HMH Middle School Grade 7 Practice Fluency Workbook 1st Edition Chapter 3 Rational Numbers
HMH Grade 7 Practice Fluency Workbook Chapter 3 Exercise 3.2 Solutions Page 17 Problem 1 Answer
An expression is given as, −3+4.
An expression is required to solve the given expression using a number line.
On the number line, start from −3 and move towards 4 intervals to the right because the number 4 is positive.
Start from −3 and move 4 intervals to the right because the number 4 is positive.
And, the result is 1.
The sum of −3+4 is 1.
HMH Middle School Grade 7 Chapter 3 Page 17 Problem 2 Answer
An expression is given as, 1+(−8).
An expression is required to solve the given expression using a number line.
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Rational Numbers Exercise 3.2 Chapter 3 Answers HMH Grade 7 Workbook Page 17 Problem 3 Answer
An expression is given as, 4+5.
An expression is required to solve the given expression.
To solve the given expression, first, determine the absolute values of the terms and then add both the numbers.
Determine the absolute values of the terms.∣4∣=4
∣5∣=5
Because the terms have the same sign, the sum has the sign of the terms, hence, the sum is positive.
Determine the sum.
4+5=+(∣4∣+∣5∣)
4+5=+9
4+5=9
Hence, 4+5=9.
The sum of 4+5 is 9.
HMH Middle School Grade 7 Chapter 3 Page 17 Problem 4 Answer
An expression is given as, −3+1/2.
An expression is required to solve the given expression.
To solve the given expression, first determine the absolute values of the terms and then add both the numbers.
Determine the absolute values of the terms.
∣−3∣=3
∣1/2∣
=1/2
The terms have different signs.
The sign of the sum is the sign of the term with the greater absolute value.
Since, ∣3∣>∣1/2∣, the sum is negative.
Determine the sum.
−3+1/2=−(∣3∣−∣1/2∣)
−3+1/2=−(3−1/2)
−3+1/2=−5/2
Hence, −3+1/2=−5/2.
The sum of−3+1/2 is −5/2.
Step-By-Step Solutions For Exercise 3.2 Rational Numbers Hmh Grade 7 Practice Workbook Page 17 Problem 5 Answer
An expression is given as, −2/9+3/9.
An expression is required to solve the given expression.
To solve the given expression, first, determine the absolute values of the terms and then add both the numbers.
Determine the absolute values of the terms.
∣−2/9∣=2/9
∣3/9∣=3/9
The terms have different signs.
The sign of the sum is the sign of the term with the greater absolute value.
Since, ∣3/9∣>∣−2/9∣ , the sum is positive.
Determine the sum.
−2/9+3/9=+(∣3/9∣−∣−2/9∣)
−2/9+3/9=+1/9
−2/9+3/9=1/9
Hence, −2/9+3/9=1/9.
The sum of−2/9+3/9 is 1/9.
HMH Middle School Grade 7 Chapter 3 Page 17 Problem 6 Answer
An expression is given as, −3.5+(−4.9).
An expression is required to solve the given expression.
To solve the given expression, first, determine the absolute values of the terms and then add both the numbers.
Determine the absolute values of the terms.
∣−3.5∣=∣3.5∣
∣−4.9∣=4.9
Because the terms have the same sign, the sum has the sign of the terms, hence, the sum is negative.
Determine the sum.
−3.5+(−4.9)=−(∣−3.5∣+∣−4..9∣)
−3.5+(−4.9)=−(3.5+4.9)
−3.5+(−4.9)=−8.4
Hence, −3.5+(−4.9)=−8.4.
The sum of−3.5+(−4.9) is −8.4.
Exercise 3.2 Rational Numbers Solutions For HMH Middle School Grade 7 Workbook Page 17 Problem 7 Answer
An expression is given as, −21/4+(−31/4).
An expression is required to solve the given expression.
To solve the given expression, first, determine the absolute values of the terms and then add both the numbers.
Determine the absolute values of the terms.
∣−21/4∣
∣=21/4∣
∣−31/4∣
=31/4
Because the terms have the same sign, the sum has the sign of the terms, hence, the sum is negative.
Determine the sum.
−21/4+(−31/4)=−(−21/4−31/4)
−21/4+(−31/4)=−(21/4+31/4)
−21/4+(−31/4)=−(9/4+13/4)
−21/4+(−31/4)=−(13+9/4)
Simplify further.
−21/4+(−31/4)=−(22/4)−21/4+(−31/4)=−11/2
Hence, −21/4+(−31/4)=−11/2.
The sum of −21/4+(−31/4) is−11/2.
HMH Middle School Grade 7 Chapter 3 Page 17 Problem 8 Answer
An expression is given as, −0.6+(−2.5).
An expression is required to solve the given expression.
To solve the given expression, first, determine the absolute values of the terms and then add both the numbers.
Determine the absolute values of the terms.
∣−0.6∣=0.6
∣−2.5∣=2.5
Because the terms have the same sign, the sum has the sign of the terms, hence, the sum is negative.
Determine the sum.
−0.6+(−2.5)=−(∣−0.6∣+∣−2.5∣)
−0.6+(−2.5)=−(0.6+2.5)
−0.6+(−2.5)=−3.1
Hence, −0.6+(−2.5)=−3.1.
The sum of −0.6+(−2.5) is −3.1.
Examples Of Problems From Exercise 3.2 Rational Numbers In HMH Grade 7 Workbook Page 17 Problem 9 Answer
An expression is given as, −3/4+1/5.
An expression is required to solve the given expression.
To solve the given expression, first determine the absolute values of the terms and then add both the numbers.
Determine the absolute values of the terms.
∣−3/4∣=3/4
∣1/5∣=1/5
The terms have different signs.
The sign of the sum is the sign of the term with the greater absolute value.
Here, ∣−3/4∣>∣1/5∣.
Determine the sum.
−3/4+1/5=−(∣−3/4∣−1/5)−3/4+1/5
−3/4+1/5 =−(3/4−1/5)−3/4+1/5
−3/4+1/5 =−(15−4/20)−3/4+1/5
−3/4+1/5 =−11/20
Hence, −3/4+1/5=−11/20.
The sum of−3/4+1/5 is −11/20.
HMH Middle School Grade 7 Chapter 3 Page 17 Problem 10 Answer
An expression is given as, 3+(−7.5)+1.2.
An expression is required to find the sum of the given expression without using a number line.
To find the sum of the given expression without using a number line, it is necessary to group the terms according to their signs.
Group the terms of the given expression in accordance with their signs.
The given expression will become (3+1.2)+(−7.5).
Now, perform the operation inside the parentheses.
(3+1.2)+(−7.5)=4.2+(−7.5)
Here, in the expression 4.2+ (−7.5), two different signs appear next to each other, hence, perform the operation subtraction.
Ignore the signs, subtract 4.2 from 7.5.
7.5−4.2=3.3
In the two numbers 4.2 and −7.5 one is positive and the other is a negative number and the larger number has a negative sign, the result will use the sign of the negative number.
Hence, the required result will be −3.3.
The sum of the given expression 3+(−7.5)+1.2 is −3.3.
Common Core Chapter 3 Exercise 3.2 Rational Numbers Detailed Solutions HMH Grade 7 Workbook Page 17 Problem 11 Answer
An expression is given as,−3+(−1.35)+2.5.
An expression is required to find the sum of the given expression without using a number line.
To find the sum of the given expression without using a number line, it is necessary to group the terms according to their signs.
Group the terms of the given expression in accordance with their signs.
The given expression will become [(−3)+(−1.35)]+2.5.
Now, perform the operation inside the parentheses.
Add the numbers 3 and 1.35 ignoring the negative signs and assign a negative sign to the result.
[(−3)+(−1.35)]+2.5=−4.35+2.5
An expression is known that the addition of a positive and negative number would imply the subtracting of the two numbers.
Ignore the signs, subtract 4.35 from 2.5.
4.35−2.5=1.85
In the two numbers −4.35 and2.5 one is positive and the other is a negative number and the larger number has a negative sign, the result will use the sign of the negative number.
Hence, the required result will be −1.85.
The sum of the given expression −3+(−1.35)+2.5 is −1.85.
HMH Middle School Grade 7 Chapter 3 Page 17 Problem 12 Answer
An expression is given as, −6.5+(−0.15)+(−0.2).
An expression is required to find the sum of the given expression without using a number line.
To find the sum of the given expression without using a number line, it is necessary to group the terms according to their signs.
Group the terms of the given expression in accordance with their signs.
An expression is known that the addition of negative numbers would imply the adding of the numbers.
Ignoring the signs, add 6.5,0.15 and 7.5.
6.5+0.15+0.2=6.85
Since, the numbers −6.5,−0.15 and −7.5 are negative numbers, and the larger number −6.5 has a negative sign, the result will use the sign of the negative number.
Hence, the required result will be −6.85.
The sum of the given expression −6.5+(−0.15)+(−0.2) is−6.85.
Student Edition Chapter 3 Exercise 3.2 Rational Numbers HMH Grade 7 Workbook guide Page 17 Problem 13 Answer
An expression is given as, −3/2−7/4+1/8.
An expression is required to find the sum of the given expression without using a number line.
To find the sum of the given expression without using a number line, it is necessary to group the terms according to their signs.
Perform the operations from left to right side of the given expression.
Add −3/2 and −7/4 as the both the fractions have a negative sign.
3/2+7/4=6/4+7/4
3/2+7/4=13/4
The result will have a negative sign.
Hence,−3
2−7/4=−13/4.
Now, the given expression −3/2−7/4+1/8 can be written as, −13/4+1/8.
The above expression has a positive and a negative fraction, so, subtract by ignoring the sign.
13/4−1/8=26/8−1/8
13/4−1/8=25/8
The result will have a negative sign since the sign of the larger fraction, −13/4, is negative.
Hence, the required result is −25/8.
The sum of the given expression−3/2−7/4+1/8 is −25/8.
HMH Middle School Grade 7 Chapter 3 Page 17 Problem 14 Answer
An expression is given that Alex borrowed$12.50 and paid back $8.75.
An expression is required to find the amount of money he owes after paying back.
To find the amount of money he owes after paying back, it is necessary to assign signs to the given values.
And then, use the required operations.
Consider the amount of money Alex borrowed is represented by negative numbers and the amount of money he pays back is represented by positive numbers.
Establish an expression for the given situation considering the above mentioned.
−12.50+8.75
Now, solve the above expression.
Since the numbers have a positive and a negative sign, hence, operate subtraction.
Ignore the signs and subtract 8.75 from 12.50.
12.50−8.75=3.75
The result will have a negative sign, since, the larger number −12.50 is negative.
Hence, −12.50+8.75=−3.75.
The required amount of money is$3.75.
The amount of money Alex owes after paying back is $3.75.
Step-by-step answers for Exercise 3.2 Rational Numbers HMH Grade 7 Practice Workbook Page 17 Problem 15 Answer
An expression is given that a football team gains 18 yards and then losses 12 yards in the next.
An expression is required to find the total yardage of the team.
To find the total yardage of the team, it is necessary to assign signs to the given values.
Consider the number of yards the team gains is represented by positive numbers and the number of yards it loses by negative numbers.
Establish an expression for the given situation considering the above-mentioned.
18+(−12)
Now, solve the above expression.
Since the numbers have a positive and a negative sign, hence, operate subtraction.
Ignore the signs and subtract 12 from 18.
18−12=6
The result will have a positive sign since the larger number 18 is positive.
Hence, 18+(−12)=6.
The required number of yardage is 6.
The total yardage of the team is 6.
HMH Middle School Grade 7 Chapter 3 Page 17 Problem 16 Answer
An expression is given that Dee Dee spends $0.85,$4.50 and $1.50 individually on various items.
An expression is required to find the total amount of the money spent by Dee Dee.
To find the total amount of money Dee Dee spend, it is necessary to add the given individual amounts.
The amount of money spent by Dee Dee will be the addition of the money he spent on various items.
Establish an expression for the given situation.
0.85+4.50+1.50
Now, solve the above expression.
0.85+4.50+1.50=5.35+1.50
0.85+4.50+1.50=6.85
The required amount of money is$6.85.
The total amount of money that Dee Dee spent is $6.85.
Page 18 Problem 17 Answer
An expression is given that Andre first hiked 4.5mi away from his house, then, hiked 2.4mi closer to his house, and lastly, hiked 1.7mi away from his house.
An expression is required to find the distance between Andre and his house.
To find the distance between Andre and his house,it is necessary to assign signs to the given values.
Then, add all the values.
Consider the distance Andre hikes away is represented by positive numbers and the distances he hikes closer to the house with negative numbers.
Establish an expression for the given situation considering the above mentioned.
4.5+(−2.4)+1.7
Now, solve the above expression from left to right.
Group the terms of the given expression in accordance with their signs.
4.5+1.7+(−2.4)
Add 4.5 and 1.7.
4.5+1.7=6.2
Since the two numbers, 4.5 and 1.7 are positive numbers, hence, the result will use the sign of the positive number.
Now, the expression4.5+(−2.4)+1.7 can be written as, 6.2+(−2.4).
Here, two different signs appear next to each other, hence, perform the operation subtraction.
Ignore the signs and subtract 6.2 from −2.4.
6.2−2.4=3.8
In the two numbers 6.2 and−2.4 one is positive and the other is a negative number and the larger number has a negative sign, the result will use the sign of the negative number.
Hence, the required result will be 3.8.
Andre is 3.8 mi away from his house.
HMH Middle School Grade 7 Chapter 3 Page 18 Problem 18 Answer
An expression is given as, 3+(−8).
An expression is required to find the sum.
Apply bodmas rule to find the sum.
Write the given expression.
3+(−8)
Subtract the expression.
3+(−8)=3−8
3+(−8)=−5
Hence, 3+(−8)=−5.
The value of 3+(−8) is −5.
Page 18 Problem 19 Answer
An expression is given as, 2.4+(−1.8).
An expression is required to find the sum.
Apply bodmas rule to find the sum.
Write the given expression.
2.4+(−1.8)
Subtract the expression.
2.4+(−1.8)=2.4−1.8
2.4+(−1.8)=0.6
Hence, 2.4+(−1.8)=0.6.
The value of 2.4+(−1.8) is 0.6.
HMH Middle School Grade 7 Chapter 3 Page 18 Problem 20 Answer
An expression is given as, 1.1+3.6.
An expression is required to find the sum.
Apply bodmas rule to find the sum.
Write the given expression.
1.1+3.6
Add the expression.
Hence, 1.1+3.6=4.7.
The value of 1.1+3.6 is 4.7.
Page 18 Problem 21 Answer
An expression is given as, −2.1+(−3.9).
An expression is required to find the sum.
Apply bodmas rule to find the sum.
Write the given expression.
−2.1+(−3.9)
Solve the expression.
−2.1+(−3.9)=−2.1−3.9
−2.1+(−3.9)=−6.0
Hence,−2.1+(−3.9)=−6.0.
The value of −3.9 is −6.
HMH Middle School Grade 7 Chapter 3 Page 18 Problem 22 Answer
An expression is given as, 4/5+(−1/5).
An expression is required to find the sum.
Apply bodmas rule to find the sum.
Write the given expression.
4/5+(−1/5)
Solve the expression.
4/5+(−1/5)=4/5−1/5
4/5+(−1/5)=4−1/5
4/5+(−1/5)=3/5
Hence, 4/5+(−1/5)=3/5.
The value of 4/5+(−1/5) is 3/5.
Page 18 Problem 23 Answer
An expression is given as, −11/3+(−1/3).
An expression is required to find the sum.
Apply bodmas rule to find the sum.
Write the given expression.
Write the given expression.
−11/3+(−1/3)
Solve the expression.
−11/3+(−1/3)=−4/3−1/3
−11/3+(−1/3)=−4−1/3
−11/3+(−1/3)=−5/3
Hence, −11/3+(−1/3)=−5/3.
The value of −11/3+(−1/3) is −5/3.
HMH Middle School Grade 7 Chapter 3 Page 18 Problem 24 Answer
An expression is given as, −7/8+1/3.
An expression is required to find the sum.
Apply bodmas rule to find the sum.
Write the given expression.
−7/8+1/3
Solve the expression.
−7/8+1/3 =−7(3)+1(8)/8⋅3
−7/8+1/3 =−21+8/24
−7/8+1/3 =−13/24
Hence, −7/8+1/3 =−13/24.
The value of −7/8+1/3 is −13/24.