## Envision Math Accelerated Grade 7 Volume1 Chapter 1 Integers And Rational Numbers

**Page 2 Question 1 Answer**

**Given:**

There are four properties of operations in math.

These properties apply to addition, multiplication, and subtraction, but not to division and subtraction.

Because it shows several ways to reach the solution, the characteristics of operations can be utilized to solve problems with integers.

**Finally, we concluded that there are different ways used to solve problems involving integers and rational numbers. **

**Page 4 Exercise 1 Answer**

**Given:
**

We have to explore the habitability with low temperatures

The lowest record temperature in the world is −136° F(−92.21C) occurred in Antarctica.

Low temperatures also freeze water, rendering it unavailable as a liquid.

Life appears to be limited to a temperature range of minus 15 to 115 degrees Celsius. This is a liquid range.

**Finally, we concluded that the low temperature of Life seems limited to a temperature.**

**Page 5 Exercise 1 Answer**

**Given:
**

**Correct answer:**Commutative property is the correct answer.

**Commutative property:** The commutative qualities state that you can add or multiply two numbers in any order and get the same result. Assume that a and b are real numbers. wrong answer

**Absolute value:** It refers to a number’s distance from zero on the number line, without taking direction into account.

**Distributive property:** According to the distributive property, If p,q, and r are three rational numbers, then the connection between them is p(q+r)=(pq)+(pr)

**Integer:** Integer, positive or negative whole-valued number, or 0.

The integers are made up of the counting numbers 1,2,3 and….. as well as the subtraction procedure.

The consequence of subtracting a counting number from itself is zero.

**Rational number:** A rational number is one that has the form \(\frac{p}{q} \) where p and q are both integers and q is not zero.

**The final answer is, The commutative property explains why a × b = b × a and a + b = b + a**

**Page 5 Exercise 2 Answer**

**Given:
**

**Correct answer:**An integer is a correct answer

**Integer: ** Integer, positive or negative whole-valued number, or 0.

The integers are made up of the counting numbers 1,2,3 and….. as well as the subtraction procedure.

The consequence of subtracting a counting number from itself is zero.

On the number line, two opposed numbers have the same distance from zero but on opposite sides as −6 = 6 wrong answer.

**Commutative property:** The commutative qualities state that you can add or multiply two numbers in any order and get the same result. Assume that a and b are real numbers.

**Absolute value:** It refers to a number’s distance from zero on the number line, without taking direction into account.

**Distributive property:** According to the distributive property, If p,q, and r are three rational numbers, then the connection between them is p (q + r) = (pq) + (pr).

**Associative property:** The associative property of addition is a law that states that when we add, we can group the numbers in any order or combination

**Rational number:** A rational number is one that has the form \(\frac{p}{q}\), where p and q are both integers and q is not zero.

**The final answer is The Integer of −6 = 6 because it is the unit from zero on the number line.**

**Page 5 Exercise 3 Answer**

**Given:
**

**Correct answer:**An integer is a correct answer

**Integer: **Integer, positive or negative whole-valued number, or 0.

The integers are made up of the counting numbers 1,2,3 and….. as well as the subtraction procedure.

The consequence of subtracting a counting number from itself is zero

The number\(\frac{5}{3}\) is an integer. wrong answer.

**Commutative property:** The commutative qualities state that you can add or multiply two numbers in any order and get the same result. Assume that a and b are real numbers.

**Absolute value:** It refers to a number’s distance from zero on the number line, without taking direction into account.

**Distributive property:** According to the distributive property, If p,q, and r are three rational numbers, then the connection between them is p(q + r) = (pq) + (pr).

**Associative property:** The associative property of addition is a law that states that when we add, we can group the numbers in any order or combination

**Rational number:** A rational number is one that has the form \(\frac{p}{q} \) where p and q are both integers and q is not zero.

**The final answer is The number \(\frac{5}{3}\) is an integer because it is 6 units from zero on the number line.**

**Page 5 Exercise 4 Answer**

**Given:
**

**Correct answer:**Integer is the correct answer

**Integer: **Integer, positive or negative whole-valued number, or 0.

The integers are made up of the counting numbers 1,2,3 and….. as well as the subtraction procedure.

The consequence of subtracting a counting number from itself is zero.

The set on natural numbers is made up of the counting numbers (1,2,3,4,5).

This sequence of numbers begins with 0 and continues indefinitely.

The new set of whole numbers is created when we add 0 to the set of natural numbers. (zero, one, two, three, four, five)

We’re dealing with integers if we also include a number on the other side.

Positive and negative whole numbers, including 0.

Are integers, however, they cannot be expressed as fractions or decimals. wrong answer

**Commutative property:** The commutative qualities state that you can add or multiply two numbers in any order and get the same result. Assume that a and b are real numbers.

**Absolute value:** It refers to a number’s distance from zero on the number line, without taking direction into account.

**Distributive property:** According to the distributive property, If p,q, and r are three rational numbers, then the connection between them is p(q + r)=(pq) + (pr).

**Associative property:** The associative property of addition is a law that states that when we add, we can group the numbers in any order or combination

**Rational number:** A rational number is one that has the form \(\frac{p}{q} \) where p and q are both integers and q is not z

**The final answer is, The set integer consists of the counting number, their opposite, and zero.**

**Page 5 Exercise 5 Answer**

**Given:
**

**Correct answer:**Associative property is the correct answer

** Associative property: **Because when we add, we can group the numbers in any order or combination that is (a+b)+c is equal to the sum of a + (b + c) wrong answer

**Commutative property:** The commutative qualities state that you can add or multiply two numbers in any order and get the same result. Assume that a and b are real numbers.

**Absolute value:** It refers to a number’s distance from zero on the number line, without taking direction into account.

**Distributive property:** According to the distributive property, If p,q, and r are three rational numbers, then the connection between them is p(q + r) = (pq) + (pr).

**Integer:** Integer, positive or negative whole-valued number, or 0.

The integers are made up of the counting numbers 1,2,3 and….. as well as the subtraction procedure.

The consequence of subtracting a counting number from itself is zero

**Rational number:** A rational number is one that has the form p q, where p and q are both integers and q is not zero.

**The final answer is The sum of (a + b) + c is equal to the sum of a + (b + c) as explained by the associative property.**

**Page 5 Exercise 6 Answer**

**Given:
**

**Correct answer:**Distributive property is the correct answer

**Distributive property:** Distributive property states that the outcome of multiplying the sum of two or more addends by a number is the same as.

Multiplying each addend by the number separately and then putting the products together.

According to the distributive property n,y, and z are three rational numbers.

Then the connection between them is n × (y + z) can be written as (n × y) + (n × z) wrong answer.

**Commutative property:** The commutative qualities state that you can add or multiply two numbers in any order and get the same result. Assume that a and b are real numbers.

**Associative property:** The associative property of addition is a law that states that when we add, we can group the numbers in any order or combination.

**Absolute value:** It refers to a number’s distance from zero on the number line, without taking direction into account.

**Integer:** Integer, positive or negative whole-valued number, or 0.

The integers are made up of the counting numbers 1,2,3….. as well as the subtraction procedure

The consequence of subtracting a counting number from itself is zero

**Rational number:** A rational number is one that has the form \(\frac{p}{q} \), where p and q are both integers and q is not zero.

**The final answer is If you evaluate n × (y + z) by writing it as (n × y) + (n × z) ,you have used the distributive property**

**Page 5 Exercise 7 Answer**

**Given:**

To add the given sum

\(2 \frac{1}{3}+6 \frac{3}{5}\)

First, we have to add the whole number

⇒ 2+6=8

Now combine the fraction

⇒ \(\frac{1}{3}+\frac{3}{5}\)=\(\frac{14}{15}\)

We get \(8 \frac{14}{15}\)

**Finally, we concluded the solution is \(8 \frac{14}{15}\).**

**Page 5 Exercise 8 Answer**

**Given:**

To subtract the given sum.

\(9 \frac{1}{10}-4 \frac{3}{4}\)

First, we have to subtract the whole number

⇒ 9−4 = 5

Now combine the fraction

⇒ \(\frac{1}{10}-\frac{3}{4}\)=\(\frac{7}{20}\)

We get \(4 \frac{7}{20}\)

**Finally, we concluded the solution is \(4 \frac{7}{20}\)**

**Page 5 Exercise 9 Answer**

**Given:**

19.86 + 7.091

To add the given sum

Add the decimals

⇒ 19.860 + 7.091

19.860

+7.091

−−−−

26.951

**Finally, we concluded the solution is 26.951.**

**Page 5 Exercise 10 Answer**

**Given:**

57 − 10.62

To add the given sum.

Subtract the decimals

57 − 10.62

57.00

10.62

–

−−−−

46.38

**Finally, we concluded the solution is 46.38.**

**Page 5 Exercise 11 Answer**

**Given:**

4.08 × 29.7

To multiply the given decimal values

Multiply the numbers

⇒ 4.08 × 29.7

= 121.176

**Finally, we concluded the solution is 121.176**

**Page 5 Exercise 12 Answer**

**Given:**

⇒ 15,183.3 ÷ 473

**To divide the given decimal values.**

**Finally, we concluded the solution is 32.1.**

**Page 5 Exercise 13 Answer**

**Given:**

To multiply the given fraction values.

To multiply

⇒ \(\frac{15}{16} \times 9 \frac{1}{5}\)

**Factor the number 15**

=\(\frac{5 \times 3 \times 46}{16 \times 5}\)

**Cancel the factor**

=\(\frac{69}{8}\)

Finally, we concluded the solution is \(8 \frac{5}{8}\).

**Page 5 Exercise 14 Answer**

**Given:**

To divide the given fraction values

**Finally, we concluded the solution is \(\frac{172}{57}\)**

**Page 5 Exercise 15 Answer**

**Given:**

To find how much pepper will be added in each shake

\(1 \frac{7}{10}\)convert it into whole number we get \(\frac{17}{10}\)

To add \(\frac{7}{8}\) in each shakers

Each will contain \(\frac{1}{8}\)

\(\left(\frac{17}{10}\right)\left(\frac{1}{8}\right)\) = \(\frac{17}{80}\)

\(\frac{17}{80}\) kg pepper will be added in each shakers.

**Finally we concluded the solution is 17 \(\frac{17}{80}\) kg**

**Page 6 Exercise 2 Answer**

**To explain about fractions and decimals:**

Fractions can be defined as the components of a whole and are represented as a numerical values.

A fraction is a chunk or sector of any quantity taken from a whole, the whole being any number.

When writing a number that is not a whole, decimals are utilized. Decimal numbers are numbers that fall in the middle of a range of whole numbers.

Divide the numerator by the denominator to convert a fraction to a decimal.

You can accomplish this with a calculator if necessary. As a result, we’ll have a decimal answer.

**Finally, we concluded the A fraction describes the number of parts that make up a whole. The numerator and the denominator are used to express it.**

**A decimal is a fraction with a denominator of ten and can be expressed with a decimal point.**

**Page 6 Exercise 2 Answer**

**To explain about fractions and decimals:**

Fractions can be defined as the components of a whole and are represented as numerical values.

A fraction is a chunk or sector of any quantity taken from a whole, the whole being any number.

When writing a number that is not a whole, decimals are utilized. Decimal numbers are numbers that fall in the middle of a range of whole numbers.

Divide the numerator by the denominator to convert a fraction to a decimal.

You can accomplish this with a calculator if necessary. As a result, we’ll have a decimal answer.

**Finally, we concluded the A fraction describes the number of parts that make up a whole. ****The numerator and the denominator are used to express it.**

**A decimal is a fraction with a denominator of ten and can be expressed with a decimal point.**

**Page 6 Exercise 3 Answer**

**Given:
**

The number on the other side of the 0 number line and at the same distance from 0 is called the opposite of a number

It can be defined as an absolute value.

If two integers have the same absolute value but different signs, they are opposites.

**Finally, we concluded the opposite of a number is the number on the other side of the 0 number line, and the same distance from 0 It can be defined as an absolute value.**

**Page 6 Exercise 4 Answer**

**Given:
**

They might have either a positive or negative value. The value of a positive integer is larger than zero.

Negative integers are those that have a value that is less than zero.

There is no such thing as zero, which is neither positive nor negative.

The positive has the sign of(+), and the negative has the sign of (−).

**Finally, we concluded that Positive numbers are any numbers greater than zero, and negative number are less than zero.**

**Page 6 Exercise 6 Answer**

**Given:
**

On a number line, we can arrange all of the whole numbers.

A number line is a horizontal line with evenly spaced points that correspond to the full numbers.

On the number line, two opposed numbers have the same distance from zero but on opposite sides.

**Finally, we concluded that the opposite number was located on the same distance away from the zero of the number line.**

**Page 6 Exercise 7 Answer**

**Given:**

Real-life integers are used to check financial status.

If there is a profit, we have positive numbers.

If there is a loss, we have negative numbers.

Fractions, integers, numbers with terminating decimals, and numbers with repeating decimals are considered to be rational numbers.

Except for complex and irrational numbers (π, root of imperfect numbers), all numbers are rational.

As a result, rational numbers are employed almost everywhere in real life, with a few exceptions.

**Finally, we concluded that integers and rational numbers are used to have positive and negative numbers in real life.**

**Page 6 Exercise 8 Answer**

**Given:
**

Standard numbers, anything greater than zero, are described as ‘positive’ numbers.

We don’t put a plus sign (+) in front of them because we don’t need to since the general understanding is that numbers without a sign are positive.

‘Negative’ numbers are numbers that are less than zero. These are preceded by a negative symbol (−) to indicate that they are less than zero.

Integer values can also be calculated in real-life scenarios. For real-life scenarios, the integer value is either positive or negative.

Positive numbers represent kindness, happiness, togetherness, and well-being, whereas negative numbers represent boredom, melancholy, and low feelings, among other things.

**Finally, we concluded that it is important of a positive or negative number is to calculate the difference.**

**Page 6 Exercise 9 Answer**

**Given:
**

The sign of the result when adding or subtracting positive and negative numbers is determined by whether the signs are similar or which number has a bigger value.

When both numbers have the same sign, adding positive and negative numbers is simple.

The difference between a positive number to a negative number is always positive.

**Finally, we concluded that adding a positive number to a negative number has different of signs.**