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.

## McGraw-Hill Math Grade 8 Answer Key Lesson 10.5 Rational Numbers

**Exercises**

**CALCULATE**

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

Question 1.

-16

whole

integer

rational

Answer:

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

Answer:

rational

Explanation:

Any number expressed in fraction are called rational numbers.

So, 0.006 is a rational number.

Question 3.

7

whole

integer

rational

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

\(\frac{-23}{1}\)

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

Answer:

\(\frac{156}{1000}\)

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

Answer:

\(\frac{19}{1}\)

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\(\frac{2}{3}\)

Answer:

\(\frac{26}{3}\)

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

Answer:

\(\frac{-8}{1}\)

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\(\frac{7}{9}\)

Answer:

\(\frac{25}{9}\)

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

Answer:

\(\frac{1945}{1000}\)

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

Answer:

\(\frac{78}{1}\)

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\(\frac{1}{2}\)

Answer:

\(\frac{27}{2}\)

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

Answer:

\(\frac{7638}{100}\)

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

Answer:

\(\frac{-302}{1}\)

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.

\({9 . \overline{3}}\)

Answer:

\(\frac{28}{3}\)

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