Math in Focus

Go through the Math in Focus Grade 6 Workbook Answer Key Chapter 3 Lesson 3.3 Dividing Decimals to finish your assignments.

Math in Focus Grade 6 Course 1 A Chapter 3 Lesson 3.3 Answer Key Dividing Decimals

Math in Focus Grade 6 Chapter 3 Lesson 3.3 Guided Practice Answer Key

Complete.

Question 1.
Find 1 ÷ 0.5
Method 1

Answer:
There are two 0.5s in 1 whole.

Explanation:
There are two 0.5s are in 1 whole.

Method 2
1 ÷ 0.5 = 1 ÷ \(\frac{5}{10}\)
= 1 × \(\frac{10}{5}\)
= 2.

Question 2.
Find 48 ÷ 0.3

Answer:
48 ÷ 0.3 = 160.

Explanation:
48 ÷ 0.3 = 48 ÷ \(\frac{3}{10}\)
= 48 × \(\frac{10}{3}\)
= 16 × 10
= 160.

Complete.

Question 3.
Complete the model to show the division expression 98 ÷ 0.14.

Answer:
98 ÷ 0.14 = 700.

Explanation:

Method 2
98 ÷ 0.14 = 98 ÷ \(\frac{14}{100}\)
= 98 × \(\frac{100}{14}\)
= 7 × 100
= 700.

Divide.

Question 4.

Answer:
75 ÷ 0.15 = 500.

Explanation:
75 ÷ 0.15 = 75 ÷ \(\frac{15}{100}\)
= 75 × \(\frac{100}{15}\)
= 5 × 100
= 500.

Question 5.

Answer:
156 ÷ 0.13 = 1200.

Explanation:
Given the division expression is 156 ÷ 0.13,
156 ÷ 0.13 = 156 ÷ \(\frac{13}{100}\)
= 156 × \(\frac{100}{13}\)
= 12 × 100
= 1200.

Complete.

Question 6.
Find 0.9 ÷ 0.3.

Answer:
There are three 0.3s in 0.9.

Explanation:
Given the division expression is 0.9 ÷ 0.3,
0.9 ÷ 0.3 = \(\frac{9}{10}\) ÷ \(\frac{3}{10}\)
= \(\frac{9}{10}\) × \(\frac{10}{3}\)
= 3.
So each small interval represents 0.3 and there are 3 intervals.

Complete.

Question 7.
Find 0.72 ÷ 0.03.
Method 1

Answer:
0.72 ÷ 0.03 = 24.

Explanation:
Given the division expression is 0.72 ÷ 0.03,
Method 1
0.72 = \(\frac{72}{100}\)  and 0.03 = \(\frac{3}{100}\)
= \(\frac{72}{100}\) ÷ \(\frac{3}{100}\)
= \(\frac{72}{100}\) × \(\frac{100}{3}\)
= 24.

Method 2
0.72 ÷ 0.03 = \(\frac{0.72}{0.03}\)
= \(\frac{0.72}{0.03}\) × \(\frac{100}{100}\)
= \(\frac{72}{3}\)
= 24.

Complete.

Question 8.
Find 0.78 ÷ 0.6.

Answer:
0.78 ÷ 0.6 = 1.3.

Explanation:
Given the division expression is 0.78 ÷ 0.6,
Method 1
0.78 = \(\frac{78}{100}\)  and 0.6 = \(\frac{6}{10}\)
= \(\frac{78}{100}\) ÷ \(\frac{6}{10}\)
= \(\frac{78}{100}\) × \(\frac{10}{6}\)
= \(\frac{13}{10}\)
= 1.3.

Method 2
0.78 ÷ 0.6 = \(\frac{0.78}{0.6}\)
= \(\frac{0.78}{0.6}\) × \(\frac{10}{10}\)
= \(\frac{7.8}{6}\)
= 1.3.

Question 9.
Find 6.75 ÷ 0.3.

Answer:

Explanation:
Given the division expression is 6.75 ÷ 0.3,
Method 1
6.75 = \(\frac{675}{100}\)  and 0.3 = \(\frac{3}{10}\)
= \(\frac{675}{100}\) ÷ \(\frac{3}{10}\)
= \(\frac{675}{100}\) × \(\frac{10}{3}\)
= \(\frac{225}{10}\)
= 22.5.

Method 2
6.75 ÷ 0.3 = \(\frac{6.75}{0.3}\)
= \(\frac{6.75}{0.3}\) × \(\frac{10}{10}\)
= \(\frac{67.5}{3}\)
= 22.5

Math in Focus Course 1A Practice 3.3 Answer Key

Write a division expression that represents each model.

Question 1.

Answer:
1 ÷ 0.2 = 5.

Explanation:
In 1 whole there are five 0.2s, so the division expression will be 1 ÷ 0.2 which is 5.

Question 2.

Answer:
3 ÷ 0.2 = 15.

Explanation:
In 3 wholes there are 15 0.2s, so the division expression will be 3 ÷ 0.2 which is 15.

Divide.

Question 3.
2 ÷ 0.4
Answer:
2 ÷ 0.4 = 5.

Explanation:
Given the division expression is 2 ÷ 0.4,
2 ÷ 0.4 = 2 ÷ \(\frac{4}{10}\)
= 2 × \(\frac{10}{4}\)
= 5.

Question 4.
4 ÷ 0.5
Answer:
4 ÷ 0.5 = 8.

Explanation:
Given the division expression is 4 ÷ 0.5,
4 ÷ 0.5 = 4 ÷ \(\frac{5}{10}\)
= 4 × \(\frac{10}{5}\)
= 8.

Question 5.
5 ÷ 0.2
Answer:
5 ÷ 0.2 = 25.

Explanation:
Given the division expression is 5 ÷ 0.2,
5 ÷ 0.2 = 5 ÷ \(\frac{2}{10}\)
= 5 × \(\frac{10}{2}\)
= 5 × 5
= 25.

Question 6.
8 ÷ 0.8
Answer:
8 ÷ 0.8 = 10.

Explanation:
Given the division expression is 8 ÷ 0.8,
8 ÷ 0.8 = 8 ÷ \(\frac{8}{10}\)
= 8 × \(\frac{10}{8}\)
= 10.

Question 7.
9 ÷ 0.3
Answer:
9 ÷ 0.3 = 30.

Explanation:
Given the division expression is 9 ÷ 0.3,
9 ÷ 0.3 = 9 ÷ \(\frac{3}{10}\)
= 9 × \(\frac{10}{3}\)
= 3 × 10
= 30.

Question 8.
7 ÷ 0.4
Answer:
7 ÷ 0.4 = 17.5.

Explanation:
Given the division expression is 7 ÷ 0.4,
7 ÷ 0.4 = 7 ÷ \(\frac{4}{10}\)
= 7 × \(\frac{10}{4}\)
= 7 × \(\frac{5}{2}\)
= \(\frac{35}{2}\)
= 17.5.

Question 9.
12 ÷ 0.3
Answer:
12 ÷ 0.3 = 40.

Explanation:
Given the division expression is 12 ÷ 0.3,
12 ÷ 0.3 = 12 ÷ \(\frac{3}{10}\)
= 12 × \(\frac{10}{3}\)
= 4 × 10
= 40.

Question 10.
42 ÷ 0.7
Answer:
42 ÷ 0.7 = 60.

Explanation:
Given the division expression is 42 ÷ 0.7,
42 ÷ 0.7 = 42 ÷ \(\frac{7}{10}\)
= 42 × \(\frac{10}{7}\)
= 6 × 10
= 60.

Question 11.
55 ÷ 0.5
Answer:
55 ÷ 0.5 = 110.

Explanation:
Given the division expression is 55 ÷ 0.5,
55 ÷ 0.5 = 55 ÷ \(\frac{5}{10}\)
= 55 × \(\frac{10}{5}\)
= 11 × 10
= 110.

Question 12.
69 ÷ 0.2
Answer:
69 ÷ 0.2 = 345

Explanation:
Given the division expression is 69 ÷ 0.2,
69 ÷ 0.2 = 69 ÷ \(\frac{2}{10}\)
= 69 × \(\frac{10}{2}\)
= 69 × 5
= 345.

Question 13.
86 ÷ 0.5
Answer:
86 ÷ 0.5 = 172

Explanation:
Given the division expression is 86 ÷ 0.5,
86 ÷ 0.5 = 86 ÷ \(\frac{5}{10}\)
= 86 × \(\frac{10}{5}\)
= 86 × 2
= 172.

Question 14.
93 ÷ 0.4
Answer:

Explanation:
Given the division expression is 93 ÷ 0.4,
93 ÷ 0.4 = 93 ÷ \(\frac{4}{10}\)
= 93 × \(\frac{10}{4}\)
= 93 × \(\frac{5}{2}\)
= \(\frac{465}{2}\)
= 232.5.

Question 15.
1 ÷ 0.02
Answer:
1 ÷ 0.02 = 50.

Explanation:
Given the division expression is 1 ÷ 0.02,
1 ÷ 0.02 = 1 ÷ \(\frac{2}{100}\)
= 1 × \(\frac{100}{2}\)
= 50.

Question 16.
3 ÷ 0.06
Answer:
3 ÷ 0.06 = 50.

Explanation:
Given the division expression is 3 ÷ 0.06,
3 ÷ 0.06 = 3 ÷ \(\frac{6}{100}\)
= 3 × \(\frac{100}{6}\)
= \(\frac{100}{2}\)
= 50.

Question 17.
6 ÷ 0.15
Answer:
6 ÷ 0.15 = 40.

Explanation:
Given the division expression is 6 ÷ 0.15,
6 ÷ 0.15 = 6 ÷ \(\frac{15}{100}\)
= 6 × \(\frac{100}{15}\)
= 2 × \(\frac{100}{5}\)
= 2 × 20
= 40.

Question 18.
7 ÷ 0.35
Answer:
7 ÷ 0.35 = 20.

Explanation:
Given the division expression is 7 ÷ 0.35,
7 ÷ 0.35 = 7 ÷ \(\frac{35}{100}\)
= 7 × \(\frac{100}{35}\)
= 20.

Question 19.
8 ÷ 0.32
Answer:
8 ÷ 0.32 = 25.

Explanation:
Given the division expression is 8 ÷ 0.32,
8 ÷ 0.32 = 8 ÷ \(\frac{32}{100}\)
= 8 × \(\frac{100}{32}\)
= 25.

Question 20.
9 ÷ 0.72
Answer:
9 ÷ 0.72 = 12.5.

Explanation:
Given the division expression is 9 ÷ 0.72,
9 ÷ 0.72 = 9 ÷ \(\frac{72}{100}\)
= 9 × \(\frac{100}{72}\)
= 12.5.

Draw a model to show each division expression.

Question 21.
2 ÷ 0.5
Answer:
2 ÷ 0.5 = 4.

Explanation:
Given the division expression is 2 ÷ 0.5,
2 ÷ 0.5 = 2 ÷ \(\frac{5}{10}\)
= 2 × \(\frac{10}{5}\)
= 4.

Question 22
5 ÷ o.2
Answer:
5 ÷ o.2 = 10.

Explanation:
Given the division expression is 5 ÷ o.2,
5 ÷ o.2 = 5 ÷ \(\frac{2}{10}\)
= 5 × \(\frac{10}{5}\)
= 10.

Divide.

Question 23.
36 ÷ 0.36
Answer:
36 ÷ 0.36 = 100.

Explanation:
Given the division expression is 36 ÷ 0.36,
36 ÷ 0.36 = 36 ÷ \(\frac{36}{100}\)
= 36 × \(\frac{100}{36}\)
= 100.

Question 24.
49 ÷ 0.14
Answer:
49 ÷ 0.14 = 350.

Explanation:
Given the division expression is 49 ÷ 0.14,
49 ÷ 0.14 = 49 ÷ \(\frac{14}{100}\)
= 49 × \(\frac{100}{14}\)
= 49 × 50
= 350.

Question 25.
56 ÷ 0.28
Answer:
56 ÷ 0.28 = 200.

Explanation:
Given the division expression is 56 ÷ 0.28,
56 ÷ 0.28 = 56 ÷ \(\frac{28}{100}\)
= 56 × \(\frac{100}{28}\)
= 2 × 100
= 200.

Question 26.
72 ÷ 0.20
Answer:
72 ÷ 0.20 = 360.

Explanation:
Given the division expression is 72 ÷ 0.20,
72 ÷ 0.20 = 72 ÷ \(\frac{20}{100}\)
= 72 × \(\frac{100}{20}\)
= 72 × 5
= 360.

Question 27.
81 ÷ 0.54
Answer:
81 ÷ 0.54 = 150.

Explanation:
Given the division expression is 81 ÷ 0.54,
81 ÷ 0.54 = 81 ÷ \(\frac{54}{100}\)
= 81 × \(\frac{100}{54}\)
= 3 × \(\frac{100}{2}\)
= 3 × 50
= 150.

Question 28.
256 ÷ 0.64
Answer:
256 ÷ 0.64 = 400.

Explanation:
Given the division expression is 256 ÷ 0.64,
256 ÷ 0.64 = 256 ÷ \(\frac{64}{100}\)
= 256 × \(\frac{100}{64}\)
= 4 × 100
= 400.

Question 29.
749 ÷ 0.7
Answer:
749 ÷ 0.7 = 1,070.

Explanation:
Given the division expression is 749 ÷ 0.7,
749 ÷ 0.7 = 749 ÷ \(\frac{7}{10}\)
= 749 × \(\frac{10}{7}\)
= 107 × 10
= 1,070.

Question 30.
972 ÷ 0.8
Answer:
972 ÷ 0.8 = 1,215.

Explanation:
Given the division expression is 972 ÷ 0.8,
972 ÷ 0.8 = 972 ÷ \(\frac{8}{10}\)
= 972 × \(\frac{10}{8}\)
= 972 × \(\frac{5}{4}\)
= 243 × 5
= 1,215.

Question 31.
96 ÷ 0.16
Answer:
96 ÷ 0.16 = 1600.

Explanation:
Given the division expression is 96 ÷ 0.16,
96 ÷ 0.16 = 96 ÷ \(\frac{16}{100}\)
= 96 × \(\frac{100}{16}\)
= 16 × 100
= 1600.

Question 32.
545 ÷ 0.25
Answer:
545 ÷ 0.25 = 218.

Explanation:
Given the division expression is 545 ÷ 0.25,
545 ÷ 0.25 = 545 ÷ \(\frac{25}{10}\)
= 545 × \(\frac{10}{25}\)
= 545 × \(\frac{2}{5}\)
= 109 × 2
= 218.

Question 33.
0.6 ÷ 0.3
Answer:
0.6 ÷ 0.3 = 2.

Explanation:
Given the division expression is 0.6 ÷ 0.3,
0.6 ÷ 0.3 = \(\frac{6}{10}\) ÷ \(\frac{3}{10}\)
= \(\frac{6}{10}\) × \(\frac{10}{3}\)
= 2.

Question 34.
0.64 ÷ 0.04
Answer:
0.64 ÷ 0.04 = 64.

Explanation:
Given the division expression is 4 ÷ 0.5,
0.64 ÷ 0.04 = \(\frac{64}{100}\) ÷ \(\frac{4}{100}\)
= \(\frac{64}{100}\) × \(\frac{100}{4}\)
= 16.

Question 35.
0.78 ÷ 0.06
Answer:
0.78 ÷ 0.06 = 13.

Explanation:
Given the division expression is 0.78 ÷ 0.06,
0.78 ÷ 0.06 = \(\frac{78}{100}\) ÷ \(\frac{6}{100}\)
=\(\frac{78}{100}\) × \(\frac{100}{6}\)
= 13.

Question 36.
0.85 ÷ 0.5
Answer:
0.85 ÷ 0.5 = 17.

Explanation:
Given the division expression is 0.85 ÷ 0.5,
0.85 ÷ 0.5 = \(\frac{85}{100}\) ÷ \(\frac{5}{10}\)
= \(\frac{85}{10}\)× \(\frac{10}{5}\)
= 17.

Question 37.
0.025 ÷ 0.5
Answer:
0.025 ÷ 0.5 = 0.05.

Explanation:
Given the division expression is 0.025 ÷ 0.5,
0.025 ÷ 0.5 = \(\frac{25}{1000}\) ÷ \(\frac{5}{10}\)
= \(\frac{25}{1000}\) × \(\frac{10}{5}\)
= \(\frac{5}{100}\)
= 0.05.

Question 38.
0.816 ÷ 0.34
Answer:
0.816 ÷ 0.34 = 2.4.

Explanation:
Given the division expression is 0.816 ÷ 0.34,
0.816 ÷ 0.34 = \(\frac{816}{1000}\) ÷ \(\frac{34}{100}\)
= \(\frac{816}{1000}\) × \(\frac{100}{34}\)
= \(\frac{24}{10}\)
= 2.4.

Question 39.
4.5 ÷ 0.2
Answer:
4.5 ÷ 0.2 = 22.5.

Explanation:
Given the division expression is 4.5 ÷ 0.2,
4.5 ÷ 0.2 = \(\frac{45}{10}\) ÷ \(\frac{2}{10}\)
= \(\frac{45}{10}\) × \(\frac{10}{2}\)
= \(\frac{45}{2}\)
= 22.5.

Question 40.
8.82 ÷ 0.6
Answer:
8.82 ÷ 0.6 = 14.7.

Explanation:
Given the division expression is 8.82 ÷ 0.6,
8.82 ÷ 0.6 = \(\frac{882}{100}\) ÷ \(\frac{6}{10}\)
= \(\frac{882}{100}\) × \(\frac{10}{6}\)
= \(\frac{147}{10}\)
= 14.7.

Go through the Math in Focus Grade 6 Workbook Answer Key Chapter 2 Lesson 2.1 Negative Numbers to finish your assignments.

Math in Focus Grade 6 Course 1 A Chapter 2 Lesson 2.1 Answer Key Negative Numbers

Math in Focus Grade 6 Chapter 2 Lesson 2.1 Guided Practice Answer Key

Write a positive or negative number to represent each situation.

Question 1.
36°F below zero
Answer:
-36°F
Explanation:
The given situation is 36°F below zero. The word ‘below zero’ represents negative sign. The given situation is represented with negative number -36°F.

Question 2.
A debit of $10,540
Answer:
-$10,540
Explanation:
The given situation is a debit of $10,540. The word debit is represented with negative sign and credit is represented with positive sign. The given situation is represented with negative number -$10,540.

Question 3.
29,035 feet below sea level
Answer:
-29,035 feet
Explanation:
The given situation is 29,035 feet below sea level. The word ‘below sea level’ is represented with negative sign. So, the given situation is represented with negative number -29,035 feet.

Question 4.
A gain of 45 yards
Answer:
45 yards
Explanation:
The given situation is a gain of 45 yards. The word ‘gain’ is represented with positive sign. The word ‘loss’ is represented with negative sign. So, the given situation is represented with positive number 45 yards.

Answer the questions.

The table shows the elevations of four locations compared to sea level.

Question 5.
New Orleans is 8 feet sea level.
Answer:
New Orleans is 8 feet below sea level.

Question 6.
Mount Davidson is feet above sea level.
Answer:
Mount Davidson is 928 feet above sea level.

Question 7.
The deepest location among the four locations is .
Answer:
The deepest location among the four locations is Death Valley.

Question 8.
The highest location among the four locations is
Answer:
The highest location among the four locations is Pilot Mountain.

Question 9.
The location nearest to sea level is .
Answer:
The location nearest to sea level is New Orleans.

Copy and complete each inequality using > or <.

Question 10.

Answer:

-13 < -12 < -11 < -10 < -9 < -8 < -7 < -6 < -5 < -4
Explanation:
The missing numbers on the horizontal number line are -13, -11, -9, -6. On a horizontal number line, the numbers become greater as you move to the right, and less as you move to the left as we can observe in the above image.

Draw a horizontal number line to represent each set of numbers.

Question 11.
-8, -5, -4, -2, 2, 5, 7
Answer:

The given numbers -8, -5, -4, -2, 2, 5, 7 are represented in the above horizontal number line. On a horizontal number line, the numbers become greater as you move to the right, and less as you move to the left.

Question 12.
-16, -19, -20, -22, -25
Answer:

The given numbers -16, -19, -20, -22, -25 are represented in the above horizontal number line. On a horizontal number line, the numbers become greater as you move to the right, and less as you move to the left.

Write the opposite of each number.

Question 13.
-14
Answer:
The opposite number of -14 is 14.

Question 14.
-9
Answer:
The opposite number of -9 is 9.

Question 15.
-17
Answer:
The opposite number of -17 is 17.

Question 16.
27
Answer:
The opposite number of 27 is -27.

Question 17.
-23
Answer:
The opposite number of -23 is 23.

Question 18.
46
Answer:
The opposite number of 46 is -46.

Copy and complete each Inequality using > or <.

Question 19.
-15 -6
Answer:
-15  -6
Explanation:
The given numbers are -15 and -6. Here we have to compare both the numbers. By comparing the above given numbers the number -15 is less than -6.

Question 20.
-20 -23
Answer:
-20  -23
The given numbers are -20 and -23. Here we have to compare both the numbers. By comparing the above given numbers the number -20 is greater than -23.

Question 21.
-30 -3
Answer:
-30 -3
The given numbers are -30 and -3. Here we have to compare both the numbers. By comparing the above given numbers the number -30 is less than -3.

Question 22.
-19 0
Answer:
-19   0
The given numbers are -19 and 0. Here we have to compare both the numbers. By comparing the above given numbers the number -19 is less than 0.

Question 23.
12 -31
Answer:
12 -31
The given numbers are 12 and -31. Here we have to compare both the numbers. By comparing the above given numbers the number 12 is greater than -31.

Question 24.
-75 46
Answer:
-75  46
The given numbers are -75 and 46. Here we have to compare both the numbers. By comparing the above given numbers the number -75 is less than 46.

Hands-On Activity

Materials:

• number cards

Work in pairs. Your teacher will give you and your partner a set of number cards with these numbers on them:

Step 1.
Draw a number line and divide it into ten equal intervals. Label the endpoints -100 and 0. Shuffle the cards and place them face down on a flat surface.
Step 2.
Choose one card and turn it over. Mark the number shown on the card on the drawn number line.
Step 3.
Have your partner choose another card and mark the number shown on the number line.
Step 4.
Work together to write a statement of inequality for the two numbers you represented on the number line.
Step 5.
Repeat Step 2 through Step 4 using the other number cards.

Interpret and explain statements of order for positive and negative numbers in real-world situations.

a) The table shows the lowest recorded temperature in Alaska for each month from July through December.

September’s lowest recorded temperature of -13°F is lower than August’s lowest recorded temperature of 8°F.
To compare these two temperatures using an inequality, you can write -13°F < 8°F.
Answer:

b) The table shows the elevations of some natural features.

The elevation of Death Valley, which is -282 feet, ¡s greater than the elevation of Lake Assai, which is -509 feet.
To compare the two elevations using an inequality, you can write -282 ft > -509 ft.
The elevation of Lake Assai, which is -509 feet, is less than the elevation of Driskill Mountain, which has an elevation of 535 feet.
To compare the two elevations using an inequality, you can write -509 ft < 535 ft.

You can also write the inequalities above as -509ft < -282 ft and 535 ft > -509 ft.

Write an inequality for each statement using > or <.

Question 25.
0°C is warmer, than -5°C.
Answer:
0°C > -5°C
Explanation:
The given statement is 0°C is warmer, than -5°C. Here we have to compare both the temperatures. After comparing the temperatures 0°C is greater than -5°C.

Question 26.
The elevation of the Valdes Peninsula, which is -131 feet, is less than the elevation of the Caspian Sea, which is -92 feet.
Answer:
-131 feet < -92 feet
Explanation:
The elevation of the Valdes Peninsula is -131 feet.
The elevation of the Caspian Sea is -92 feet.
After comparing both the elevations -131 feet is less than -92 feet.

Write a statement to describe each inequality.

Question 27.
-61 °F < -47°F
Answer:
The lowest recorded temperature yesterday was -61°F, which is colder than today’s lowest recorded temperature of -47°F.

Question 28. –
520 feet > -893 feet
Answer:
A dog is standing on a cliff, 520 feet above sea level which is greater than a dolphin which is swimming 893 feet below sea level.

Math in Focus Course 1A Practice 2.1 Answer Key

Write a positive or negative number to represent each situation.

Question 1.
438°C above zero
Answer:
438°C
Explanation:
The given situation is 438°C above zero. The word ‘below zero’ represents negative number and ‘above zero’ represents positive number. So the situation is represented with positive number 438°C, which is above zero.

Question 2.
164°F below zero
Answer:
-164°F
Explanation:
The given situation is 164°F below zero. The word ‘below zero’ represents negative number and ‘above zero’ represents positive number. So the situation is represented with negative number -164°F, which is below zero.

Question 3.
8,327 feet below sea level
Answer:
-8,327 feet
Explanation:
The given situation is 8,327 feet below sea level. The word ‘below sea level’ represents negative number and ‘above sea level’ represents positive number. So the situation is represented with negative number -8,327 feet, which is below sea level.

Question 4.
12,316 feet above sea level
Answer:
12,316 feet
Explanation:
The given situation is 12,316 feet above sea level. The word ‘below sea level’ represents negative number and ‘above sea level’ represents positive number. So the situation is represented with positive number 12,316 feet, which is above sea level.

Question 5.
A loss of 20 yards
Answer:
-20 yards
Explanation:
The given situation is a loss of 20 yards. In general loss is represented with negative number and gain is represented with positive number. So the given situation is represented with negative number -20 yards.

Question 6.
A credit of $3,401
Answer:
$3,401
Explanation:
The given situation is a credit of $3,401. In general debit is represented with ‘negative sign’ and credit is represented with ‘positive sign’. So, the given situation is represented with positive number $3,401.

Copy and complete each number line by filling in the missing numbers.

Question 7.

Answer:

Explanation:
The missing numbers are -11, -9, -7, -3. The above number line is filled with the missing numbers as we can observe in the above image.

Question 8.

Answer:

Explanation:
The missing numbers are -35, -33, -32, -29. The above number line is filled with the missing numbers as we can observe in the above image.

Write the opposite of each number.

Question 9.
8
Answer:
The opposite number of 8 is -8.

Question 10.
-5
Answer:
The opposite number of -5 is 5.

Question 11.
21
Answer:
The opposite number of 21 is -21.

Question 12.
-29
Answer:
The opposite number of -29 is 29.

Question 13.
24
Answer:
The opposite number of 24 is -24.

Question 14.
-106
Answer:
The opposite number of -106 is 106.

Draw a horizontal number line to represent each set of numbers.

Question 15.
Even negative numbers from -24 to -1o
Answer:
Even negative numbers from -24 to -1o are -24, -22, -20 ,-18, -16, -14, -12, -10.

Explanation:
The even negative numbers are  -24, -22, -20 ,-18, -16, -14, -12, -10 are represented in the above horizontal number line. On a horizontal number line, the numbers become greater as you move to the right, and less as you move to the left.

Question 16.
The opposites of the whole numbers from 35 to 45
Answer:
The opposites of the whole numbers from 35 to 45 are -35, -36, -37, -38, -39, -40, -41, -42, -43, -44, -45.

Explanation:
The opposites of the whole numbers from 35 to 45 are -35, -36, -37, -38, -39, -40, -41, -42, -43, -44, -45 are represented in the above horizontal number line. On a horizontal number line, the numbers become greater as you move to the right, and less as you move to the left.

Draw a vertical number line to represent each set of numbers.

Question 17.
Odd numbers between -91 and -103
Answer:
Odd numbers between -91 and -103 are -93, -95, -97, -99, -101.

Explanation:
The odd numbers between -91 and -103 are -93, -95, -97, -99, -101 are represented in the above vertical number line. On a vertical number line, the numbers become greater as you move up, and lesser as you move down.

Question 18.
Even numbers greater than -6 but less than 12
Answer:
Even numbers greater than -6 but less than 12 are -4, -2, 0, 2 , 4, 6, 8, 10.

Explanation:
Even numbers greater than -6 but less than 12 are -4, -2, 0, 2 , 4, 6, 8, 10 are represented in the above vertical number line. On a vertical number line, the numbers become greater as you move up, and lesser as you move down.

Use the number line to compare each pair of numbers using > or <.

Question 19.
-9 -2
Answer:
-9  -2
Explanation:
In the above horizontal number line, the numbers become greater as you move to the right, and less as you move to the left.
Here -9 is to the left of -2.
So, -9 < -2.

Question 20.
-10 -4
Answer:
-10  -4
Explanation:
In the above horizontal number line, the numbers become greater as you move to the right, and less as you move to the left.
Here -10 is to the left of -4.
So, -10 < -4.

Question 21.
-5 4
Answer:
-5  4
Explanation:
In the above horizontal number line, the numbers become greater as you move to the right, and less as you move to the left.
Here -5 is to the left of 4.
So, -5 < 4.

Question 22.
2 -6
Answer:
2  -6
Explanation:
In the above horizontal number line, the numbers become greater as you move to the right, and less as you move to the left.
Here 2 is to the right of -6.
So, 2 > -6.

Question 23.
-5 -12
Answer:
-5  -12
Explanation:
In the above horizontal number line, the numbers become greater as you move to the right, and less as you move to the left.
Here -5 is to the right of -12.
So, -5 > -12.

Question 24.
-10 3
Answer:
-10 3
Explanation:
In the above horizontal number line, the numbers become greater as you move to the right, and less as you move to the left.
Here -10 is to the left of 3.
So, -10 < 3.

Copy and complete each inequality using > or <.

Question 25.
-27 -3
Answer:
-27  -3
Explanation:
The given numbers are -27 and -3. Here we have to compare both the numbers. By comparing the above given numbers the number -27 is less than -3.

Question 26.
-45 15
Answer:
-45  15
Explanation:
The given numbers are -45 and 15. Here we have to compare both the numbers. By comparing the above given numbers the number -45 is less than 15.

Question 27.
25 -25
Answer:
25  -25
Explanation:
The given numbers are 25 and -25. Here we have to compare both the numbers. By comparing the above given numbers the number 25 is greater than -25.

Question 28.
19 -15
Answer:
19  -15
Explanation:
The given numbers are 19 and -15. Here we have to compare both the numbers. By comparing the above given numbers the number 19 is greater than -15.

Question 29.
14 -16
Answer:
14  -16
Explanation:
The given numbers are 14 and -16. Here we have to compare both the numbers. By comparing the above given numbers the number 14 is greater than -16.

Question 30.
-81 -80
Answer:
-81  -80
Explanation:
The given numbers are -81 and -80. Here we have to compare both the numbers. By comparing the above given numbers the number -81 is less than -80.

Order the numbers in each set from least to greatest.

Question 31.
3, 7, -2, -9, 0, -5
Answer:
The above given numbers from least to greatest are -9, -5, -2, 0, 3, 7.

Question 32.
-10, 8, 34, -13, 10, -17
Answer:
The above given numbers from least to greatest are -17, -13, -10, 8, 10, 34.

Order the numbers in each set from greatest to least.

Question 33.
-14, 43, -20, -57, 19, 31
Answer:
The above given numbers from greatest to least are 43, 31, 19, -14, -20, -57.

Question 34.
98, -101, -76, 125, -92, 113
Answer:
The above given numbers from greatest to least are 125, 113, 98, -76, -92, -101.

Answer the questions.

Question 35.
Name two numbers that are each 2 units away from -7. Give the opposites of these two numbers.
Answer:

Question 36.
Math Journal Is the opposite of a number always negative? Explain
Answer:
No. The opposite of a negative integer is a positive number. For example, the opposite of -1 is 1.
Explanation:
The opposite of any positive integer is negative. The opposite of any negative integer is positive. Zero is its own opposite.

Question 37.
Write an inequality using > or < for the following statement: -22°C is colder than -4°C.
Answer:
-22°C < -4°C
Explanation:
The given statement is -22°C is colder than -4°C. Here we have to compare both the temperatures. After comparing the temperatures -22°C is less than -4°C.

Question 38.
Your friend says that the statement 0 < -15 is correct. Explain why the statement is incorrect.
Answer:
The statement 0 < -15 is incorrect.
-15 is the negative integer.
0 is the positive integer.
Explanation:
Consider a horizontal number line, In that line the numbers become greater as you move to the right, and less as you move to the left.
Here -15 is to the left of 0.
So, -15 < 0.

Question 39.
The elevation of the deepest part of the Pacific Ocean is -36,200 feet. The elevation of the deepest part of the Indian Ocean is -24,442 feet.
Write an inequality to compare the elevations. In which of the two oceans is the deepest part farther from sea level?

Answer:
The elevation of the deepest part of the Pacific Ocean is -36,200 feet.
The elevation of the deepest part of the Indian Ocean is -24,442 feet.
 -36,200 ft < -24,442 ft
Pacific ocean is the deepest part farther from seal level.

Question 40.
The temperature at which a substance boils is called its boiling point. The boiling points of two elements are shown in the table.

Write an inequality to compare the two boiling points. Which element has the greater boiling point?
Answer:
The boiling point of the oxygen is -183°C.
The boiling point of the Nitrogen is -196 °C.
-183°C > -196 °C
The oxygen has the greatest boiling point with -183°C.

Write a statement to describe each inequality.

Question 41.
-45 feet > -80 feet
Answer:
The given inequality is -45 feet > -80 feet. The statement for the given inequality is the elevation of the deepest part of the North Atlantic ocean is -45 feet which is greater than the elevation of the deepest part of the South Atlantic Ocean is -80 feet.

Question 42.
-436°F < -271 °F
Answer:
The given inequality is -436°F < -271 °F. The statement for the given inequality is –436°F is colder than -271 °F.

Go through the Math in Focus Grade 6 Workbook Answer Key Chapter 1 Lesson 1.4 Squares and Square Roots to finish your assignments.

Math in Focus Grade 6 Course 1 A Chapter 1 Lesson 1.4 Answer Key Squares and Square Roots

Math in Focus Grade 6 Chapter 1 Lesson 1.4 Guided Practice Answer Key

Find the square of each number.

Question 1.
2
Answer:
2 x 2 = 4

Explanation:
The square of 2 is 4.

Question 2.
6
Answer:
6 x 6 = 36

Explanation:
The square of 6 is 36.

Question 3.
9
Answer:
9 x 9 = 81

Explanation:
The square of 9 is 81.

Question 4.
11
Answer:
11 x 11 = 121

Explanation:
The square of 11 is 121.

Find a square root of a perfect square.

a) A square has an area of 9 square inches. Find the length of each side of the square.

You know that
Area of square = length × length.
To find the length of a side of the square, you need to find the number whose square is 9.
Recalling the multiplication facts of 3, you know that 3 × 3 = 9.
So, the length of each side of the square is 3 inches.
3 is called a square root of 9. This can be written as \(\sqrt{9}\) = 3.
You read this as “the square root of 9 equals 3”.

b) Find the square root of 100.

I can relate this to finding the length of the side of a square, given that it has an area of 1oo units².

Method 1
Recalling the multiplication facts of 10, you know that
10 × 10 = 100
So, \(\sqrt{100}\) = 10.

Method 2
By prime factorization,

Find the square root of each number.

Question 5.
25
Answer:
5

Explanation:
Recalling the multiplication facts of 25, you know that
25 = 5 x 5
= 5²
So, \(\sqrt{25}\) = 5

Question 6.
64
Answer:
8

Explanation:
Recalling the multiplication facts of 64, you know that
64 = 8 x 8
= 8²
So, \(\sqrt{64}\) = 8

Question 7.
144
Answer:
12

Explanation:
Recalling the multiplication facts of 144, you know that
144 = 12 x 12
= 12²
So, \(\sqrt{144}\) = 12

Question 8.
196
Answer:
13

Explanation:
Recalling the multiplication facts of 169, you know that
169 = 13 x 13
= 13²
So, \(\sqrt{169}\) = 13

Math in Focus Course 1A Practice 1.4 Answer Key

Find the square of each number.

Question 1.
3
Answer:
3 x 3 = 9

Explanation:
The square of 3 is 9.

Question 2.
7
Answer:
7 x 7 = 49

Explanation:
The square of 7 is 49.

Question 3.
12
Answer:
144

Explanation:
The square of 12 is 144.

Question 4.
10
Answer:
100

Explanation:
The square of 10 is 100.

Find the square root of each number.

Question 5.
36
Answer:
6

Explanation:
Recalling the multiplication facts of 36, you know that
36 = 6 x 6
= 6²
So, \(\sqrt{36}\) = 6

Question 6.
81
Answer:
9

Explanation:
Recalling the multiplication facts of 81, you know that
81 = 9 x 9
= 9²
So, \(\sqrt{81}\) = 9

Question 7.
121
Answer:
11

Explanation:
Recalling the multiplication facts of 121, you know that
121 = 11 x 11
= 11²
So, \(\sqrt{121}\) = 11

Question 8.
49
Answer:
7

Explanation:
Recalling the multiplication facts of 49, you know that
49 = 7 x 7
= 7²
So, \(\sqrt{49}\) = 7

Solve.

Question 9.
List the perfect squares that are between 25 and 100.
Answer:

Find the value of each of the following.

Question 10.
35²
Answer:

35 x 35 = 1225

Explanation:
The square of 35 is 1225.

Question 11.
56²
Answer:

56 x 56 = 3136

Explanation:
The square of 56 is 3136.

Question 12.
64²
Answer:

64 x 64 = 4096

Explanation:
The square of 64 is 4096.

Question 13.
\(\sqrt{289}\)
Answer:
17

Explanation:
Recalling the multiplication facts of 289, you know that
289 = 17 x 17
= 17²
So, \(\sqrt{289}\) = 17

Question 14.
\(\sqrt{400}\)
Answer:
20

Explanation:
Recalling the multiplication facts of 400, you know that
400 = 20 x 20
= 20²
So, \(\sqrt{400}\) = 20

Question 15.
\(\sqrt{484}\)
Answer:
22

Explanation:
Recalling the multiplication facts of 484, you know that
484 = 22 x 22
= 22²
So, \(\sqrt{484}\) = 22

Solve.

Question 16.
Given that 41² = 1,681, find the square of 410.
Answer:
168100

Explanation:
If 41² = 1,681 then 410² = 168100.

Question 17.
Given that 51² = 2,601, find the square root of 260,100.
Answer:
510

Explanation:
If 51² = 2601 then the square root of 260100 will be 510.

Question 18.
Given that \(\sqrt{676}\) = 26, evaluate \(\sqrt{2,704}\).
Answer:
52

Explanation:
Recalling the multiplication facts of 400, you know that
2704 = 52 x 52
= 52²
So, \(\sqrt{2704}\) = 52

Question 19.
Given that \(\sqrt{1,521}\) = 39, evaluate 390².
Answer:
152100

Explanation:
If \(\sqrt{1,521}\) = 39 then 390² = 152100.

Question 20.
Heather wants to make a giant square quilt with sides of length 28 feet. She uses square patches of fabric that have sides of length 4 feet. How many patches of fabric will Heather need to make the giant square quilt?

Answer:
7 patches of fabric Heather will need to make the giant square quilt.

Explanation:
Heather wants to make a giant square quilt with sides of length 28 feet.
She uses square patches of fabric that have sides of length 4 feet.
4 x 7 = 28
So, 7 patches of fabric Heather will need to make the giant square quilt.

Question 21.
This week, customers at a carpet store pay $3 for a square foot of carpet. Next week the store will be having a sale. During the sale, each square foot of carpet will cost only $2. Neil wants to carpet two square rooms in his house. The floor in one room is 10 feet by 10 feet. The floor in the other room is 14 feet by 14 feet. How much money will Neil save if he waits to buy carpet during the sale?
Answer:
296

Explanation:
Neil wants to carpet two square rooms in his house.
The floor in one room is 10 feet by 10 feet.
10 x 10 = 100 square feet
The floor in the other room is 14 feet by 14 feet
14 x 14 = 196
Neil wants to carpet two square rooms in his house
100+196=296
During the sale, each square foot of carpet is reduced by 1 so, $296 Neil will save.

Go through the Math in Focus Grade 6 Workbook Answer Key Chapter 1 Positive Numbers and the Number Line to finish your assignments.

Math in Focus Grade 6 Course 1 A Chapter 1 Answer Key Positive Numbers and the Number Line

Math in Focus Grade 6 Chapter 1 Quick Check Answer Key

Find the factors of each number.

Question 1.
30
Answer:
30 = 1 x 30, 30 = 2 x 15,
30 = 3 x 10, 30 = 5 x 6

Explanation:
1, 2, 3, 5, 6, 10, 15 and 30 are the factors of number 30.
a number or algebraic expression that divides another number or expression evenly,
with no remainder.

Question 2.
63
Answer:
1 x 63 = 63, 3 x 21 = 63, 7 x 9 = 63.

Explanation:
1, 3, 7, 9, 21 and 63 are the factors of number 63.
a number or algebraic expression that divides another number or expression evenly,
with no remainder.

Question 3.
56
Answer:
1 x 56 = 56, 2 x 28 = 56
4 x 14 = 56, 7 x 8 = 56

Explanation:
1, 2, 4, 7, 8, 14, 28 and 56 are the factors of number 56.
a number or algebraic expression that divides another number or expression evenly,
with no remainder.

Question 4.
84
Answer:
1 x 84 = 84, 2 x 42 = 84, 3 x 28 = 84
4 x 21 = 84, 6 x 14 = 84, 7 x 12 = 84

Explanation:
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84 are the factors of number 84.
a number or algebraic expression that divides another number or expression evenly,
with no remainder.

Find the first five multiples of each number.

Question 5.
4
Answer:
4, 8, 12, 16 and 20

Explanation:
4 x 1 = 4, 4 x 2 = 8, 4 x 3 = 12, 4 x 4  = 16, 4 x 5 = 20
4, 8, 12, 16 and 20 are the first five multiples of number 4.

Question 6.
6
Answer:
6, 12, 18, 24 and 30

Explanation:
6 x 1 = 6, 6x 2 = 12, 6 x 3 = 18, 6 x 4 = 24, 6 x 5 = 30
6, 12, 18, 24 and 30 are the first five multiples of number 6.

Question 7.
9
Answer:
9, 18, 27, 36 and 45

Explanation:
9 x 1 = 9, 9 x 2 = 18, 9 x 3 = 27, 9 x 4 = 36,9 x 5 = 45
9, 18, 27, 36 and 45 are the first five multiples of number 9.

Question 8.
13
Answer:
13, 26, 6, 52, 65

Explanation:
13 x 1 = 13, 13 x 2 = 26, 13 x 3 = 36, 13 x 4 = 52, 13 x 5 = 65
13, 26, 39, 52 and 65 are the first five multiples of number 13.

Complete.

Question 9.
Identify all the prime numbers in the following set of numbers.
2, 5, 13, 21, 23, 39, 47, 51, 53, 57
Answer:
2, 5, 13, 23, 47, 53.

Explanation:
2, 5, 13, 23, 47, 53 are the prime numbers in the given set.

Simplify.

Question 10.
(40 – 28) + 8 × 7
Answer:
68

Explanation:
(40-28) + 8 x 7
=12 + 56
=68
(40 – 28) + 8 × 7 = 68.

Question 11.
75 × (45 ÷ 5) – 70
Answer:
605

Explanation:
75 (45 ÷  5) – 70
=75 (9) – 70
=675 – 70
=605
75 × (45 ÷ 5) – 70 = 605.

Go through the Math in Focus Grade K Workbook Answer Key Chapter 10 Ordinal Numbers to finish your assignments.

Math in Focus Kindergarten Chapter 10 Answer Key Ordinal Numbers

Lesson 1 Sequencing Events

Pair.

Answer:
Definition of ordinal numbers: Ordinal numbers are the numbers that indicate the exact position of something or someone at a place. If the number of objects/persons are specified in a list: the position of the objects/persons is defined by ordinal numbers.
According to the definition we need to map the correct sequence of the above-given diagram.

The first stage is laying eggs.
The second stage is the eggs slowly broke up.
The third stage is the little birds comes out from the broken eggs.

Color the frames

Answer:
Definition of ordinal numbers: Ordinal numbers are the numbers that indicate the exact position of something or someone at a place. If the number of objects/persons are specified in a list: the position of the objects/persons is defined by ordinal numbers.
According to the definition we need to map the correct sequence of the above-given diagram.

Explanation:
In the first stage, we need to wear socks.
In the second stage, we need to wear shoes.
In the third stage, we need to tie up the shoe lays.

Color.

Question 1.

Answer:
The apple is red in colour.
To eat apples, first of all, we need to wash the apple. This is the first stage.

Question 2.

Answer:
The peel-off is the second stage of eating apples. Because wax is present above the apples. So definitely we need to peel off the first layer of the apple.

Question 3.

Answer:
After peeling off eating is the third stage.
Now we can happily eat the apple because we removed the first layer which is not good for health.

Question 4.

Answer:
After completion of eating the apple, we need to throw it out in the dustbin which is the last stage. Do not leave the remaining part here and there which is not good for society and human health also.

Lesson 2 Physical Position

Color the child that comes before Baby Bear. Circle the child that comes after Baby Bear.

Answer:
– The baby bear is in the middle of the baby boy and baby girl.
– So here we need to colour the person who is present before the baby bear. That’s why I coloured baby boy because he is in front of the baby bear.
–  The baby girl is the back of the bear so she is standing after the baby bear so I circled her.

Lesson 3 Showing Your Preferences

Pair.

Answer:
I preferred according to the alphabetical order. Here the above-given animals are lions, elephants, and bears.
As per alphabets, we get the first letter B, E, and L
according to that I mapped the choices:

Go through the Math in Focus Grade K Workbook Answer Key Chapter 1 Numbers to 5 to finish your assignments.

Math in Focus Kindergarten Chapter 1 Answer Key Numbers to 5

Lesson 1 All About 1 and 2

Two big potatoes met in a lane, Bowed most politely, bowed once again How do you do? How do you do? How do you do again?

Two tall green beans met in a lane, Bowed most politely, bowed once again How do you do? How do you do? How do you do again?

Two thin chillies met in a lane, Bowed most politely, bowed once again. How do you do? How do you do? How do you do again?

Two little peas met in a lane, Bowed most politely, bowed once again. How do you do? How do you do? How do you do again?

Match.

Answer:

Explanation:
Matched 2 cookies with 2 cookies
and 1 cookie with 1 cookie

Trace.

Answer:

Explanation:
Counted and traced the number

Count and write.

Question 1.

Answer:

Explanation:
Counted and traced the number

Question 2.

Answer:

Explanation:
Counted and traced the number

Question 3.

Answer:

Explanation:
Counted and traced the number

Question 4.

Answer:

Explanation:
Counted and traced the number

Question 5.

Answer:

Explanation:
Counted and traced the number

Question 6.

Answer:

Explanation:
Counted and traced the number

Lesson 2 Finding Matches

Color the same object.

Question 1.

Answer:

Explanation:
Colored the same object

Question 2.

Answer:

Explanation:
Colored the same object

Question 3.

Answer:

Explanation:
Colored the same object

Question 4.

Answer:

Explanation:
Colored the same object

Circle the groups of 2.

Explanation:

Circled the that have group of 2

Draw the same object.

Question 1.

Answer:

Explanation:
Drawn the same object

Question 2.

Answer:

Explanation:
Drawn the same object

Write the same number.

Question 1.

Answer:

Explanation:
Written the same number

Question 2.

Answer:

Explanation:
Written the same number

Draw an object that is not the same.

Question 1.

Answer:

Explanation:
Drawn the object that is not same

Question 2.

Answer:

Explanation:
Drawn the object that is not same

Write a number that is not the same.

Question 1.

Answer:

Explanation:
Written the number  that is not same

Question 2.

Answer:

Explanation:
Written the number  that is not same

Lesson 3 Not the Same but Different: All About 3

Match.

Answer:

Explanation:
Counted the number of balloons and matched with same number of balloons

Trace.

Answer:

Explanation:
Traced the given numbers

Look and Say.

Count and write.

Question 1.

Answer:

Explanation:
Counted and written the number

Question 2.

Answer:

Explanation:
Counted and written the number

Question 3.

Answer:

Explanation:
Counted and written the number

Question 4.

Answer:

Explanation:
Counted and written the number

Question 5.

Answer:

Explanation:
Counted and written the number

Question 6.

Answer:

Explanation:
Counted and written the number

Lesson 4 Why is this Different? All about 4

Look and Stay.

Match.

Answer:

Explanation:
Counted the number of spoons and matched with the same number of spoons

Trace.

Answer:

Explanation:
Traced the numbers 1 , 2 , 3 , 4

Count and write.

Question 1.

Answer:

Explanation:
Counted and written the number

Question 2.

Answer:

Explanation:
Counted and written the number

Question 3.

Answer:

Explanation:
Counted and written the number

Question 4.

Answer:

Explanation:
Counted and written the number

Question 5.

Answer:

Explanation:
Counted and written the number

Question 6.

Answer:

Explanation:
Counted and written the number

Look and win.

Lesson 5 All about 5

Look and Say

Draw a pretend animal.

Answer:

Match.

Answer:

Explanation:
Counted the number of trees and matched with the same number of trees

Question 1.

Answer:

Explanation:
Counted and written the number

Question 2.

Answer:

Explanation:
Counted and written the number

Question 3.

Answer:

Explanation:
Counted and written the number

Question 4.

Answer:

Explanation:
Counted and written the number

Question 5.

Answer:

Explanation:
Counted and written the number

Question 6.

Answer:

Explanation:
Counted and written the number

Lesson 6 Spotting Small Differences

Color 5 differences.

Explanation:

Colored the five differences

Circle the differences.

Circle the differences.

Explanation:

Circled the 5 differences in the picture

Go through the Math in Focus Grade K Workbook Answer Key Chapter 5 Size and Position to finish your assignments.

Math in Focus Kindergarten Chapter 5 Answer Key Size and Position

Lesson 1 Big and Small Things

Draw.

Answer:

Explanation:
Drawn one more big balloon and a small balloon

Count and write.

Answer:

Explanation:
There are 3 big boxes, 4 small boxes and 7 boxes in all

Lesson 2 Does It Fit?

Which will fit? Color.

Question 1.

Answer:

Explanation:
The pillow will not fit in the box and brush the brush is colored

Question 2.

Answer:

Explanation:
The ball will not fit in the cup so marbles are colored

Question 3.

Answer:

Explanation:
the elephant will not fit in the net
so fish is colored

Lesson 3 Positions

Pair.

Answer:

Explanation:
The pencil will be on book
the spoon will be in cup
The bell will be hanged on the wall
The ball is placed on the ground

Lesson 4 ‘Before’ and ‘After’

Color the box.

Question 1.

Answer:

Explanation:
The food is before the boy

Question 2.

Answer:

Explanation:
The book is after the pencil and eraser

Question 3.

Answer:

Explanation:
The boys are waving bye after completing the school

Question 4.

Answer:

Explanation:
The boy is brushing before going to school

What do you d0 before school? Color.

Answer:

Explanation:
Before going to school we have to brush our teeth.

What do you d0 after school? Color.

Answer:

Explanation:
After coming from school We take the snacks

This handy Math in Focus Grade 1 Workbook Answer Key Chapter 2 Practice 2 Making Number Bonds detailed solutions for the textbook questions.

Math in Focus Grade 1 Chapter 2 Practice 2 Answer Key Making Number Bonds

Look at the pictures.

Complete the number bonds.

Example

Question 1.

Answer:

Explanation:
4 + 1 = 5
4 bees with basket and one bee is without basket
so, total there are 5 bees

Question 2.

Answer:

Explanation:
Three monkeys are with crowns and three monkeys are with out crowns
so, 3 + 3 = 6
The sum of 3 and 3 is 6

Look at the pictures. Complete the number bonds.

Question 3.

Answer:

Explanation:
2 + 1 = 3
There are 2 roses and a hibiscus
The sum of two and one is 3

Question 4.

Answer:

Explanation:
There are 5 jokers
Three are smiling jokers and 2 are crying jokers
3 + 2 = 5
The sum of 3 and 2 is 5

Question 5.

Answer:

Explanation:
Four mice are waiting in the restaurant  and three mice are preparing the food
3 + 4 = 7
the sum of 4 and 3 is 7

Question 6.

Answer:

Explanation:
6 + 4 = 10
there 6 boys and 4 girls
The sum of 6 and 4 is 10

Practice the problems of Math in Focus Grade 6 Workbook Answer Key Chapter 7 Lesson 7.5 Real-World Problems: Algebraic Expressions to score better marks in the exam.

Math in Focus Grade 6 Course 1 A Chapter 7 Lesson 7.5 Answer Key Real-World Problems: Algebraic Expressions

Math in Focus Grade 6 Chapter 7 Lesson 7.5 Guided Practice Answer Key

Complete.

Question 1.
Raoul is y years old. Kayla is 6 years older than Raoul and Isaac is 4 years younger than Raoul.
a) Find Kayla’s age.

Kayla is years old.
Answer:
y + 6 years

Explanation:
Raoul is y years old.
Kayla is 6 years older than Raoul and Isaac is 4 years younger than Raoul.
So, Kayla is y + 6  years old.

b) Find Isaac’s age.

Isaac is years old.
Answer:
y – 4 years
Explanation:
Raoul is y years old.
Kayla is 6 years older than Raoul and Isaac is 4 years younger than Raoul.
So, Isaac is y – 4 years old.

c) If y = 12, find the sum of Raoul’s age and Isaac’s age.
When y =12,
Isaac’s age:
– = –
= years old
Sum of Raoul’s age and Isaac’s age:
+ =
The sum of Roul’s age and Isaac’s age is years.
Answer:
20 years.
Explanation:
When y =12,
Isaac’s age:
12 –  4 =  8 years old
Sum of Raoul’s age and Isaac’s age:
12 + 8 = 20
The sum of Roul’s age and Isaac’s age is 20 years.

Question 2.
A pickup truck uses 1 gallon of gas for every 14 miles traveled,
a) How far can it travel on 3p gallons of gas?

1 gallon → miles
3p gallons → • = miles
It can travel miles on 3p gallons of gas.
Answer:
42 miles
Explanation:
1 gallon → 14 miles
3p gallons → 3p • 14 = 42 p miles
It can travel 42 p miles on 3p gallons of gas.

b) How many gallons of gas have been used after the pickup truck has traveled v miles? Evaluate this expression when v = 56.

14 miles → gallon
v miles → ÷ = gallons
gallons have been used.
When v = 56,
=
=
Answer:
4 groups
Explanation:
14 miles → 4 gallon
v miles → 56 ÷ 14 = 4 gallons
4 gallons have been used.
When v = 56,
56 = 14 x 4
= 4 groups

Question 3.
There were three questions in a mathematics test. Salma earned m points for the first question and twice the number of points for the second question,
a) How many points did she earn for the first two questions?

+ =
She earned points for the first two questions.
Answer:
3m points
Explanation:
m + 2m = 3m
She earned 3m points for the first two questions.

b) If she received a total of 25 points on the test, how many points did she earn for the third question?

She earned points for the third question.
Answer:
10 points
Explanation:
Salma received a total of 25 points on the test,
Third question: 25 – 3m = 25 – (3 •5)
= 25 – 15
= 10

c) If m = 5, find the points she earned for each question.
First question: m = 5
Second question: 2m = 2 •
=
Third question: 25 – 3m = 25 – (3 • )
= 25 –
=
She earned points for the first question, points for the second question and points for the third question.
Answer:
10 points
Explanation:
First question: m = 5
Second question: 2m = 2 • 5 = 10
Third question: 25 – 3m = 25 – (3 •5)
= 25 – 15
= 10
She earned 5 points for the first question, 10 points for the second question and 10 points for the third question.

Math in Focus Course 1A Practice 7.5 Answer Key

Question 1.
Jenny is x years old. Thomas is 3 times as old as she is. Jenny is 5 years older than Alexis.
a) Find Alexis’s age in terms of x.
Answer:
x+5
Explanation:
Jenny age x years
Thomas age 3x
Alexis are x + 5

b) Find Thomas’s age in terms of x.
Answer: 3x
Explanation:
Jenny is x years old.
Thomas is 3 times as old as she is.
Thomas age 3x.
c) If x = 12, how much older is Thomas than Jenny?
Answer:
36 years
Explanation:
Thomas is 3x = 3(12) = 36 years

Question 2.
A van travels from Town A to Town B. It uses 1 gallon of gas for every 24 miles traveled.
a) How many gallons of gas does the van use if it travels 3x miles?
Answer:
\(\frac{3x}{24}\) gallons of gas
Explanation:
1 gallon = 24 miles
3x miles = \(\frac{3x}{24}\) gallons of gas.

b) The van uses 2y gallons of gas for its journey from Town A to Town B. Find the distance between Town A and Town B.
Answer:
48y miles
Explanation:
1 gallon = 24 miles
2y gallons = 2y x 24 miles
= 48y miles

Question 3.
Brian bought x apples and some oranges. Brian bought 3 more oranges than apples.

a) Find the total number of fruit Brian bought in terms of x.
Answer:
2x + 3
Explanation:
x apples
x + 3 oranges
the total number of fruit Brian bought in terms of x is
= x + x +3 = 2x + 3

b) Find the total amount of money, in cents, that Brian spent on the fruit. Give your answer in terms of x.
Answer:
80x + 150 cents
Explanation:
2x ( 40 ) + 3 ( 50)
= 80x + 150 cents

c) If Brian could have bought exactly 12 pears with the amount of money that was spent on the apples and oranges, find the cost of each pear, in cents, in terms of x.
Answer:
\(\frac{80x+150}{12}\)
Explanation:
12p = 80x + 150 cents
p = \(\frac{80x+150}{12}\)

Question 4.
A rectangle has a width of x centimeters and a perimeter of 8x centimeters. A square has sides of length \(\frac{1}{4}\) that of the length of the rectangle.
a) Find the length of the rectangle.
Answer: 3x
Explanation:
8x = 2(x + l)
=> 8x/2= x + l
=> 4x = x + l
=> 4x – x = l
length = 3x

b) Find the perimeter of the square.
Answer: 3x
Explanation:
A square has sides of length \(\frac{1}{4}\)
the perimeter of the square = 4 x \(\frac{3x}{4}\) = 3x

c) Find how many centimetres greater the rectangle’s perimeter is than the square’s perimeter if x = 4.
Answer:
20 centimetres greater the rectangle’s perimeter is than the square’s perimeter.
Explanation:
rectangle’s perimeter = 8x
square’s perimeter = 3x
if x = 4.
rectangle’s perimeter = 8x = 8 x 4 = 32 cm
square’s perimeter = 3x = 3 x = 12 cm
32 – 12 = 20 cm
20 centimetres greater the rectangle’s perimeter is than the square’s perimeter

d) Find how many square centimetres greater the rectangle’s area is than the square’s area if x = 4.
Answer:
39 sq cm
Explanation:
Square area = side x side
= \(\frac{3x}{4}\) x \(\frac{3x}{4}\)
= \(\frac{3x}{4}\) x \(\frac{3x}{4}\) substitute x = 4
= \(\frac{3 x 4}{4}\) x \(\frac{3 x 4}{4}\) = 9 sq cm
Rectangle  area = length x width
= 3x . x = 3 x 4 . 4 = 48 sq cm
48 – 9 = 39 sq cm many square centimeters greater the rectangle’s area is than the square’s area.

Question 5.
Jose bought 4 comic books and 2 nonfiction books. The 4 comic books cost him 8y dollars. If the cost of one nonfiction book is (3 + 7y) dollars more expensive than the cost of one comic book, find
a) the cost of the 2 nonfiction books in terms of y.
Answer:
(15y + 6)/2
Explanation:
4 comic books = 8y
1 comic book = 8y/4 = y/2
one notification book = y/2 + (3 + 7y) = (15y + 6)/2

b) the total amount that Jose spent on the books if y = 4.
Answer:
$98
Explanation:
8y + 15y + 6
if y = 4
= 8.4 + 15.4 + 6
= 32 + 60 + 6
= 98$

Question 6.
Wyatt has (2x – 1) one-dollar bills and (4x + 2) five-dollar bills. Susan has 3x dollars more than Wyatt.
a) Find the total amount of money that Wyatt has in terms of x.
Answer:
22x – 9
Explanation:
Wyatt has (2x – 1) one-dollar bills and (4x + 2) five-dollar bills
2x-1 + 5(4x + 2)
= 2x – 1 + 20x + 10
= 22x – 9

b) Find the number of pens that Wyatt can buy if each pen costs 50 cents.
Answer:
44x -1 8 pens
Explanation:
Wyatt has (2x – 1) one-dollar bills and (4x + 2) five-dollar bills
2x-1 + 5(4x + 2)
= 2x – 1 + 20x + 10
= 22x – 9/(1/2)
= (22x – 9 ) x 2
= 44x -1 8 pens can buy

c) If x = 21, find how much money Susan will have now if Wyatt gives her half the number of five-dollar bills that he has.
Answer:
516$
Explanation:
Susan has 3x dollars more than Wyatt
Wyatt has 22x – 9
2x – 1 + (5(4x + 2))/2
= (4x – 2 + 20x + 10)/2
= (24x – 8)/2
now Susan has
x = 21
= 2x – 1+(4x + 2)/2 + 3x
= 2x-1 + (4 x 21 +2 )/2 + 3 x 21
= 2×21 -1 + 86/2 + 63
= 41 + 43 + 63
= 147$ (to be  re calculated)

Brain @ Work

Question 1.
Find the perimeter of the figure in terms of x, given that all the angles in the figure are right angles. If x = 5.5, evaluate this expression.

Answer:
65.1 cm
Explanation:
Perimeter of the given figure
= 3x + 16 + 5x + 16 – 2x
= 3 x 5.5 + 16 + 5 x 5.5 + 16 – 2 x 5.5
= 16.5 + 16 + 27.5 + 16 – 11
= 65.1 cm

Practice the problems of Math in Focus Grade 6 Workbook Answer Key Chapter 7 Algebraic Expressions to score better marks in the exam.

Math in Focus Grade 6 Course 1 A Chapter 7 Answer Key Algebraic Expressions

Math in Focus Grade 6 Chapter 7 Quick Check Answer Key

Draw a bar model to show each operation.

Question 1.
15 + 4
Answer:
19
Explanation:

Question 2.
17 – 9
Answer:
8
Explanation:

Question 3.
6 × 5
Answer:
30
Explanation:

Question 4.
28 ÷ 4
Answer:
7
Explanation:

Find the common factors and greatest common factor of each pair of numbers.

Question 5.
6 and 9
Answer:
Common Factor 1,3
Greatest Common Factor 3
Explanation:
To find the greatest common factor (GCF) between numbers,
take each number and write it’s prime factorization.
6 factors 1, 2, 3, 6
9 factors 1, 3,
Then, identify the factors common to each number and multiply those common factors together.

Question 6.
4 and 12
Answer:
Common Factor 1, 2, 4
Greatest Common Factor 4
Explanation:
To find the greatest common factor (GCF) between numbers,
take each number and write it’s prime factorization.
4 factors 1, 2, 4
12 factors 1, 2, 3, 4, 6
Then, identify the factors common to each number and multiply those common factors together.

Question 7.
5 and 15
Answer:
Common Factor 1, 5
Greatest Common Factor 5
Explanation:
To find the greatest common factor (GCF) between numbers,
take each number and write it’s prime factorization.
5 factors 1, 5
15 factors 1, 3, 5
Then, identify the factors common to each number and multiply those common factors together.

Question 8.
8 and 28
Answer:
Common Factor 1, 2, 4
Greatest Common Factor 4
Explanation:
To find the greatest common factor (GCF) between numbers,
take each number and write it’s prime factorization.
8 factors 1, 2, 4, 8
28 factors 1, 2, 4, 7, 14, 28
Then, identify the factors common to each number and multiply those common factors together.

Complete with quotient, sum, difference, product, dividend, or divisor.

Question 9.
The “5 less than 7” is 7 – 5.
Answer:
Difference
Explanation:
“5 less than 7” is 7 – 5.
the difference of 7 – 5 = 2

Question 10.
The of 5 and 7 is \(\frac{5}{7}\). 7 is the and 5 is the .
Answer:
The fraction of 5 and 7 is \(\frac{5}{7}\). 7 is the divisor and 5 is the dividend.
Explanation:
The fractions are defined as the parts of a whole.
The dividend is the number that is being divided in the division process.
The number by which dividend is being divided by is called divisor.

Question 11.
The of 5 and 7 is 7× 5.
Answer:
Product
Explanation:
The product of 5 and 7 is 7× 5.
When we multiply 2 numbers we call as product.

Question 12.
The of 5 and 7 is 5 + 7.
Answer:
Sum
Explanation:
The sum of 5 and 7 is 5 + 7.
sum can be defined as the result or answer we get on adding two or more numbers.