Go through the Math in Focus Grade 7 Workbook Answer Key Chapter 1 Lesson 1.1 Representing Rational Numbers on the Number Line to finish your assignments.

## Math in Focus Grade 7 Course 2 A Chapter 1 Lesson 1.1 Answer Key Representing Rational Numbers on the Number Line

### Math in Focus Grade 7 Chapter 1 Lesson 1.1 Guided Practice Answer Key

**Solve.**

Question 1.

Find the absolute values of 3\(\frac{2}{7}\) and –\(\frac{18}{5}\)

Answer:

3(2/7) = (21+2)/7 = **23/7**

The simplified form of 3(2/7) is** 23/7**

The absolute value of |3(2/7)| is **3(2/7)**

The absolute value of |-(18/5)| is **18/5**

Question 2.

Graph the two numbers on a number line and indicate their distances from 0. Which number is farther from 0?

Answer:

The number **-18/5** is farther from 0.

Explanation:

In the above image we can observe a number line. On the number line the two numbers 3(2/7) and -18/5 are indicated. The two numbers distance from 0 are graphed. The number -18/5 is farther from 0.

**Write each number in \(\frac{m}{n}\) form where m and n are integers.**

Question 3.

11\(\frac{1}{6}\)

Answer:

11(1/6)

= (66 + 1)/6

=** 67/6**

The number 11(1/6) in m/n form is 67/6.

Here m = 67 and n= 6

Question 4.

48

Answer:

48 = **48/1**

The number 48 in m/n form is 48/1.

Here m = 48 and n = 1

Question 5.

-5\(\frac{4}{12}\)

Answer:

-5(4/12)

= – (60 + 4)/12

= -64/12

= **-16/3**

The number -5(4/12) in m/n form is -16/3.

Here m = -16 and n = 3

Question 6.

–\(\frac{25}{10}\)

Answer:

**-25/10 = -5/2**

The given number -25/10 is already in m/n form.

**Write each decimal as \(\frac{m}{n}\) where m and n are integers with n ≠ 0.**

Question 7.

11.5

Answer:

11.5 = **23/2**

The given decimal number 11.5 is represented in m/n form. The m/n form of 11.5 is 23/2.

Question 8.

-7.8

Answer:

-7.8 = **-78/10**

The given decimal number -7.8 is represented in m/n form. The m/n form of -7.8 is -78/10.

Question 9.

0.36

Answer:

0.36 = **36/100**

The given decimal number 0.36 is represented in m/n form. The m/n form of 0.36 is 36/100.

Question 10.

-0.125

Answer:

-0.125 = **– 125/1000**

The given decimal number -0.125 is represented in m/n form. The m/n form of -0.125 is 125/1000.

**Copy and complete.**

Question 11.

Locate the rational numbers -1.5 and \(\frac{15}{4}\) on the number line.

STEP 1

Find the integers that the rational number lies between.

\(\frac{15}{4}\) can be written as a mixed number, 3\(\frac{3}{4}\), and 3\(\frac{3}{4}\) lies between 3 and 4. The negative decimal -1.5 lies between —2 and —1.

STEP 2

Graph a number line and label the integers.

Answer:

The integers are labeled on a number line.

STEP 3

Divide the distance between the integers into equal segments.

You divide the distance between —2 and —1 into segments and the distance between 3 and 4 into segments.

Answer:

Divide the distance between —2 and —1 into **1 **segments and the distance between 3 and 4 into **3** segments.

STEP4

Use the segments to locate -1.5 and 3\(\frac{3}{4}\).

Answer:

Located the rational numbers -1.5 and 15/4 on the number line.

**Locate the following rational numbers on the number line.**

Question 12.

\(\frac{1}{6}\) and \(\frac{15}{3}\)

Answer:

1/6 and 15/3

Explanation:

First we have to find the integers that where the rational number lies between on the number line.

The fraction 1/6 lies between 0 and 1. The simplified form of 15/3 is 5. The fraction 15/3 lies on number 5.

Next we have to label the integers and locate the rational numbers on a number line.

In the above image we can observe the rational numbers 1/6 and 15/3 are located on the number line.

Question 13.

-0.4 and \(\frac{11}{5}\)

Answer:

-0.4 and 11/5

Explanation:

First we have to find the integers that where the rational number lies between on the number line.

The negative decimal -0.4 lies between —1 and 0.The fraction 11/5 lies between 2 and 3.

Next we have to label the integers and locate the rational numbers on a number line.

Divide the distance between —1 and 0 into **4 **segments and the distance between 2 and 3 into **4** segments.

In the above image we can observe the rational numbers -0.4 and 11/5 are located on the number line.

Question 14.

\(\frac{12}{15}\) and -1.8

Answer:

12/15 and -1.8

Explanation:

First we have to find the integers that where the rational number lies between on the number line.

The negative decimal -1.8 lies between —2 and -1.The fraction 12/15 lies between 0 and 1.

Next we have to label the integers and locate the rational numbers on a number line.

Divide the distance between —2 and -1 into **4 **segments and the distance between 0 and 1 into **4** segments.

In the above image we can observe the rational numbers -1.8 and 12/15 are located on the number line.

Question 15.

\(-\frac{5}{15}\) and \(-\frac{25}{30}\)

Answer:

-5/15 and 25/30

Explanation:

First we have to find the integers that where the rational number lies between on the number line.

The negative fractions -25/30 and -5/15 lies between —1 and 0.

Next we have to label the integers and locate the rational numbers on a number line.

In the above image we can observe the rational numbers -25/30 and -5/15 are located on the number line.

### Math in Focus Course 2A Practice 1.1 Answer Key

**Find the absolute value of each fraction. Use a number line to show how far the fraction is from 0. Write fractions in simplest form.**

Question 1.

\(\frac{7}{10}\)

Answer:

7/10

The absolute value of above fraction is 7/10.

Explanation:

First we have to find where the fraction lies between on the number line.

The fraction 7/10 lies between 0 and 1.

Next we have to label the fraction on a number line.

In the above image we can observe the fraction is 7/10 units far from the 0 on the number line.

Question 2.

\(\frac{18}{8}\)

Answer:

The absolute value of 18/8 is 18/8.

18/8 = **9/4**

The simplest form of 18/8 is 9/4.

Explanation:

First we have to find where the fraction lies between on the number line.

The fraction 18/8 lies between 2 and 3.

Next we have to label the fraction on a number line.

In the above image we can observe the fraction is 18/8 units far from the 0 on the number line.

Question 3.

–\(\frac{5}{13}\)

Answer:

The absolute value of -5/13 is 5/13.

Explanation:

First we have to find where the fraction lies between on the number line.

The fraction -5/13 lies between -1 and 0.

Next we have to label the fraction on a number line.

In the above image we can observe the fraction is -5/13 units far from the 0 on the number line.

Question 4.

–\(\frac{48}{15}\)

Answer:

-48/15

The absolute value of -48/15 is 48/15.

Explanation:

First we have to find where the fraction lies between on the number line.

The fraction -48/15 lies between -3 and 0.

Next we have to label the fraction on a number line.

In the above image we can observe the fraction is -48/15 units far from the 0 on the number line.

**Write each integer or fraction as \(\frac{m}{n}\) in simplest form where m and n are integers.**

Question 5.

67

Answer:

67

=** 67/1**

The number 67 in m/n form is 67/1.

Here m = 67 and n= 1

Question 6.

-345

Answer:

-345

= **-345/1**

The number -345 in m/n form is -345/1.

Here m = -345 and n= 1

Question 7.

\(\frac{25}{80}\)

Answer:

25/80

=** 5/16**

The simplest form of 25/80 is 5/16.

The fraction 25/80 in m/n form is 5/16.

Here m = 5 and n= 16

Question 8.

–\(\frac{264}{90}\)

Answer:

-264/90

= **-44/15**

The simplest form of -264/90 is -44/15.

The fraction -264/90 in m/n form is -44/15.

Here m = -44 and n= 15

Question 9.

–\(\frac{14}{70}\)

Answer:

-14/70

=** -1/5**

The simplest form of -14/70 is -1/5.

The fraction -14/70 in m/n form is -1/5.

Here m = -1 and n= 5

Question 10.

\(\frac{600}{480}\)

Answer:

600/480

= 50/40

= **5/4**

The simplest form of 600/480 is 5/4.

The fraction 600/480 in m/n form is 5/4.

Here m =5 and n = 4

**Write each mixed number or decimal \(\frac{m}{n}\) as in simplest form where m and n are integers.**

Question 11.

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

Answer:

7(7/9)

= (63 + 7)/9

= **70/9**

The simplest form of the mixed number 7(7/9) is 70/9.

Here m = 70 and n = 9 both are integers.

Question 12.

-5\(\frac{1}{10}\)

Answer:

-5(1/10)

= -(50 + 1)/10

=** -51/10**

The simplest form of the mixed number -5(1/10) is -51/10.

Here m = -51 and n = 10 both are integers.

Question 13.

2\(\frac{5}{12}\)

Answer:

2(5/12)

= (24 + 5)/12

=** 29/12**

The simplest form of the mixed number 2(5/12) is 29/12.

Here m = 29 and n = 12 both are integers.

Question 14.

-10\(\frac{11}{36}\)

Answer:

-10(11/36)

=-(360 + 11)/36

= **-371/36**

The simplest form of the mixed number-10(11/36) is -371/36.

Here m =-371 and n = 36 both are integers.

Question 15.

0.4

Answer:

0.4

= 4/10

=** 2/5**

The simplest form of the decimal number 0.4 is 2/5.

Here m = 2 and n = 5 both are integers.

Question 16.

-0.625

Answer:

-0.625

= -625/1000

= **-5/8**

The simplest form of the decimal number -0.625 is -5/8.

Here m = -5 and n = 8 both are integers.

Question 17.

5.80

Answer:

5.80

=** 29/5**

The simplest form of the decimal number 5.80 is 29/5.

Here m = 29 and n = 5 both are integers.

Question 18.

9.001

Answer:

9.001

= **9001/1000**

The simplest form of the decimal number 9.001 is 9001/1000.

Here m = 9001 and n =1000 both are integers.

Question 19.

-10.68

Answer:

-10.68

= **-267/25**

The simplest form of the decimal number -10.68 is -267/25.

Here m = -267 and n = 25 both are integers.

**Copy and complete.**

Question 20.

Locate the following rational numbers correctly on the number line.

–\(\frac{1}{4}\), -1.5, 0.8, \(\frac{5}{2}\)

Answer:

Explanation:

First we have to find where the given rational numbers lies between on the number line.

The negative decimal -1.5 lies between -2 and -1.

The negative fraction -1/4 lies between -1 and 0.

The decimal 0.8 lies between 0 and 1.

The fraction 5/2 lies between 2 and 3.

The above given rational numbers are located correctly on the number line.

Question 21.

Locate the following rational numbers correctly on the number line.

1\(\frac{7}{10}\), –\(\frac{13}{5}\), 2.25, -0.7

Answer:

Explanation:

First we have to find where the given rational numbers lies between on the number line.

The negative fraction -13/5 lies between -3 and -2

The negative decimal -0.7 lies between -1 and 0.

The mixed fraction 1(7/10) in fraction as 17/10 lies between 1 and 2.

The decimal 2.25 lies between 2 and 3.

The above given rational numbers are located correctly on the number line.

**Graph each rational number on a separate number line.**

Question 22.

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

Answer:

67(1/8)

= (536 + 1)/8

= **537/8**

Explanation:

First we have to find where the given rational number lies between on the number line.

The mixed fraction 67(1/8) in fraction as 537/8 lies between 67 and 68.

The above given rational number is drawn correctly on the number line.

Question 23.

\(\frac{305}{20}\)

Answer:

305/20

Explanation:

First we have to find where the given rational number lies between on the number line.

The fraction 305/20 lies between 15 and 16.

The above given rational number is drawn correctly on the number line.

Question 24.

\(\frac{98}{28}\)

Answer:

98/28

Explanation:

First we have to find where the given rational number lies between on the number line.

The fraction 98/28 lies between 3 and 4.

The above given rational number is drawn correctly on the number line.

Question 25.

–\(\frac{21}{12}\)

Answer:

-21/12

Explanation:

First we have to find where the given rational number lies between on the number line.

The fraction -21/12 lies between -2 and -1.

The above given rational number is correctly drawn on the number line.

Question 26.

-25.8

Answer:

Explanation:

First we have to find where the given rational number lies between on the number line.

The decimal lies between -26 and -25.

The above given rational number is drawn correctly on the number line.

Question 27.

-45.3

Answer:

Explanation:

First we have to find where the given rational number lies between on the number line.

The decimal lies between -46 and -45.

The above given rational number is correctly drawn on the number line.

A video game gives you 10 minutes to find a treasure. The results of your first 8 games show the amount of time left unused when you have found the treasure. A negative time means you have gone beyond the 10 minutes allotted. Use these data for questions 28 to 35.

\(\frac{23}{8}\), 0, -7\(\frac{1}{5}\), 6, –\(\frac{17}{4}\), 8, 7.8, -9.1

Question 28.

Order the times left from most to least time using the symbol >.

Answer:

The time left from most to least are **8, 7.8, 6, 23/8, 0, -17/4, -7(1/5), -9.1**.

Question 29.

Write the absolute value of each number.

Answer:

23/8, 0, -7(1/5), 6 , -17/4, 8, 7.8, -9.1

The absolute value of 23/8 is **23/8**.

The absolute value of 0 is **0**.

The absolute value of -7(1/5) is **7(1/5) or 36/5**.

The absolute value of 6 is **6**.

The absolute value of -17/4 is **17/4**.

The absolute value of 8 is **8**.

The absolute value of 7.8 is **7.8**.

The absolute value of -9.1 is **9.1**.

Question 30.

Which number has the greatest absolute value?

Answer:

The decimal number – **9.1** has the greatest absolute value.

Question 31.

Order the absolute values from least to greatest. Use the symbol <.

Answer:

The absolute values from least to greatest are **0 < 23/8 < 17/4 < 6 < 7(1/5) < 7.8 < 8 < 9.1.**

Question 32.

Graph the original numbers on a number line.

Answer:

23/8, 0, -7(1/5), 6 , -17/4, 8, 7.8, -9.1

The original numbers on a number line is drawn on the graph.

Question 33.

Which negative number in the list is farthest from 0?

Answer:

The negative number –**9.1** in the given list is farthest from 0.

Question 34.

Which positive number in the list is closest to 10?

Answer:

The positive number **8** in the given list is closest to 10.

Question 35.

Which time is closest to —5 minutes?

Answer:

The time **-17/4** is closest to – 5 minutes.