HMH Middle School Grade 7 Practice Fluency Workbook 1st Edition Chapter 3 Rational Numbers
HMH Grade 7 Rational Numbers Exercise 3.4 Solutions Page 21 Problem 1 Answer
An expression is given as, 4(−1/2).
It is required to find the product of the given expression using a number line.
To find the product of the given expression using a number line, it is necessary to represent the expression on a number line.
In the given expression,−1/2 is multiplied 4 times.
So, there will be 4 jumps of 1/2 or 0.5unit each along the number line.
Because the two numbers have different signs, hence, there will be a jump from 0 to the left.
The above-mentioned is represented on a number line as shown below.
The numbers where each jump ends are−1/2,−1,−11/2 and −2.
The number where the final jump ends is −2.
Hence, the required result is−2.
The product of the given expression4(−1/2) using a number line is −2. The same is represented on a number line as shown below.
Read and Learn More HMH Middle School Grade 7 Practice Fluency Workbook 1st Edition Solutions
HMH Middle School Grade 7 Chapter 3 Page 21 Problem 2 Answer
The product of the given expression−5(−2/3) using a number line is 10/3. The same is represented on a number line as shown below.
Practice Fluency Workbook Chapter 3 Rational Numbers Answers Page 21 Problem 3 Answer
An expression is given as, −2(3.1).
It is required to find the product of the given expression.
To find the product of the expression −2(3.1), it is necessary to operate multiplication on the given expression.
Perform multiplication on the expression −2(3.1).
Multiply the numerical values of the two numbers ignoring the negative sign and the decimal point.
2(31)=2⋅31
2(31)=62
Now, it is known the decimal point is placed in the product in such a way that the number of decimal places in the product is the sum of the decimal places in the factors.
Also, the sign of the product will be negative since the given numbers have different signs.
Hence, the required product is obtained as −6.2.
The product of the given expression −2(3.1) is−6.2.
HMH Middle School Grade 7 Chapter 3 Page 21 Problem 4 Answer
An expression is given as, 4(−5.4).
It is required to find the product of the given expression.
To find the product of the expression 4(−5.4), it is necessary to operate multiplication on the given expression.
Perform multiplication on the expression 4(−5.4).
Multiply the numerical values of the two numbers ignoring the negative sign and the decimal point.
4(54)=4⋅54
4(54)=216
Now, it is known the decimal point is placed in the product in such a way that the number of decimal places in the product is the sum of the decimal places in the factors.
Also, the sign of the product will be negative since the given numbers have different signs.
Hence, the required product is obtained as −21.6.
The product of the given expression4(−5.4) is−21.6.
Hmh Middle School Math Workbook Chapter 3 Guide Page 21 Problem 5 Answer
An expression is given as, −3.3(6).
It is required to find the product of the given expression.
To find the product of the expression −3.3(6), it is necessary to operate multiplication on the given expression.
Perform multiplication on the expression −3.3(6).
Multiply the numerical values of the two numbers ignoring the negative sign and the decimal point.
33(6)=33⋅6
33(6)=198
Now, it is known that the decimal point is placed in the product in such a way that the number of decimal places in the product is the sum of the decimal places in the factors.
Also, the sign of the product will be negative since the given numbers have different signs.
Hence, the required product is obtained as −19.8.
The product of the given expression−3.3(6) is−19.8.
HMH Middle School Grade 7 Chapter 3 Page 21 Problem 6 Answer
An expression is given as, 4.5(8).
It is required to find the product of the given expression.
To find the product of the expression 4.5(8), it is necessary to operate multiplication on the given expression.
Perform multiplication on expression 4.5(8).
Multiply the numerical values of the two numbers ignoring the decimal point.
45(8)=45⋅8
45(8)=360
Now, it is known that the decimal point is placed in the product in such a way that the number of decimal places in the product is the sum of the decimal places in the factors.
Also, the sign of the product will be positive since the given numbers have the same signs.
Hence, the required product is obtained as 36.0 or 36.
The product of the given expression 4.5(8) is 36.
7th Grade HMH Rational Numbers Exercise 3.4 step-by-step Page 21 Problem 7 Answer
An expression is given as, 2(−1.05).
It is required to find the product of the given expression.
Multiply the given integers, also multiply the sign.
Write the given expression.
2(−1.05)
Now, multiply both the integers, also it is well known that when the(−) sign is multiplied with (+) sign, then, the result gives (−) sign.
So, 2(−1.05)=−2.1
The product of 2(−1.05) is −2.1.
HMH Middle School Grade 7 Chapter 3 Page 21 Problem 8 Answer
An expression is given as, −2.05(4).
It is required to find the product of the given expression.
Multiply the given integers, also multiply the sign
Write the given expression.
−2.05(4)
Now, multiply both the integer, also it is well known that when(+) sign is multiplied with a (−) sign and the result gives a (−)sign.
So,−2.05(4)=−8.2
The product of −2.05(4) is −8.2.
Rational numbers Grade 7 Practice Fluency Workbook help Page 21 Problem 9 Answer
An expression is given as,−3.5(−9).
It is required to find the product of the given expression.
Multiply the given integers, also multiply the sign.
Write the given expression.
−3.5(−9).
Now, multiply both the integers, also it is well known that when the(−) sign is multiplied with(−) sign, then, the result gives (+) sign.
So,−3.5(−9)=31.5
The product of the given integer,−3.5(−9) is 31.5.
HMH Middle School Grade 7 Chapter 3 Page 21 Problem 10 Answer
An expression is given as, (2/3)×(−6)×5.
It is required to find the product of the given expression.
Multiply the given integers, also multiply the sign.
Write the given expression.
(2/3)×(−6)×5.
Now, multiply both the integer, also it is well known that when (+) sign is multiplied with a (−) sign and the result gives a (−) sign.
So,(2/3)×(−6)×5=2(−6)(5)/3
(2/3)×(−6)×5=−60/3
(2/3)×(−6)×5=−20
The product of the given integer, (2/3)×(−6)×5 is −20.
Grade 7 Math Practice Fluency Workbook Exercise 3.4 explained Page 21 Problem 11 Answer
An expression is given as, (−3/5)(−10/3)(−2/9).
It is required to find the product of the given expression.
Multiply the given integers, also multiply the sign.
Write the given expression.
(−3/5)(−10/3)(−2/9)
Now, multiply both the integers, also it is well known that when the (−) sign is multiplied with (−) sign, then, the result gives (+) sign.
Then, again, (+) sign is multiplied with a (−) sign and the result gives a (−) sign.
Or, the(−) sign can be taken as common from the expression.
(−3/5)(−10/3)(−2/9)=−(3⋅10⋅2)/5⋅3⋅9
(−3/5)(−10/3)(−2/9)=−60/135
(−3/5)(−10/3)(−2/9)=−12/27
Hence,(−3/5)(−10/3)(−2/9)=−12/27.
The product of the given integer, (−3/5)(−10/3)(−2/9) is−12/27.
HMH Middle School Grade 7 Chapter 3 Page 21 Problem 12 Answer
An expression is given as, −7×(−3/5)(15/7).
It is required to find the product of the given expression.
Multiply the given integers, also multiply the sign.
Write the given expression.
−7×(−3/5)(15/7).
Now, multiply both the integers, also it is well known that when the (−) sign is multiplied with (−) sign, then, the result gives (+) sign.
−7×(−3/5)(15/7)=−7(−3)(15)/5×7
−7×(−3/5)(15/7)=315/35
−7×(−3/5)(15/7)=9
Hence, −7×(−3/5)(15/7)=9.
The product of the given integer,−7×(−3/5)(15/7) is 9.
Rational Numbers problems explained for 7th Grade Page 21 Problem 13 Answer
An expression is given as, 2(4)(1/16).
It is required to find the product of the given expression.
Multiply the given integers, also multiply the sign.
Write the given expression.
2(4)(1/16).
Now, multiply both the integers.
So, 2(4)(1/16)=2(4)(1)/16
2(4)(1/16)=8/16
2(4)(1//16)=1/2
Hence,2(4)(1/16)=1/2.
The product of the given integer, 2(4)(1/16) is 1/2.
HMH Middle School Grade 7 Chapter 3 Page 21 Problem 14 Answer
It is given that a box-shaped fish trap measures 1/4×2/3×3/4m.
It is required to find the volume of the fish.
Since three dimensions are given of the fish, it is a cuboid.
Multiply the given integers as the volume of a cuboid is given by the product of its length, height and breadth.
Given, a box-shaped fish trap measures 1/4×2/3×3/4m.
The fish is in the shape of a cuboid.
Let V be the volume of the fish.
V=lbh , where, l,b,h are the length, height and breadth respectively.
V=1/4⋅2/3⋅3/4
V=1⋅2⋅3/4⋅3⋅4
V=6/48
V=1/8m
Hence, V=1/8m.
The volume of the box-shaped fish trap is 1/8m.
Exercise 3.4 Rational Numbers Grade 7 Practice Workbook help Page 21 Problem 15 Answer
It is given that the temperature at noon is 75∘F. The temperature drops every half hour by 3∘F.
It is required to find the temperature at 4PM.
Multiply the given integer with the interval of every half an hour till 4PM.
As, it is given, the temperature at noon is 75∘F. Also, temperature drops at every half hour. It could be written as−3∘F.
So, Since 12 noon to 4PM, it has 8 intervals of every half an hour.
So, the total temperature drop between 12 noon to 4PM is,−3∘F⋅8=−24∘F.
At noon, the temperature was 75∘F and till 4PM it falls by −24∘F.
So, 75−24=51∘F.
The temperature at 4PM will be 51∘F.
HMH Middle School Grade 7 Chapter 3 Page 22 Problem 16 Answer
An expression is given as,6×1/4.
It is required to find that how many times 1/4 is multiplied and in which direction on the number line. It is also required to find the product of the given expression.
To find that how many times 1/4 is multiplied, multiply the number with 1/4.
In the given expression, 1/4 is multiplied six times.
These two numbers have the same sign, so, jump from 0 to the right side of the number line.
Move from 0 six times to 1/4,2/4,3/4,4/4,5/4,6/4.
Find the product of the given expression.
6×1/4=6/4
6×1/4=3/2
6×1/4=11/2
Hence, 6×1/4=11/2.
In the expression, 1/4 is multiplied six times in the right direction of the number line from 0.
The product of 6×1/4 is 11/2.
HMH Middle School Grade 7 Chapter 3 Page 22 Problem 17 Answer
An expression is given as, −8(−3.3).
It is required to find that how many times 3.3 is multiplied and in which direction on the number line.
It is also required to find the product of the given expression.
To find that how many times 3.3 is multiplied, multiply the number with 3.3.
In the given expression, 3.3 is multiplied eight times.
These two numbers have the same sign, so, jump from 0 to the right side of the number line.
Move eight times from 0 to 3.3, 6.6, 9.9, 13.2, 16.5, 19.8, 23.1, 26.4.
Find the product of the given expression.
−8(−3.3)=26.4
Hence,−8(−3.3)=26.4.
In the expression, 3.3 is multiplied eight times in the right direction of the number line from 0.
The product of −8(−3.3)
HMH Middle School Grade 7 Chapter 3 Page 22 Problem 18 Answer
An expression is given as, 4.6×5.
It is required to find that how many times 4.6 is multiplied and in which direction on the number line. It is also required to find the product of the given expression.
To find that how many times 4.6 is multiplied, multiply the number with 4.6.
In the given expression, 4.6 is multiplied five times.
These two numbers have the same sign, so, jump from 0 to the right side of the number line.
Move five times from 0 to 4.6,9.2,13.8,18.4,23.
Find the product of the given expression.
Hence, 4.6×5=23.
In the expression, 4.6 is multiplied six times in the right direction of the number line from 0. The product of 4.6×5 is 23.