Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 10.5 Rational Numbers to secure good marks & knowledge in the exams.

Exercises

CALCULATE

Circle each group the number belongs to (there can be more than one).

Question 1.
-16
whole
integer
rational
integer, rational
Explanation:
Any number expressed in fraction are called rational numbers.
An integer is a whole number with a positive or negative numbers.
So, -16 is an integer and rational number.

Question 2.
0.006
whole
integer
rational
rational
Explanation:
Any number expressed in fraction are called rational numbers.
So, 0.006 is a rational number.

Question 3.
7
whole
integer
rational
whole, integer, rational
Explanation:
Whole numbers are a set of numbers including all natural numbers and 0.
They are a part of real numbers that do not include fractions, decimals, or negative.
Any number expressed in fraction are called rational numbers.
An integer is a whole number with a positive or negative numbers.
So, 7 is an integer, whole and rational number.

Question 4.
-1.953
whole
integer
rational
rational
Explanation:
Any number expressed in fraction are called rational numbers.
So, -1.953 is a rational number.

Question 5.
–$$\frac{8}{17}$$
whole
integer
rational
rational
Explanation:
Any number expressed in fraction are called rational numbers.
So, –$$\frac{8}{17}$$ is a rational number.

Question 6.
3$$\frac{4}{5}$$
whole
integer
rational
rational
Explanation:
Any number expressed in fraction are called rational numbers.
So, –$$\frac{8}{17}$$ is a rational number.

Question 7.
-1$$\frac{3}{4}$$
whole
integer
rational
rational
Explanation:
Any number expressed in fraction are called rational numbers.
So, -1$$\frac{3}{4}$$ is a rational number.

Question 8.
$$\frac{78}{79}$$
whole
integer
rational
rational
Explanation:
Any number expressed in fraction are called rational numbers.
So, $$\frac{78}{79}$$ is a rational number.

Change each number to a fraction.

Question 9.
-23
$$\frac{-23}{1}$$
Explanation:
The given number -23 is an integer.
So, just put that integer as the numerator of a fraction with a denominator of 1.
-23 = $$\frac{-23}{1}$$

Question 10.
0.156
$$\frac{156}{1000}$$
Explanation:
To convert a decimal to a fraction, place the decimal number over its place value.
0.156, the six is in the thousandths place, to create the equivalent fraction.
so, 0.156 = $$\frac{156}{1000}$$

Question 11.
19
$$\frac{19}{1}$$
Explanation:
Given number 19 is whole number,
to convert the whole number place the given number in numerator and 1 in the denominator.
So, 19 = $$\frac{19}{1}$$

Question 12.
8$$\frac{2}{3}$$
$$\frac{26}{3}$$
Explanation:
To convert mixed fraction into improper fraction,
Multiply the whole number by the denominator.
Add that number to the numerator.
Write that sum on top of the original denominator.
8$$\frac{2}{3}$$ = $$\frac{26}{3}$$

Question 13.
-8
$$\frac{-8}{1}$$
Explanation:
The given number -8 is an integer.
So, just put that integer as the numerator of a fraction with a denominator of 1.
-8 = $$\frac{-8}{1}$$

Question 14.
2$$\frac{7}{9}$$
$$\frac{25}{9}$$
Explanation:
To convert mixed fraction into improper fraction,
Multiply the whole number by the denominator.
Add that number to the numerator.
Write that sum on top of the original denominator.
2$$\frac{7}{9}$$ = $$\frac{25}{9}$$

Question 15.
1.945
$$\frac{1945}{1000}$$
Explanation:
To convert a decimal to a fraction, place the decimal number over its place value.
Count the numbers after decimal and place the tenths place, hundredths, thousandths and so on to create the equivalent fraction.
so, 1.945 = $$\frac{1945}{1000}$$

Question 16.
78
$$\frac{78}{1}$$
Explanation:
Given number 78 is whole number,
to convert the whole number place the given number in numerator and 1 in the denominator.
So, 78 = $$\frac{78}{1}$$

Question 17.
13$$\frac{1}{2}$$
$$\frac{27}{2}$$
Explanation:
To convert mixed fraction into improper fraction,
Multiply the whole number by the denominator.
Add that number to the numerator.
Write that sum on top of the original denominator.
13$$\frac{1}{2}$$ = $$\frac{27}{2}$$

Question 18.
76.38
$$\frac{7638}{100}$$
Explanation:
To convert a decimal to a fraction, place the decimal number over its place value.
Count the numbers after decimal and place the tenths, hundredths, thousands and son on to create the equivalent fraction.
so, 76.38 = $$\frac{7638}{100}$$

Question 19.
-302
$$\frac{-302}{1}$$
Explanation:
The given number -8 is an integer.
So, just put that integer as the numerator of a fraction with a denominator of 1.
-302 = $$\frac{-302}{1}$$

Question 20.
$${9 . \overline{3}}$$
$$\frac{28}{3}$$
Explanation:
Let x = 9.333333……Â  Â Equation (1)
multiplying Equation (1) by 10 on both sides
10 x = 93.333333….. Equation (2)
subtracting (1) from (2)
10x = 93.3333333……
– x = 9. 33333……
= 9x =93 – 9
9x = 84
x = 84/9
x = 28/3

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