1/2÷(−3) is −1/6.
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HMH Middle School Grade 7 Chapter 3 Page 23 Problem 2 Answer
An expression is given as,−6÷(−3/4).
It is required to find the quotient.
To find the quotient, first rewrite the problem and then multiply with the reciprocal.
Rewrite the problem to multiply by the reciprocal.
Hence, −6÷(−3/4)=−6⋅(−4/3).
Multiply with the reciprocal.
−6⋅(−4/3)=(−6)⋅(−4)/3
−6⋅(−4/3)=(−2⋅3)⋅(−4)/3
−6⋅(−4/3)=(−2)⋅(−4)
−6⋅(−4/3)=8
Hence, −6⋅(−4/3)=8.
Check the sign.
A negative divided by a negative is positive.
So, −6÷(−3/4)=9.
The quotient of −6÷(−3/4) is 9.
HMH Middle School Grade 7 Chapter 3 Page 23 Problem 3 Answer
Practice Fluency Workbook Chapter 3 Exercise 3.5 answers Page 23 Problem 4 Answer
An expression is given as, 5.25/15.
It is required to find the quotient.
To find the quotient, first rewrite the problem and then multiply with the reciprocal.
Rewrite the problem to multiply by the reciprocal.
5.25/15=51/4/15
5.25/15=21/4⋅1/15
Hence, 5.25/15=21/4⋅1/15.
Multiply with the reciprocal.
21/4⋅1/15=3⋅7/4⋅1/3⋅5
21/4⋅1/15=7⋅1/4⋅5
21/4⋅1/15=7/20
Hence,21/4⋅1/15=7/20.
Check the sign.
A positive divided by a positive is positive.
So, 5.25/15=7/20.
The quotient of 5.25/15 is 7/20.
HMH Middle School Grade 7 Chapter 3 Page 23 Problem 5 Answer
An expression is given as, −0.125÷(−0.5).
It is required to find the quotient.
To find the quotient, first rewrite the problem and then multiply with the reciprocal.
Rewrite the problem to multiply by the reciprocal.
−0.125÷(−0.5)=−1/8÷(−1/2)
−0.125÷(−0.5)=−1/8⋅(−2)
Hence, −0.125÷(−0.5)=−1/8⋅(−2).
Multiply with the reciprocal.
1/8⋅(−2)=(−1)⋅(−2)/8
1/8⋅(−2)=2/8
1/8⋅(−2)=1/4
Hence, 1/8⋅(−2)=1/4.
Check the sign.
A positive divided by a negative is positive.
So, −0.125÷(−0.5)=1/4.
The quotient of −0.125÷(−0.5) is 1/4.
HMH Middle School Grade 7 Chapter 3 Page 23 Problem 6 Answer
An expression is given as, −1/7÷(−3/14).
It is required to find the quotient.
To find the quotient, first rewrite the problem and then multiply with the reciprocal.
Rewrite the problem to multiply by the reciprocal.
Hence, −1/7÷−3/14=−1/7⋅(−14/3).
Multiply with the reciprocal.
−1/7⋅(−14/3)=−1/7⋅−2⋅7/3
−1/7⋅(−14/3)=(−1)⋅(−2)/3
−1/7⋅(−14/3)=2/3
Hence, −1/7⋅(−14/3)=2/3.
Check the sign.
A positive negative by a negative is positive.
So, −1/7÷(−3/14)=2/3.
The quotient of −1/7÷(−3/14) is 2/3.
7th Grade HMH Rational Numbers Exercise 3.5 step-by-step Page 23 Problem 7 Answer
An expression is given as, (3/2)/(−9/8).
It is required to find the quotient.
In order to find the quotient, find the multiplicative inverse of −9/8 and multiply it with 3/2.
Find the multiplicative inverse of −9/8.
So, the multiplicative inverse of −9/8 is −8/9.
Now, multiply −8/9 with 3/2.
(3/2)/(−9/8)=3/2⋅(−8/9)
(3/2)/(−9/8)=−4/3
Hence, the quotient for the given expression is−4/3.
The quotient for the given expression is −4/3.
HMH Middle School Grade 7 Chapter 3 Page 23 Problem 8 Answer
An expression is given as, −11/2÷31/3.
It is required to find the quotient.
In order to find the quotient, find the multiplicative inverse of 31/3 and multiply it with−11/2.
Convert the mixed fraction into an improper fraction.
−11/2÷31/3=−3/2÷10/3.
Find the multiplicative inverse of 10/3.
So, the multiplicative inverse of 10/3 is 3/10.
Now, multiply 3/10 with −3/2.
−3/2÷10/3=−3/2⋅(3/10)
−3/2÷10/3=−3/2⋅(3/10)
−3/2÷10/3=−9/20
Hence, −3/2÷10/3=−9/20.
The quotient for the given expression is −9/20.
Rational Numbers Grade 7 Practice Fluency Workbook help Exercise 3.5 Page 23 Problem 9 Answer
An expression is given as,21/4÷3/8.
It is required to find the quotient.
In order to find the quotient, find the multiplicative inverse of 3/8 and multiply with 21/4.
Convert the mixed fraction into an improper fraction.
21/4÷3/8=9/4÷3/8.
Find the multiplicative inverse of 3/8.
So, the multiplicative inverse of 3/8 is 8/3.
Now, multiply 8/3 with 9/4.
9/4÷3/8=9/4⋅8/3
9/4÷3/8=72/12
9/4÷3/8=6
Hence, 9/4÷3/8=6.
The quotient for the given expression is 6.
HMH Middle School Grade 7 Chapter 3 Page 23 Problem 10 Answer
An expression is given as, 4.2−2.4.
It is required to find the quotient.
In order to find the quotient, find the multiplicative inverse of −24/10 and multiply it with 42/10.
Given, 4.2−2.4.
Divide both the numerator and the denominator by 10.
4.2−2.4=42/10−24/10.
Find the multiplicative inverse of −24/10.
So, the multiplicative inverse of −24/10 is −10/24.
Now, multiply −10/24 with 42/10.
42/10−24/10=42/10⋅(−10/24)
42/10−24/10=−420/240
42/10−24/10=−7/4
Hence, 42/10−24/10=−7/4.
The quotient for the given expression is −7/4.
Grade 7 Rational Numbers Exercise 3.5 explained step-by-step Page 23 Problem 11 Answer
An expression is given as, −5/8÷(−5/16).
It is required to find the quotient.
In order to find the quotient, find the multiplicative inverse of −5/16 and multiply it with−5/8.
Find the multiplicative inverse of −5/16.
So, the multiplicative inverse of −5/16 is −16/5.
Now, multiply −16/5 with −5/8.
−5/8÷(−5/16)=−5/8⋅(−16/5)
−5/8÷(−5/16)=80/40
−5/8÷(−5/16)=2
Hence, −5/8÷(−5/16)==2.
The quotient for the given expression is 2.
HMH Middle School Grade 7 Chapter 3 Page 23 Problem 12 Answer
It is given that, 0.25÷_____=−0.25.
It is required to fill in the blank.
In order to fill in the blank, let the number to be filled in blank be x. Find the multiplicative inverse of x and multiply it with 0.25. Then, simplify further.
Let the number to be filled in the blank be x .
So, the multiplicative inverse of x is 1/x.
Now, multiply 1/x with 0.25.
0.25÷x=−0.25
0.25⋅1/x=−0.25
0.25/x=−0.25
Multiply both sides with x.
0.25=−0.25x
Divide both sides by −0.25.
Hence, x=−1.
To make the given statement true, the blank has to be filled with the value −1.
It is given that, −1/2÷_____=−7/3.
It is required to fill in the blank.
In order to fill in the blank, let the number to be filled in blank be x, find the multiplicative inverse of x and multiply with −1/2.
Then, simplify further.
Let the number to be filled in the blank be x.
Find the multiplicative inverse of x.
So, the multiplicative inverse of x is 1/x.
Now, multiply 1/x by −1/2.
−1/2÷x=−7/3
−1/2⋅1/x=−7/3
−1/2x=−7/3
Multiply by x on both sides.
Hence, −1/2=−7/3x.
Multiply by −3/7 on both sides of −1/2=−7/3x.
x=−1/2⋅(−3/7)
x=3/14
Hence, x=3/14.
To make the given statement true, the blank has to be filled with the value 3/14.
HMH Chapter 3 Rational Numbers Exercise 3.5 answers Page 23 Problem 14 Answer
It is given that, 1/7÷_____=14.
It is required to fill in the blank.
In order to fill in the blank, let the number to be filled in blank be x, find the multiplicative inverse of x and multiply with 1/7.
Then, simplify further.
Let the number to be filled in the blank be x.
Find the multiplicative inverse of x.
So, the multiplicative inverse of x is 1/x.
Now, multiply 1/x with 1/7.
1/7÷x=14
1/7⋅1/x=14
1/7x=14
Hence, 1/7x=14.
HMH Middle School Grade 7 Chapter 3 Page 23 Problem 15 Answer
It is given that the total plant food is of 8 pounds.
It is required to find how many quarter-pound (1/4) packets can be made out of the total plant food.
In order to find how many quarter-pound (1/4) packets can be made out of total plant food, make an expression using given information and simplify.
Let the number of packets that can be made out be x.
Make an expression using the given information.
8÷1/4=x
Further, evaluate the multiplicative inverse of 1/4.
So, the multiplicative inverse of 1/4 is 4.
Now, multiply 4 with 8.
8÷1/4=x
8⋅4=x
32=x
Hence, 32=x.
The number of packets that can be made are 32.
Online help for Rational Numbers Grade 7 Exercise 3.5 Page 23 Problem 16 Answer
It is given that the assembly of a machine takes 3/4 hour and there are 12 steps in total.
It is required to find the average time for each step.
In order to find the average time for each step, make an expression using the given information and simplify.
Let the average time for each step be x.
The assembly takes 3/4 hour and there are 12 steps in total.
Make an expression using given information
3/4÷12=x.
Evaluate the multiplicative inverse of 12.
So, the multiplicative inverse of 12 is 1/12.
Now, multiply 1/12 with 3/4.
3/4÷12=x
3/4⋅1/12=x
3/48=x
1/16=x
Hence, 1/16=x.
The average time for each step is 1/16 hour.
HMH Middle School Grade 7 Chapter 3 Page 23 Problem 17 Answer
It is given that the total length of a cable is 35m and it is cut into pieces of measure 1.25m.
It is required to find the number of pieces in which the cable is cut.
In order to find the number of pieces, make an expression using the given information and simplify.
Let the number of pieces be x.
The total length of the cable is 35m and it is cut into pieces which measure 1.25m.
Make an expression using given information.
Hence, 35÷1.25=x.
Evaluate the multiplicative inverse of 1.25.
So, the multiplicative inverse of 1.25 is 1/1.25.
Now, multiply 1/1.25 with 35.
35÷1.25=x
35⋅1/1.25=x
35/1.25=x
x=28
Hence, x=28.
The number of pieces in which the cable is cut are 28.
Step-by-step Rational Numbers solutions for 7th Grade Exercise 3.5 Page 23 Problem 18 Answer
It is given that 41/8 tons of gravel are spread evenly across 21/6 acres.
It is required to find how many tons of gravel is on each acre.
In order to find how many tons of gravel is on each acre, make an expression using the given information and simplify.
Let the tons of gravel that are on each acre be x.
Make an expression using the given information.
Since 41/8 tons of gravel is spread evenly across 21/6 acres,
41/8÷21/6=x
Convert the mixed fraction into an improper fraction.
Hence, 33/8÷13/6=x.
Evaluate the multiplicative inverse of 13/6.
So, the multiplicative inverse of 13/6 is 6/13.
Now, multiply 6/13 with 33/8.
33/8÷13/6=x
33/8⋅6/13=x
99/52=x
Hence, 99/52=x.
The tons of gravel on each acre are 99
52 tons or 147
52 tons.
HMH Middle School Grade 7 Chapter 3 Page 24 Problem 19 Answer
An expression is given as, 41/4÷31/2.
It is required to determine the sign of the quotient of the given expression.
To determine the sign of the quotient of the given expression, it is necessary to check the signs of the terms in the expression.
The terms in the given expression, 41/4 and 31/2 are both positive.
The quotient of division of two positive terms invariably gives a positive result.
Hence, the required sign of the quotient will be positive.
The sign of the quotient of the given expression 41/4÷31/2 will be positive.
Exercise 3.5 Rational Numbers Practice Workbook Grade 7 explained Page 24 Problem 20 Answer
An expression is given as,−3.5÷0.675.
It is required to determine the sign of the quotient of the given expression.
To determine the sign of quotient of the given expression, it is necessary to check the signs of the terms in the expression.
The terms in the given expression, −3.5 is a negative term and 0.675 is a positive term.
The quotient of division of a positive and a negative term invariably gives a negative result.
Hence, the required sign of the quotient will be negative.
The sign of the quotient of the given expression −3.5÷0.675 will be negative.
HMH Middle School Grade 7 Chapter 3 Page 24 Problem 21 Answer
An expression is given as, −1/7÷(−5/9).
It is required to find the quotient of the given expression by completing each step.
To find the quotient of the given expression by completing each step, it is necessary to reciprocate the second term of the expression.
Rescript the problem to multiply by the reciprocal.
−1/7÷(−5/9)=−1/7⋅(−9/5) Multiply.
−1/7⋅(−9/5)=(−1)⋅(−9)/7⋅5
(−1)⋅(−9)/7⋅5=9/35
Assign a sign to the quotient.
It is known that a negative divided by a negative is positive. Hence, the result is obtained as positive.
−1/7÷(−5/9)=9/35
The required quotient is 9/35.
The quotient of the given expression−1/7÷(−5/9) after completing each step is 9/35.
Page 24 Problem 22 Answer
An expression is given as,7/8÷8/9.
It is required to find the quotient of the given expression by completing each step.
To find the quotient of the given expression by completing each step, it is necessary to reciprocate the second term of the expression.
Re script the problem to multiply by the reciprocal.
7/8÷8/9=7/8⋅9/8 Multiply.
7/8⋅9/8=7⋅9/8⋅8
7⋅9/8⋅8=63/64
Assign a sign to the quotient.
It is known that a positive divided by a positive is positive. Hence, the result is obtained as positive.
7/8÷8/9=63/64
The required quotient is 63/64.
The quotient of the given expression 7/8÷8/9 after completing each step is 63/64.