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Go through the Math in Focus Grade 5 Workbook Answer Key Chapter 1 Practice 2 Numbers to 10,000,000 to finish your assignments.

Math in Focus Grade 5 Chapter 1 Practice 2 Answer Key Numbers to 10,000,000

Complete the table. Then write the number in standard form and in word form.

Question 1.

Number in standard form: ______
Number in word form: _____
Answer:
Place value in Maths describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.

Number in standard form: 9,156,342
Number in word form: Nine million, one hundred fifty-six thousand, three hundred forty-two.

Write the number in standard form and in word form.

Number in standard form: __________________
Number in word form: _____________________
Answer:
Place value in Maths describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.
1. Place value tells you how much each digit stands for
2. Use a hyphen when you use words to write 2-digit numbers greater than 20 that have a digit other than zero in the one’s place.
3. A place-value chart tells you how many hundreds, tens, and ones to use.

Number in standard form:3,240,000.
Number in word form: Three million two hundred forty thousand.

Write each number in standard form.

Question 3.
two million, one hundred fifty-six thousand, four _____
Answer: 2,156,004
Standard form definition: A standard form of a number in Maths is basically mentioned for the representation of large numbers or small numbers. We use exponents to represent such numbers in standard form.
How to write the standard form of a number:
The steps to write the standard form of a number are as follows:
Step 1: Write the first number from the given number.
Step 2: Add the decimal point after the first number.
Step 3: Now, count the number of digits after the first number from the given number and write it in the power of 10.
The number is 2,156,004. Thus the standard form of a number is obtained as follows:
Step 1: The first number is 2.
Step 2: Adding the decimal point after 2, “it becomes 2.”
Step 3: The number of digits after 2 is 6.
Hence, the standard form of 2,156,004 is 2 × 10^6.

Question 4.
five million, two hundred thirty-eight thousand _____
Answer: 5,230,000.
Standard form definition: A standard form of a number in Maths is basically mentioned for the representation of large numbers or small numbers. We use exponents to represent such numbers in standard form.
How to write the standard form of a number:
The steps to write the standard form of a number are as follows:
Step 1: Write the first number from the given number.
Step 2: Add the decimal point after the first number.
Step 3: Now, count the number of digits after the first number from the given number and write it in the power of 10.
The number is 5,230,000. Thus the standard form of a number is obtained as follows:
Step 1: The first number is 5.
Step 2: Adding the decimal point after 5, “it becomes 5.”
Step 3: The number of digits after 5 is 6.
Hence, the standard form of 5,230,000 is 2 × 10^6.

Question 5.
seven million, one hundred fifty thousand _____
Answer: 7,150,000
Standard form definition: A standard form of a number in Maths is basically mentioned for the representation of large numbers or small numbers. We use exponents to represent such numbers in standard form.
How to write the standard form of a number:
The steps to write the standard form of a number are as follows:
Step 1: Write the first number from the given number.
Step 2: Add the decimal point after the first number.
Step 3: Now, count the number of digits after the first number from the given number and write it in the power of 10.
The number is 7,150,000. Thus the standard form of a number is obtained as follows:
Step 1: The first number is 7.
Step 2: Adding the decimal point after 7, “it becomes 7.”
Step 3: The number of digits after 7 is 6.
Hence, the standard form of 7,150,000 is 2 × 10^6.

Question 6.
six million, sixty thousand, fifty _____
Answer: 6,060,050
Standard form definition: A standard form of a number in Maths is basically mentioned for the representation of large numbers or small numbers. We use exponents to represent such numbers in standard form.
How to write the standard form of a number:
The steps to write the standard form of a number are as follows:
Step 1: Write the first number from the given number.
Step 2: Add the decimal point after the first number.
Step 3: Now, count the number of digits after the first number from the given number and write it in the power of 10.
The number is 6,060,050. Thus the standard form of a number is obtained as follows:
Step 1: The first number is 6.
Step 2: Adding the decimal point after 6, “it becomes 6.”
Step 3: The number of digits after 6 is 6.
Hence, the standard form of 6,060,050 is 2 × 10^6.

Question 7.
three million, three ____
Answer:3,000,003
Standard form definition: A standard form of a number in Maths is basically mentioned for the representation of large numbers or small numbers. We use exponents to represent such numbers in standard form.
How to write the standard form of a number:
The steps to write the standard form of a number are as follows:
Step 1: Write the first number from the given number.
Step 2: Add the decimal point after the first number.
Step 3: Now, count the number of digits after the first number from the given number and write it in the power of 10.
The number is 3,000,003. Thus the standard form of a number is obtained as follows:
Step 1: The first number is 3.
Step 2: Adding the decimal point after 3, “it becomes 3.”
Step 3: The number of digits after 3 is 6.
Hence, the standard form of 3,000,003 is 2 × 10^6.

Write each number in word form.

Question 8.
5,050000 _____
Answer:
Numbers in words are written using the English alphabet. Numbers can be expressed both in words and figures. For example, 100,000 in words is written as One Lakh or One hundred thousand. Numbers in words can be written for all the natural numbers, based on the place value of digits, such as ones, tens, hundreds, thousands, and so on.
How to write numbers in words:
The rules to write the numbers in words are discussed here. To write any number in the form of words, we have to check the place value. Let us learn this by observing the below steps.
1. The place value of one’s, a number from 1 to 9 is written in words as, one, two, three, four, five, six, seven, eight and nine.
2. The least number which is at tens place is 10, which is written in words as ten.
3. The numbers from 11 to 19 are written in words as, eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen and nineteen. And the next number is twenty.
4. After twenty, the numbers follow the pattern in such a way that they are written in words as thirty, forty, fifty, sixty, seventy, eighty, ninety and so on.
5. The preceding numbers are linked with these words and mentioned from one to nine. For example, twenty-one, twenty-two, etc.
If we have to write 5,050,000 in words, then it will be written as:
Number in word form: Five million fifty thousand.

Question 9.
8,147,600 ____
Answer:
Numbers in words are written using the English alphabet. Numbers can be expressed both in words and figures. For example, 100,000 in words is written as One Lakh or One hundred thousand. Numbers in words can be written for all the natural numbers, based on the place value of digits, such as ones, tens, hundreds, thousands, and so on.
How to write numbers in words:
The rules to write the numbers in words are discussed here. To write any number in the form of words, we have to check the place value. Let us learn this by observing the below steps.
1. The place value of one’s, a number from 1 to 9 is written in words as, one, two, three, four, five, six, seven, eight and nine.
2. The least number which is at tens place is 10, which is written in words as ten.
3. The numbers from 11 to 19 are written in words as, eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen and nineteen. And the next number is twenty.
4. After twenty, the numbers follow the pattern in such a way that they are written in words as thirty, forty, fifty, sixty, seventy, eighty, ninety and so on.
5. The preceding numbers are linked with these words and mentioned from one to nine. For example, twenty-one, twenty-two, etc.
If we have to write 8,147,600 in words, then it will be written as:
Number in word form: Eight million one hundred forty-seven thousand six hundred.

Question 10.
7,230,014 ____
Answer:
Numbers in words are written using the English alphabet. Numbers can be expressed both in words and figures. For example, 100,000 in words is written as One Lakh or One hundred thousand. Numbers in words can be written for all the natural numbers, based on the place value of digits, such as ones, tens, hundreds, thousands, and so on.
How to write numbers in words:
The rules to write the numbers in words are discussed here. To write any number in the form of words, we have to check the place value. Let us learn this by observing the below steps.
1. The place value of one’s, a number from 1 to 9 is written in words as, one, two, three, four, five, six, seven, eight and nine.
2. The least number which is at tens place is 10, which is written in words as ten.
3. The numbers from 11 to 19 are written in words as, eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen and nineteen. And the next number is twenty.
4. After twenty, the numbers follow the pattern in such a way that they are written in words as thirty, forty, fifty, sixty, seventy, eighty, ninety and so on.
5. The preceding numbers are linked with these words and mentioned from one to nine. For example, twenty-one, twenty-two, etc.
If we have to write 7,230,014 in words, then it will be written as:
Number in word form: Seven million two hundred thirty thousand fourteen.

Question 11.
5,192,622 ____
Answer:
Numbers in words are written using the English alphabet. Numbers can be expressed both in words and figures. For example, 100,000 in words is written as One Lakh or One hundred thousand. Numbers in words can be written for all the natural numbers, based on the place value of digits, such as ones, tens, hundreds, thousands, and so on.
How to write numbers in words:
The rules to write the numbers in words are discussed here. To write any number in the form of words, we have to check the place value. Let us learn this by observing the below steps.
1. The place value of one’s, a number from 1 to 9 is written in words as, one, two, three, four, five, six, seven, eight and nine.
2. The least number which is at tens place is 10, which is written in words as ten.
3. The numbers from 11 to 19 are written in words as, eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen and nineteen. And the next number is twenty.
4. After twenty, the numbers follow the pattern in such a way that they are written in words as thirty, forty, fifty, sixty, seventy, eighty, ninety and so on.
5. The preceding numbers are linked with these words and mentioned from one to nine. For example, twenty-one, twenty-two, etc.
If we have to write 5,192,622 in words, then it will be written as:
Number in word form: Five million one hundred ninety-two thousand six hundred twenty-two.

Question 12.
9009,009 ____
Answer:
Numbers in words are written using the English alphabet. Numbers can be expressed both in words and figures. For example, 100,000 in words is written as One Lakh or One hundred thousand. Numbers in words can be written for all the natural numbers, based on the place value of digits, such as ones, tens, hundreds, thousands, and so on.
How to write numbers in words:
The rules to write the numbers in words are discussed here. To write any number in the form of words, we have to check the place value. Let us learn this by observing the below steps.
1. The place value of one’s, a number from 1 to 9 is written in words as, one, two, three, four, five, six, seven, eight and nine.
2. The least number which is at tens place is 10, which is written in words as ten.
3. The numbers from 11 to 19 are written in words as, eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen and nineteen. And the next number is twenty.
4. After twenty, the numbers follow the pattern in such a way that they are written in words as thirty, forty, fifty, sixty, seventy, eighty, ninety and so on.
5. The preceding numbers are linked with these words and mentioned from one to nine. For example, twenty-one, twenty-two, etc.
If we have to write 9,009,009 in words, then it will be written as:
Number in word form: nine million nine thousand nine.

Go through the Math in Focus Grade 5 Workbook Answer Key Chapter 3 Practice 3 Fractions, Mixed Numbers, and Division Expressions to finish your assignments.

Math in Focus Grade 5 Chapter 3 Practice 3 Answer Key Fractions, Mixed Numbers, and Division Expressions

Look at the diagram. Complete.

Example

Question 1.

Answer:

Explanation:
based on diagram written the fraction

Write each division expression as a fraction.

Question 2.

Answer:

Explanation:
Written division expression as a fraction.

Question 3.

Answer:

Explanation:
Written division expression as a fraction.

Question 4.

Answer:

Explanation:
Written division expression as a fraction.

Question 5.

Answer:

Explanation:
Written division expression as a fraction.

Write each fraction as a division expression.

Example
\(\frac{7}{8}\) = 7 ÷ 8

Question 6.
\(\frac{5}{12}\) = ____ ÷ ____
Answer:
\(\frac{5}{12}\) = 5÷ 12
Explanation:
Written fraction as a division expression.

Question 7.
\(\frac{1}{10}\) = ____ ÷ ____
Answer:
\(\frac{1}{10}\) = 1÷ 10
Explanation:
Written fraction as a division expression.

Question 8.
\(\frac{6}{7}\) = ____ ÷ ____
Answer:
\(\frac{6}{7}\) = 6÷ 7
Explanation:
Written fraction as a division expression.

Look at the diagram. Complete.

Example

Look at the diagram. Complete.

Question 9.

Answer:

Explanation:
Based on diagram updated the fraction

Complete.

Question 10.

Answer:

Explanation:
Written division expression as a mixed fraction.

Question 11.

Answer:

Explanation:
Written division expression as a mixed fraction.

Divide. Express each quotient as a mixed number.

Example

Question 12.

Answer:

Explanation:
Written division expression as a mixed fraction.

Question 13.

Answer:

Explanation:
Written division expression as a mixed fraction.

Question 14.

Answer:

Explanation:
Written division expression as a mixed fraction.
Write each fraction in simplest form. Then divide to express each quotient as a mixed number.

Question 15.

Answer:

Explanation:
Written the fraction in simplest form and Then divide to express each quotient as a mixed number.

Question 16.

Answer:

Explanation:
Written the fraction in simplest form and Then divide to express each quotient as a mixed number.

Go through the Math in Focus Grade 5 Workbook Answer Key Chapter 4 Practice 4 Multiplying Mixed Numbers and Whole Numbers to finish your assignments.

Math in Focus Grade 5 Chapter 4 Practice 4 Answer Key Multiplying Mixed Numbers and Whole Numbers

Complete.

Question 1.

Answer:

Explanation:
Simplified the mixed fraction and multiplied.

Question 2.

Answer:

Explanation:
Simplified the mixed fraction  and multiplied.

Multiply. Express the product as a whole number or a mixed number in simplest form.

Example

Question 3.
4\(\frac{1}{5}\) × 15 =
Answer:

Explanation:
Simplified the mixed fraction and multiplied. simplified to whole number.

Question 4.
2\(\frac{3}{7}\) × 28 =
Answer:

Explanation:
Simplified the mixed fraction and multiplied. simplified to whole number.

Question 5.
24 × 1\(\frac{5}{6}\) =
Answer:

Explanation:
Simplified the mixed fraction and multiplied. simplified to whole number.

Question 7.
4\(\frac{1}{2}\) × 18 =
Answer:

Explanation:
Simplified the mixed fraction and multiplied. simplified to whole number.

Multiply. Express the product as a whole number or a mixed number in simplest form.

Question 7.
2\(\frac{3}{4}\) × 16 =
Answer:

Explanation:
Simplified the mixed fraction and multiplied. simplified to whole number.

Question 8.
32 × 3\(\frac{1}{8}\) =
Answer:

Explanation:
Simplified the mixed fraction and multiplied. simplified to whole number.

Multiply. Express the product as a whole number or a mixed number in simplest form.

Example

Question 9.
4 × 2\(\frac{7}{9}\) =
Answer:

Explanation:
Simplified the mixed fraction and multiplied. simplified to mixed fraction .

Question 10.
5 × 2\(\frac{3}{7}\) =
Answer:

Explanation:
Simplified the mixed fraction and multiplied. simplified to mixed fraction .

Multiply. Express the product as a whole number or a mixed number in simplest form.

Question 11.
2\(\frac{1}{4}\) × 7 =
Answer:

Explanation:
Simplified the mixed fraction and multiplied. simplified to mixed fraction .

Question 12.
1\(\frac{4}{5}\) × 12 =
Answer:

Explanation:
Simplified the mixed fraction and multiplied. simplified to mixed fraction .

Question 13.
12 × 2\(\frac{3}{8}\) =
Answer:

Explanation:
Simplified the mixed fraction and multiplied. simplified to mixed fraction .

Question 14.
26 × 1\(\frac{1}{6}\) =
Answer:

Explanation:
Simplified the mixed fraction and multiplied. simplified to mixed fraction .

Answer each question.

Question 15.
Is the product of 6 and 10 greater than or less than each of its factors? Explain your reasoning.
Answer:
6 x 10 = 60
Factors of 6 are 2, 3, 6, 1
Factors of 10 are 1, 2, 5, and 10.
Explanation:
The factors are lesser and equal to the product of 6 and 10

Question 16.
Is the product of \(\frac{2}{5}\) and 5 greater than or less than \(\frac{2}{5}\)? Is it greater than or less than 5? Explain your reasoning.
Answer:

Explanation:
The product of \(\frac{2}{5}\) and 5 is greater than \(\frac{2}{5}\)
The product of \(\frac{2}{5}\) and 5 is less than 5
that is 2

This handy Math in Focus Grade 5 Workbook Answer Key Chapter 13 Practice 2 Measures of Angles of a Triangle provides detailed solutions for the textbook questions.

Math in Focus Grade 5 Chapter 13 Practice 2 Answer Key Measures of Angles of a Triangle

Complete.

Question 1.

m∠A + m∠B + m∠C = ____
Answer:
m∠A + m∠B + m∠C =180°
Explanation:
The property of a triangle is : The sum of all internal angles of a triangle is always equal to 180^°.
m∠A + m∠B + m∠C = 180°

Question 2.

80° + 70° + m∠F = ___
m∠F = ___
Answer:
80° + 70° + m∠F = 180°
m∠F = 30°
Explanation:
The property of a triangle is : The sum of all internal angles of a triangle is always equal to 180^°.
80° + 70° + m∠F = 180°
m∠F = 180°- 80° + 70° = 30°

Measure the angles of the triangle. Then fill in the blanks.

Question 3.

m∠A = ___
m∠B = ___
m∠C = ____
m∠A + m∠B + m∠C = __ + ___ + ___
= ____
The sum of the angle measures in the triangle is ___
Answer:
m∠C = 40°

m∠B = 60°

The sum of angles in a triangle are 180°
40 + 60 = 100
180 – 100 = 80°
m∠A = 80°

m∠A = 80°
m∠B = 40°
m∠C = 60°
m∠A + m∠B + m∠C = 80°+ 40°+ 60° = 180°

These triangles are not drawn to scale. Find the unknown angle measures.

Question 4.
Find the measure of ∠B.

Answer:
m∠B = 75°
Explanation:
The property of a triangle is : The sum of all internal angles of a triangle is always equal to 180^°.
43° + 62° + m∠B = 180°
m∠B = 180° – 43° + 62° = 75°

Question 5.
Find the measure of ∠D.

Answer:
m∠D = 68°
Explanation:
The property of a triangle is : The sum of all internal angles of a triangle is always equal to 180^°.
72° + 50° + m∠D = 180°
m∠D = 180° – 72° + 50° = 68°

Question 6.
Find the measure of ∠H.

Answer:
m∠H  = 139°
Explanation:
The property of a triangle is : The sum of all internal angles of a triangle is always equal to 180^°.
15° + 26° + m∠H = 180°
m∠H = 180° – 15° + 26° = 139°

Question 7.
Find the measure of ∠QPS.

Answer:
m∠QPS =   38°
Explanation:
The property of a triangle is : The sum of all internal angles of a triangle is always equal to 180^°.
In Triangle PQR
60° + 32° + m∠QPR = 180°
m∠QPR = 180° – 60° + 32° = 88°
then as per the diagram
m∠QPS =  m∠QPR – m∠RPS  = 88° – 50° = 38°

This handy Math in Focus Grade 5 Workbook Answer Key Chapter 13 Practice 3 Right, Isosceles, and Equilateral Triangles provides detailed solutions for the textbook questions.

Math in Focus Grade 5 Chapter 13 Practice 3 Answer Key Right, Isosceles, and Equilateral Triangles

Complete. ABC and EFG are right triangles.

Question 1.

m∠B =___
m∠A + m∠C = ___
= ____
Answer:
m∠B =90°
m∠A + m∠C = 90°
Explanation:
Properties of Right – Angled Triangle

Question 2.

m∠E = ___
m∠F + m∠G = ___
Answer:
m∠E = 90°
m∠F + m∠G = 90°

Explanation:
Properties of Right – Angled Triangle

Measure the angles of the triangle. Then fill in the blanks.

Question 3.

m∠A _____
m∠B ______
m∠C ______
m∠A + m∠C ______
Answer:
m∠B = 90°

m∠C = 40°

m∠A = 50°
Explanation:
Sum of angles in a triangle are 180°
40 + 90 = 130
180 – 130 = 50
m∠A = 50°
m∠A + m∠C = 50° + 40° = 90°

These triangles are not drawn to scale. Identify and shade the right triangles.

Question 4.

Answer:

Explanation:

These triangles are not drawn to scale. Find the unknown angle measures.

Question 5.
Find the sum of the measures of ∠A and ∠B.

Answer:
∠A  + ∠B = 90°
Explanation:
Properties of Right – Angled Triangle

Question 6.
Find the measure of ∠C.

Answer:
33°
Explanation:
Properties of Right – Angled Triangle

Question 7.
Find the measure of ∠ADC and ∠ABC.

Answer:
∠ADC =62°
∠ABC =28°
Explanation:
In Triangle DAB, ∠DAB =90°
In Triangle ABC, ∠ACB=90°
In Triangle ACD, ∠ACD=90°
and ∠DAC=28°
So ∠ADC = 180° -(∠ACD +∠DAC) = 180° -(90°+28°) = 180° -(118°) =62°
∠BAC = ∠DAB – ∠DAC = 90° -28° = 62°
∠ABC =180° -(∠ACB +∠BAC) = 180° -(90°+62°) = 180° -(152°) =28°

Question 8.
Find the measures of ∠EGF and ∠DGE.

Answer:
∠EGF  =64°
∠DGE = 26°
Explanation:
In Triangle DGF, ∠DGF=90°
In Triangle GEF, ∠GEF=90° and ∠EFG=26°
In Triangle DEG, ∠DEG=90°
So ∠EGF= 180° -(∠GEF+∠EFG) = 180° -(90°+26°) = 180° -(116°) =64°
∠DGE= ∠DGF- ∠EGF= 90° -64° = 26°
Complete. XYZ and PQR are isosceles triangles.

Question 9.

Which two sides are of equal length?
________
Which two angles have equal measures?
_________
Answer:
XY and XZ  sides are equal length.
∠Z and ∠Y angles have equal measures.
Explanation:

Question 10.

Which two sides are of equal length?
_________
Which two angles have equal measures?
________
Answer:
PR and QR sides are of equal length.
∠P and ∠Q angles have equal measures.
Explanation:
An Isosceles Triangle has the Following Properties:

These triangles are not drawn to scale. Find the unknown angle measures.

Question 11.

Answer:

Explanation:
The properties of a triangle are:

1.  180 – (46 + 86) = 48
2. 180 – (75+74) = 31
3. 180  – (64 +52) = 64
4. 180 – (90 + 30 ) = 60
5. 180 – (80 + 80 ) = 20

These triangles are not drawn to scale. Find the unknown angle measures.

Question 12.
Find the measure of ∠F.

Answer:
∠F = 74°
Explanation:
The property of a triangle is : The sum of all internal angles of a triangle is always equal to 180^°.
∠D + ∠F = 180 – 53 = 127 °

Question 13.
Find the measure of ∠C.

Answer:
∠C  =72°

Explanation:
The property of a triangle is: The sum of all internal angles of a triangle is always equal to 180^°.
∠C + ∠B = 180 – 36 = 144°
An Isosceles Triangle has the Following Property: The angles opposite to equal sides are equal in measure
So ∠C = ∠B Then 144/2 =72°
then ∠C  =72°

Question 14.
Find the measure of ∠TRS.

Answer:
∠TRS = 180 – (∠RST+∠RTS)=180 – (20+90) = 70°
Explanation:
Triangle URS is a Isosceles Triangle.
An Isosceles Triangle has the Following Property: The angles opposite to equal sides are equal in measure Then
∠U= ∠S = 20°
The property of a triangle is : The sum of all internal angles of a triangle is always equal to 180^°.
In Triangle TRS ,
∠RST = 20°
∠RTS = 90°
∠TRS = 180 – (∠RST+∠RTS)=180 – (20+90) = 70°

Question 15.
Find the measure of ∠d.

Answer:
∠d =  172°
Explanation:
Triangle WXY is a Isosceles Triangle.
An Isosceles Triangle has the Following Property: The angles opposite to equal sides are equal in measure Then
then ∠W= ∠Y
Triangle WXZ a Right angle Triangle.
then ∠WZX = 90°
∠WXZ=86°
The property of a triangle is : The sum of all internal angles of a triangle is always equal to 180^°.
In Triangle WZX,
∠XWZ = 180 – (∠WZX+∠WXZ )=180 – (90+86) = 4°
In Triangle WXY , ∠W= ∠Y  = 4°
∠d = 180 – (4+4) = 172°

Complete. Use your protractor and centimeter ruler to measure the sides and angles. Which figure is an equilateral triangle? Check the box.

Question 16.

AB = __ cm
BC = __ cm
AC = ___ cm
m∠A = ___
m∠B = ___
m∠C = ____
Answer:

Question 17.

XY = __ cm
YZ = __ cm
XZ = ___ cm
m∠X = ___
m∠Y = ___
m∠Z = ____
Answer:

Explanation:
XY = 4 cm
YZ = 4 cm
XZ = 4 cm
m∠X = 60°
m∠Y = 60°
m∠Z = 60°
Explanation:
The angles and sides are equal

Complete. ABC is an equilateral triangle.

Question 18.
Which angles have measures equal to the measure of ∠A?
Answer:
∠A = ∠B = ∠C
Explanation:

Question 19.
Which sides have lengths equal to the length of \(\overline{A B}\)?
Answer:
\(\overline{A B}\)= \(\overline{B C}\) = \(\overline{A C}\)
Explanation:

Question 20.
What can you say about the angles of triangle ABC ?
Answer:
All angles are equal and 60° each.

Explanation:

These triangles are not drawn to scale. Identify and shade the equilateral triangles.

Question 21.

Answer:

Explanation:
Properties of an Equilateral Triangle

These triangles are not drawn to scale. Find the unknown angle measures.

Question 22.
Find the measure of ∠Q.

Answer:
∠Q = 60°
Explanation:
The property of a triangle is : The sum of all internal angles of a triangle is always equal to 180^°.
∠Q  = 180 – ∠P + ∠R = 180 – 60 + 60 = 60°

Question 23.
Find the measures of ∠Y and ∠Z

Answer:
∠Y =∠Z= 60°
Explanation:
The property of a triangle is : The sum of all internal angles of a triangle is always equal to 180^°.
∠Z + ∠Y  = 180 – ∠X  = 180 – 60  = 120°
As per diagram Triangle XYZ is a Isosceles Triangle.
An Isosceles Triangle has the Following Property: The angles opposite to equal sides are equal in measure Then
∠Y =∠Z
then ∠Y =∠Z= 120°/2 = 60°

These triangles are not drawn to scale. Find the unknown angle measures.

Question 24.
WX = XY = YW. Find the measure of ∠d.

Answer:
Explanation:
WX = XY = YW So Triangle WXY is a Equilateral Triangle So Three angles are equal
∠WXY = 60°
∠XWY= 60°
∠WYX= 60°
So In Triangle XYZ,
∠ZXY= 60°
∠XZY= 90°
∠XYZ= 180 – 90 + 60=30°
∠d = ∠WYX -∠XYZ  =60 – 30 =30°

Question 25.
Find the measure of ∠e.

Answer:
∠e = 120°
Explanation:
∠LON = 90° given
As the triangle is equalateral the angles are equal
so the measure of ∠LOE = 60°
∠LMO = 60°
NOM triangle is an isosceles triangle
90 – 60 = 30°
∠MON = 30°
∠OMN = 30°
30° + 30° = 60°
180° – 60° = 120°
∠e = 120°

Question 26.
Triangle PQR is an equilateral triangle. Triangle PST is an isosceles triangle. The measures of ∠a, ∠b, and ∠c are the same. Find the measure of ∠d.

Answer:
∠d. = 80°
Explanation:
Triangle PQR is an equilateral triangle.
In equilateral triangle all angles are equal
sum of angles in a triangle are 180°
Triangle PST is an isosceles triangle.
The measures of ∠a, ∠b, and ∠c are the same.
so, ∠a, ∠b, and ∠c = 60°
20° + 20° + 20° = 60°
In isosceles triangle
The isosceles triangle property states that when two sides are equal, the base angles are also equal
so, 180° – 20° = 160°
80° + 80 °= 160°
∠d. = 80°

This handy Math in Focus Grade 5 Workbook Answer Key Chapter 13 Practice 4 Triangle Inequalities provides detailed solutions for the textbook questions.

Math in Focus Grade 5 Chapter 13 Practice 4 Answer Key Triangle Inequalities

Complete. Measure the sides of the triangle to the nearest half-inch. Then fill in the blanks.

Explanation:

Question 1.
AB = _________ in.
Answer:
AB = 12 in.
Explanation:
With the help of ruler measured the length and updated

Question 2.
BC = _________ in.
Answer:
BC = 12 in.
Explanation:
With the help of ruler measured the length and updated

Question 3.
AC = ________ in.
Answer:
AC = 7 in.
Explanation:
With the help of ruler measured the length and updated

Question 4.
AB + BC = ________ in.
Answer:
AB + BC = 12 + 12 = 24 in.
Explanation:
With the help of ruler measured the length and updated
AB + BC = 12 + 12 = 24 in.

Question 5.
BC + AC = ________ in.
Answer: 12 + 7 = 19 in.
Explanation:
BC + AC =12 + 7 = 19 in.
With the help of ruler measured the length and updated

Question 6.
AB + AC = ________ in.
Answer:12 + 7 = 19 in.
Explanation:
AB + AC = 12 + 7 = 19 in.
With the help of ruler measured the length and updated

Use your answers ¡n Exercises 4 to 6. Fill ¡n the blanks with Yes or No.

Question 7.
Is AB + BC > AC? ______
Answer: Yes
Explanation:
AB + BC = 12 + 12 = 24
AC= 7
24 > 7

Question 8.
Is BC + AC > AB? ______
Answer: Yes
Explanation:
BC + AC = 12 + 7 = 19 in.
AB = 12 in.
19 > 7

Question 9.
Is AB + AC > BC? _______
Answer: Yes
Explanation:
AB + AC = 12 + 7 = 19 in.
BC = 12 in.
19 > 12

Complete. Measure the sides of the triangle to the nearest centimeter. Then fill in the blanks.

Explanation:

Question 10.
XY = ___ cm
Answer:
XY = 6 cm
Explanation:
With the help of ruler measured the length and updated

Question 11.
YZ = __ cm
Answer:
YZ = 4 cm
Explanation:
With the help of ruler measured the length and updated

Question 12.
XZ = __ cm
Answer:
XZ = 7 cm
Explanation:
With the help of ruler measured the length and updated

Question 13.
XY + YZ = __ cm
Answer:
XY + YZ = 6 + 4 = 10 cm
Explanation:
XY + YZ =6 + 4 = 10 cm
With the help of ruler measured the length and updated

Question 14.
YZ + XZ = __ cm
Answer:
YZ + XZ = 4 + 7 = 11 cm
Explanation:
YZ + XZ = 4 + 7 = 11 cm
With the help of ruler measured the length and updated

Question 15.
XY + XZ = __ cm
Answer:
XY + XZ = 6 + 7 = 13 cm
Explanation:
XY + XZ = 6 + 7 = 13 cm
With the help of ruler measured the length and updated

Use your answers in Exercises 10 to 15. Write the sides of the triangle to make the inequalities true.

Question 16.
XY + YZ > ______
Answer:
XY + YZ > XZ
Explanation:
XY + YZ > XZ
XY + YZ = 6 + 4 = 10 cm
XZ = 7
10 > 7

Question 17.
YZ + XZ > ______
Answer:
YZ + XZ > XY
Explanation:
YZ + XZ > XY
YZ + XZ = 4 + 7 = 11 cm
XY = 6
11 > 6

Question 18.
XY + XZ > ___
Answer:
XY + XZ > YZ
Explanation:
XY + XZ > YZ
XY + XZ = 6 + 7 = 13 cm
YZ = 4
13 > 4

Show whether it is possible to form triangles with these lengths.

Question 19.
6 in., 8 in., 12 in.
Answer:
Yes
Explanation:
6+ 8 > 12
6 + 12 > 8
12 + 8 > 6
sum of two sides should be greater than other side. so its possible to form triangle.

Question 20.
9 in., 13 in., 3 in.
Answer:
No
Explanation:
9 + 13 > 3
13  + 3  > 9
9  + 3 <   13 – sum of two sides should be greater than other side. so not possible to form triangle.

Question 21.
2 cm, 4 cm, 7 cm
Answer:
No
Explanation:
2 + 4 < 7
– sum of two sides should be greater than other side. so not possible to form triangle.

The lengths of two sides of each triangle are given. Name a possible length for the third side. The lengths are in whole centimeters or whole inches.

Question 22.

AB is greater than 10 centimeters. A possible length for \(\overline{A B}\) is
____ centimeters.
Answer:
15 centimeters
Explanation:
the sum of any 2 sides of a triangle must be greater than the measure of the third side.
13 + 9 > 15
13 + 15  > 9
15 + 9 > 13

Question 23.

QR is greater than 9 inches. A possible length for \(\overline{Q R}\) is
____________ inches.
Answer:
11 inches
Explanation:
the sum of any 2 sides of a triangle must be greater than the measure of the third side.
17 + 8 > 11
17 + 11  > 8
8  + 11  > 17

Solve.

Question 24.
In the triangle EFG, EF = 21 centimeters, FG = 11 centimeters. The length of \(\overline{E G}\) is in whole centimeters and is greater than 25 centimeters. What is a possible length of \(\overline{E G}\) ?
Answer:  \(\overline{E G}\)  = 26 centimeters
Explanation:
the sum of any 2 sides of a triangle must be greater than the measure of the third side.
21 + 11 > 26
21 + 26  > 11
26  + 11  > 21

This handy Math in Focus Grade 5 Workbook Answer Key Chapter 13 Practice 5 Parallelogram, Rhombus, and Trapezoid provides detailed solutions for the textbook questions.

Math in Focus Grade 5 Chapter 13 Practice 5 Answer Key Parallelogram, Rhombus, and Trapezoid

Complete. Figure ABCD is a parallelogram. Measure the sides and angles of the figure.

Explanation:

Question 1.
AD = ___ cm
Answer: AD = 6 cm
Explanation:
Property of a Parallelogram:

Question 2.
AB _______ cm
Answer:
AB = 7 cm
Explanation:
Property of a Parallelogram:

Question 3.
BC = __ cm
Answer:
BC = 6 cm
Explanation:
Property of a Parallelogram:

Question 4.
DC = ______ cm
Answer:
DC = 7 cm
Explanation:
Property of a Parallelogram:

Question 5.
m∠A = ____
Answer:
m∠A = 55°
Explanation:
Property of a Parallelogram:

Question 6.
m∠B = ___
Answer:
m∠B = 120°

Explanation:
Property of a Parallelogram:

Question 7.
m∠C = ___
Answer:
m∠C = 55°

Explanation:
Property of a Parallelogram:

Question 8.
m∠D = ___
Answer:
m∠D = 120°

Explanation:
Property of a Parallelogram:

Question 9.
Name the parallel sides of the figure. ______
Answer:
\(\overline{A B}\) || \(\overline{D C}\)
\(\overline{A D}\) || \(\overline{B C}\)

Question 10.
Name the opposite angles that are equal. ______
Answer:
m∠A = m∠C
m∠B = m∠D

This parallelogram is not drawn to scale. Fill in the blanks.

Question 11.
m∠Q = m∠___
= _____
Answer:
m∠Q = m∠S = 75°

Explanation:
Property of a Parallelogram:

Question 12.
m∠P = 180° – ___
= ____
Answer:
m∠P = 180° – m∠S =180° – 75° = 105°

Explanation:
Property of a Parallelogram:

Question 13.
m∠R = m∠___
= ____
Answer:
m∠R = m∠P =  105°

Explanation:
Property of a Parallelogram:

These parallelograms are not drawn to scale. Find the unknown angle measures.

Question 14.

Answer:
m∠a =  56°
Explanation:
Property of a Parallelogram:

Question 15.

Answer:
m∠b = 45°

Explanation:
Property of a Parallelogram:

Question 16.

Answer:
m∠f = 46°

Explanation:
Property of a Parallelogram:

• Sum of any two adjacent angles is 180°
  180-73=107°
  m∠f = 107 – 61 =46°

Question 17.

Answer:
m∠g =  81°
Explanation:
Property of a Parallelogram:

Question 18.

Answer:
m∠x = 90°
m∠y = 90°
m∠z = 90°

Property of a Parallelogram:

Question 19.

Answer:
m∠p = 90°

Property of a Parallelogram:

Complete. Write the name of another side or angle of each rhombus.

Question 20.
AB = BC
= ___ = ____
Answer:

AB = BC= CD= DA
Explanation:
property of a Rhombus:

Question 21.
m∠B = m∠______
Answer:
m∠B = m∠D
Explanation:
property of a Rhombus:

Question 22.
m∠A = m∠____
Answer:
m∠A = m∠C
Explanation:
property of a Rhombus:

Question 23.
UV = _______
= ___ = ___
Answer:
UV = VS= ST = TU

Explanation:
property of a Rhombus:

Question 24.
m∠S = m∠____
Answer:

m∠S = m∠U

Explanation:
property of a Rhombus:

Question 25.
m∠T = m∠______
Answer:
m∠T = m∠V

Explanation:
property of a Rhombus:

This rhombus is not drawn to scale. Fill in the blanks.

Question 26.
m∠X = m∠__ = ____
Answer:
m∠X = m∠Z= 53°

Explanation:
property of a Rhombus:

Question 27.
m∠W = ____ – ___ = ____
Answer:
m∠W = 180 – 53° = 127°

Explanation:
property of a Rhombus:

Question 28.
m∠Y = m∠___ = ____
Answer:
m∠Y = m∠W = 127°

Explanation:
property of a Rhombus:

These rhombuses are not drawn to scale. Find the unknown angle measures.

Question 29.

Answer:
m∠p =  125°

Explanation:
property of a Rhombus:

Question 30.

Answer:
m∠q = 180 – 57° = 123°

Explanation:
property of a Rhombus:

Question 31.

Answer:

m∠r = 180 – 129° = 51°

Explanation:
property of a Rhombus:

Question 32.

Answer:
m∠s =  52°

Explanation:

then in Triangle ABC AB= BC. then it is isosceles Triangle .
The isosceles triangle property states that when two sides are equal, the base angles are also equal.
So, m∠s =  52°

Question 33.

Answer:
m∠t =  90°

Explanation:

then in Triangle ABC AB= BC. then it is isosceles Triangle .
The isosceles triangle property states that when two sides are equal, the base angles are also equal.
So, m∠s =  45°
in triangle sum of three angles is 180°
So, m∠t = 180 -45+  45° = 90°

Question 34.

Answer:
m∠s =  37°

Explanation:

in triangle ABC  sum of three angles is 180°
m∠s  + m∠v = 180°- 106°=  74°

then in Triangle ABC AB= BC. then it is isosceles Triangle .
The isosceles triangle property states that when two sides are equal, the base angles are also equal.
So, m∠s =m∠v  =  74° divided by 2 = 37°

Measure the unknown angles. Then fill in the blanks. ABCD is a trapezoid where \(\overline{A B}\) || \(\overline{D C}\).

Question 35.
m∠A = ____
Answer:

Question 36.
m∠B = ___
Answer:
m∠B = 110

Question 37.
m∠C = ____
Answer:
m∠C = 70

Question 38.
m∠D = ___
Answer:
m∠D = 80

Question 39.
m∠A + m∠D = m∠___ + m∠___ = ____
Answer:
m∠A + m∠D = m∠100+ m∠80= 180
Supplementary angles = 180°

These trapezoids are not drawn to scale. Find the unknown angle measures.

Question 40.

Answer:
m∠A  = m∠116°
m∠D = m∠64°
m∠D  = 180 – 116
= 64°
Explanation:
Supplementary angles = 180°
m∠64° + m∠116° = 180°

Question 41.

Answer:
m∠G = m∠58°
m∠F = m∠122°
m∠F  = 180 – 58 = 122
Explanation:
Supplementary angles = 180°
m∠58° + m∠122° = 180°

Question 42.

Answer:
m∠L = m∠109°
m∠K = m∠71°
m∠K  = 180 – 109 = 71
Explanation:
Supplementary angles = 180°
m∠71° + m∠109° = 180°

Question 43.

Answer:
m∠P = m∠97°
m∠Q = m∠83°
m∠Q  = 180 – 97 = 83°
Explanation:
Supplementary angles = 180°
m∠83° + m∠97° = 180°
Explanation:
m∠S = m∠81°
m∠R = m∠99°
m∠R  = 180 – 81 = 99°
Explanation:
Supplementary angles = 180°
m∠81° + m∠99° = 180°

These trapezoids are not drawn to scale. Find the unknown angle measures.

Question 44.

Answer:
m∠a = 60°
Explanation:
m∠w = 30°
m∠x = 90
90 + 30 = 120
m∠a = 180 – 120 = 60°
Sum of the angles of a triangle = 180°
m∠b = 110°
m∠u = 70° given
m∠u + m∠b  = 180°
180 – 70 = 110°
110 + 70 = 180°
Supplementary angles = 180°

Question 45.

Answer:
∠d = 55°
∠c = 90°
Explanation:
In quadrilateral the sum of angles = 360°
∠w = 90°
∠Y = 85°
YX = 180°
85° + 40° = 125°
180° – 125° = 55°
∠d = 55°
125° + 55° + 90° = 270°
360° – 270° = 90°
∠c = 90°

Question 46.

Answer:
Explanation:

Question 47.

Answer:
Explanation:
The sum of angles in a triangle = 180
70 + 38 = 98
180 – 98 = 82

Go through the Math in Focus Grade 2 Workbook Answer Key Chapter 3 Practice 3 Subtraction with Regrouping in Tens and Ones to finish your assignments.

Math in Focus Grade 2 Chapter 3 Practice 3 Answer Key Subtraction with Regrouping in Tens and Ones

Regroup the tens and ones. Then subtract.

Question 1.

242 – 117 = ?
242 – 117
= 2 hundreds 4 tens 2 ones – 1 hundred 1 ten 7 ones
= 2 hundreds 3 tens _________ ones – 1 hundred 1 ten 7 ones
= ________ hundred ________ tens ________ ones
= _____
242 – 117 = ____

Use addition to check your answer.
Answer:
242 – 117 = 125,
117+125 = 242.

Explanation:
Given that 242 – 117 which is 125. So to check the answer we will perform addition, which is
117+125 = 242.
= 2 hundreds 4 tens 2 ones – 1 hundred 1 ten 7 ones
= 2 hundreds 3 tens 12 ones – 1 hundred 1 ten 7 ones
= 1 hundred 2 tens 5 ones
= 125.

Question 2.

Answer:
661-246 = 415,
415+246 = 661.

Explanation:
Given that 661-246 which is 415. So to check the answer we will perform addition, which is
415+246 = 661.

Question 3.

Answer:
743-529 = 214,
214+529 = 743.

Explanation:
Given that 743-529 which is 214. So to check the answer we will perform addition, which is
214+529 = 743.

Question 4.
861 – 312 = ___

Answer:
861-312 = 540,
312+540 = 861.

Explanation:
Given that 861-312 which is 540. So to check the answer we will perform addition, which is
312+540 = 861.

Question 5.
987 – 739 = ___

Answer:
987-739 = 248,
248+739 = 987.

Explanation:
Given that 987-739 which is 248. So to check the answer we will perform addition, which is
248+739 = 987.

Question 6.
Subtract and match. The first one is done for you.

Answer:

Go through the Math in Focus Grade 2 Workbook Answer Key Chapter 4 Practice 4 Real-World Problems: Two-Step Problems to finish your assignments.

Math in Focus Grade 2 Chapter 4 Practice 4 Answer Key Real-World Problems: Two-Step Problems

Solve.

Complete the bar models to help you.

Question 1.
Mr. Kim has 78 boxes of apples and 130 boxes of oranges. He sells some boxes of oranges. Now he has 159 boxes of apples and oranges left.
a. How many boxes of apples and oranges did Mr. Kim have at first?

b. How many boxes of oranges did Mr. Kim sell?

Answer:
a. Kim has 208 boxes of apples and oranges at first.
b. The number of boxes of oranges is 130-49 which is 81 boxes.

Explanation:
Given that Mr. Kim has 78 boxes of apples and 130 boxes of oranges. So the total number of boxes of apples and oranges is 78+130 which is 208 boxes. So Kim has 208 boxes of apples and oranges at first. As he sells some boxes of oranges and now he has 159 boxes of apples and oranges left. So the number of boxes of oranges did Mr. Kim sells is 208-159 which is 49 boxes are remaining. So the number of boxes of oranges is 130-49 which is 81 boxes.

a. Mr. Kim had ___ boxes of apples and oranges at first.

Answer:
Mr. Kim has 78 boxes of apples and 130 boxes of oranges.

Explanation:
Mr. Kim has 78 boxes of apples and 130 boxes of oranges.

b. Mr. Kim sold ___ boxes of oranges.

Answer:
Mr. Kim sold 81 boxes of oranges.

Solve.

Complete the bar models to help you.

Question 2.
Sophie has 356 stamps in her collection. Rita has 192 stamps more than Sophie.

a. How many stamps does Rita have?
Answer:
Rita has 548 stamps.

Explanation:
Given that Sophie has 356 stamps in her collection and Rita has 192 stamps more than Sophie. So the number of stamps does Rita has is 356+192 which is 548 stamps.

b. How many stamps do they have in all?

a. Rita has ____ stamps.

Answer:
Rita has 548 stamps.

Explanation:
Rita has 548 stamps.

b. They have ___ stamps in all.

Answer:
They have 904 stamps in all.

Explanation:
Sophie has 356 stamps and Rita has 548 stamps. So the total stamps they have is 356+548 which is 904 stamps.

Solve.

Draw bar models to help you.

Question 3.
Kennedy Elementary School has 784 students. 325 students are boys.

a. How many girls are in the school?

b. How many more girls than boys are in the school?

a. ____ girls are in the school.

b. ___ more girls are in the school than boys.

Answer:
a. 459 girls are in the school.
b. 134 more girls are in the school than boys.

Explanation:
Given that Kennedy Elementary School has 784 students and 325 students are boys. So the number of girls is 784-325 which is 459 girls. So the number of girls more in the school than boys is 459-325 which is 134 girls more.

Solve.

Draw bar models to help you.

Question 4.
Club A has 235 male members, and 172 female members. 45 new members join the club.

a. How many members were in the club at first?

b. How many members are in the club now?

a. ____ members were in the club at first.

b. ___ members are in the club now.

Answer:
a. 407 members were in the club at first.
b. 452 members are in the club now.

Explanation:
Given that Club A has 235 male members and 172 female members and 45 new members join the club. So the number of members who were in the club at first is 235+172 which is 407 members. And the number of members are in the club now is 407+45 which is 452 members.

Question 5.
Kate’s grandmother had $245. She spends $78. Then she gives $36 to Kate. How much money does Kate’s grandmother have now?

She has ___ now.
Answer:
She has 131 now.

Explanation:
Given that Kate’s grandmother had $245 and she spends $78 which is $167 and then she gives $36 to Kate. So $167-$36 which is $131.

Solve.

Draw bar models to help you.

Question 6.
There are 147 daisy plants and 32 tulip plants in Nursery X. Nursery Y has 66 fewer daisy and tulip plants than Nursery X. How many daisy and tulip plants are there in Nursery Y?
There are ____ daisy and tulip plants in Nursery Y.
Answer:
There are 113 daisy and tulip plants in Nursery Y.

Explanation:
Given that there are 147 daisy plants and 32 tulip plants in Nursery X, so the total number of plants is 147+32 which is 179 plants and Nursery Y has 66 fewer daisy which is 179-66 = 113 daisy and tulip plants than Nursery X.

This handy Math in Focus Grade 3 Workbook Answer Key Chapter 16 Practice 1 Telling Time provides detailed solutions for the textbook questions.

Math in Focus Grade 3 Chapter 16 Practice 1 Answer Key Telling Time

Tell the time. Use past.

Example

Question 1.

Answer: Twenty minutes past 2.
A Clock is a circular device provided with three hands viz. an hour hand, minute and second hand. The study of the clock is known as “horology”.
First of all, we need to learn the definition of time: In math, time can be defined as the ongoing and continuous sequence of events that occur in succession, from the past through the present to the future. Time is used to quantify, measure or compare the duration of events or the intervals between them, and even, sequence events.
We measure time in seconds, minutes, hours, days, weeks, months and years with clocks and calendars.
– The shorthand is the hour hand.
– The long hand is a minute hand.
In the given question, the shorthand is on 2. And the long hand is on 4.
Now we can say the time is 2 hours 20 minutes. In another, we can say twenty minutes past 2.

Question 2.

Answer: 15 minutes past 4.
This can be represented in the below diagram:

We measure time in seconds, minutes, hours, days, weeks, months and years with clocks and calendars.
– The shorthand is the hour hand.
– The long hand is a minute hand.
In the given question, the shorthand is on 4. And the long hand is on 3.
Now we can say the time is 4 hours 15 minutes. In another, we can say fifteen minutes past 4.

Question 3.

Answer: 8 minutes past 11

Count the small hands in between 1 and 2 which represents the minutes.
1 represents 5.
2 represents 10.
In between 5 and 10, there are 6, 7, 8, 9 hands also there. That I represented in the above diagram.

Tell the time. Use to.

Example

Question 4.

Answer: 35 minutes to 8
Explanation:

The shorthand represents the hour.
The long hand represents minutes.
The shorthand is on 8 and the long hand is on 7.
In the clock 7 represents 35. So the answer is 35 minutes to 8.

Question 5.

Answer: 5 minutes to 2.
Explanation: The minute hand is pointing to 11. This means that it is 5 minutes to the next hour. The hour hand is moving towards two. The representation is done in the below diagram.

Question 6.

Answer: 31 minutes to 4

The minute hand of our clock is on 31.
Count clock-wise direction in one’s 25, 26, 27, 28, 29, 30, 31.
This means that it is 31 minutes to the next hour.
The hour hand is moving towards 4.

Tell the time. Use past or to.

Question 7.

Answer: 11 minutes to 7

– Each increment on the clock face is one minute.
– Looking at the left-hand side of the clock, moving anti-clockwise from 12, each number is multiple of 5 minutes to the next hour.
– So, from 12 we can count in fives to find out how many minutes there are until the next hour is reached.
– We can count the minute up to 25, but not including 30. We don’t say 30 minutes to. Instead, we say half-past.
– According to the above diagram from 12 we can count 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and so on… up to 30 in the anti-clockwise direction.
– In the diagram, the representation is 11 minutes to 7.

Question 8.

Answer:23 minutes past 3

– Each increment on the clock face is one minute.
– Looking at the right-hand side of the clock, moving clockwise from 12, each number is multiple of 5 minutes to the next hour.
– So, from 12 we can count in fives to find out how many minutes there are until the next hour is reached.
– We can count the minute up to 25, but not including 30. We don’t say 30 minutes to. Instead, we say half-past.
– According to the above diagram from 12 we can count 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and so on… up to 30 in the clockwise direction.
– In the diagram, the representation is 23 minutes past 3.

Question 9.

Answer: 18 minutes to 6.

Explanation:
The actual time gave 5:42.
1 hour is equal to 60 minutes.
5:42 can be written as 5 hours 42 minutes.
If we subtract 42 from 60: 60-42=18.
So what is this mean, 18 minutes left to the next hour.
The next hour is 6. So I wrote 18 minutes to 6.

Question 10.

Answer: 17 minutes to 8
Explanation:
The actual time gave 7:43.
1 hour is equal to 60 minutes.
7:43 can be written as 7 hours 43 minutes.
If we subtract 43 from 60: 60-43=17.
So what is this mean, 17 minutes left to the next hour.
The next hour is 8. So I wrote 17 minutes to 8.

Question 11.

Answer: 12 minutes past 4.

– Each increment on the clock face is one minute.
– Looking at the right-hand side of the clock, moving clockwise from 12, each number is multiple of 5 minutes to the next hour.
– So, from 12 we can count in fives to find out how many minutes there are until the next hour is reached.
– We can count the minute up to 25, but not including 30. We don’t say 30 minutes to. Instead, we say half-past.
– According to the above diagram from 12 we can count 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and so on… up to 30 in the clockwise direction.
– In the diagram, the representation is 12 minutes past 4.

Question 12.

Answer: 5 minutes to 4
Explanation:
The actual time gave 3:55.
1 hour is equal to 60 minutes.
3:55 can be written as 3 hours 55 minutes.
If we subtract 55 from 60: 60-55=5.
So what is this mean, 5 minutes left to the next hour.
The next hour is 4. So I wrote 5 minutes to 4.

Tell the time in two ways.

Example

6:20
20 minutes past 6

4:55
5 minutes to 5

10 minutes to 8
50 minutes past 7

50 minutes to 3
10 minutes past 2

Question 13.

Answer:
First way:
25 minutes past 7
– Each increment on the clock face is one minute.
– Looking at the right-hand side of the clock, moving clockwise from 12, each number is multiple of 5 minutes to the next hour.
– So, from 12 we can count in fives to find out how many minutes there are until the next hour is reached.
– We can count the minute up to 25, but not including 30. We don’t say 30 minutes to. Instead, we say half-past.
– According to the above diagram from 12 we can count 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and so on… up to 30 in the clockwise direction.
– In the diagram, the representation is 25 minutes past 7.

Second way:
35 minutes to 8:
The actual time gave 7:25.
1 hour is equal to 60 minutes.
7:25 can be written as 7 hours 25 minutes.
If we subtract 25 from 60: 60-25=35.
So what is this mean, 35 minutes left to the next hour.
The next hour is 8. So I wrote 35 minutes to 8.

Question 14.

Answer:
We can write in two ways:
1. 12 minutes past 9
2. 48 minutes to 10
First way:

– Each increment on the clock face is one minute.
– Looking at the right-hand side of the clock, moving clockwise from 12, each number is multiple of 5 minutes to the next hour.
– So, from 12 we can count in fives to find out how many minutes there are until the next hour is reached.
– We can count the minute up to 25, but not including 30. We don’t say 30 minutes to. Instead, we say half-past.
– According to the above diagram from 12 we can count 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and so on… up to 30 in the clockwise direction.
– In the diagram, the representation is 12 minutes past 9.
Second way:
48 minutes to 10.
The actual time gave 9:12.
1 hour is equal to 60 minutes.
9:12 can be written as 9 hours 12 minutes.
If we subtract 55 from 60: 60-12=48.
So what is this mean, 48 minutes left to the next hour.
The next hour is 10. So I wrote 48 minutes to 10.

Question 15.

Answer:
We can say time in two ways:
1. 47 minutes past 6
2. 13 minutes to 7.
First way:

– Each increment on the clock face is one minute.
– Each number is multiple of 5 minutes to the next hour.
– So, from 12 we can count in fives to find out how many minutes there are until the next hour is reached.
– We can count the minute up to 25, but not including 30. We don’t say 30 minutes to. Instead, we say half-past.
– According to the above diagram from 12. 1, 2, 3, 4, 5, and so on… up to 60.
– In the diagram, the representation is 47 minutes past 6.
Second way:
17 minutes to 7.
The actual time gave 6:47.
1 hour is equal to 60 minutes.
6:47 can be written as 6 hours 47 minutes.
If we subtract 47 from 60: 60-47=13.
So what is this mean, 13 minutes left to the next hour.
The next hour is 7. So I wrote 13 minutes to 7.

Question 16.

Answer:
we can say two ways in time.
13 minutes past 7
47 minutes to 8
First way:

– Each increment on the clock face is one minute.
– Each number is multiple of 5 minutes to the next hour.
– So, from 12 we can count in fives to find out how many minutes there are until the next hour is reached.
– We can count the minute up to 25, but not including 30. We don’t say 30 minutes to. Instead, we say half-past.
– According to the above diagram from 12. 1, 2, 3, 4, 5, and so on… up to 60.
– In the diagram, the representation is 13 minutes past 7.
Second way:
47 minutes to 8.
The actual time gave 7:13.
1 hour is equal to 60 minutes.
7:13 can be written as 6 hours 47 minutes.
If we subtract 13 from 60: 60-13=47.
So what is this mean, 47 minutes left to the next hour.
The next hour is 8. So I wrote 47 minutes to 8.

Question 17.

Answer:
1. 39 minutes past 4
2. 21 minutes to 5
First way:
39 minutes past 4

– Each increment on the clock face is one minute.
– Each number is multiple of 5 minutes to the next hour.
– So, from 12 we can count in fives to find out how many minutes there are until the next hour is reached.
– We can count the minute up to 25, but not including 30. We don’t say 30 minutes to. Instead, we say half-past.
– According to the above diagram from 12. 1, 2, 3, 4, 5, and so on… up to 60.
– In the diagram, the representation is 39 minutes past 4.
Second way:
21 minutes to 5
The actual time gave 4:39.
1 hour is equal to 60 minutes.
4:39 can be written as 6 hours 47 minutes.
If we subtract 39 from 60: 60-39=21.
So what is this mean, 21 minutes left to the next hour.
The next hour is 5. So I wrote 21 minutes to 5.

Question 18.

Answer:
1. 52 minutes past 10
2. 8 minutes to 11
First way:
52 minutes past 10

– Each increment on the clock face is one minute.
– Each number is multiple of 5 minutes to the next hour.
– So, from 12 we can count in fives to find out how many minutes there are until the next hour is reached.
– We can count the minute up to 25, but not including 30. We don’t say 30 minutes to. Instead, we say half-past.
– According to the above diagram from 12. 1, 2, 3, 4, 5, and so on… up to 60.
– In the diagram, the representation is 52 minutes past 10.
Second way:
21 minutes to 5
The actual time gave 10:52.
1 hour is equal to 60 minutes.
10:52 can be written as 10 hours 52 minutes.
If we subtract 52 from 60: 60-52=8.
So what is this mean, 8 minutes left to the next hour.
The next hour is 11. So I wrote 8 minutes to 11.

Draw the minute hand to show the time.

Question 19.
25 minutes past 11

Answer:
We measure time in seconds, minutes, hours, days, weeks, months and years with clocks and calendars.
– The shorthand is the hour hand.
– The long hand is a minute hand.
In the given question, the shorthand is on 11. And the long hand is on 25.
Now we can say the time is 11 hours 25 minutes. In another, we can say 25 minutes past 11.

Question 20.
18 minutes to 7

Answer:

– Each increment on the clock face is one minute.
– Looking at the left-hand side of the clock, moving anti-clockwise from 12, each number is multiple of 5 minutes to the next hour.
– So, from 12 we can count in fives to find out how many minutes there are until the next hour is reached.
– We can count the minute up to 25, but not including 30. We don’t say 30 minutes to. Instead, we say half-past.
– According to the above diagram from 12 we can count 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and so on… up to 30 in the anti-clockwise direction.
– In the diagram, the representation is 18 minutes to 7.

Write the time on the clock.

Question 21.
18 minutes to 1

Answer: 12:48

18 minutes to 1
The actual time is 12:42.
1 hour is equal to 60 minutes.
12:42 can be written as 10 hours 52 minutes.
If we subtract 42 from 60: 60-42=18.
So what is this mean, 18 minutes left to the next hour.
The next hour is 1. So I wrote 18 minutes to 1.

Question 22.
25 minutes past 2

Answer: 2:25

– Each increment on the clock face is one minute.
– Looking at the right-hand side of the clock, moving clockwise from 12, each number is multiple of 5 minutes to the next hour.
– So, from 12 we can count in fives to find out how many minutes there are until the next hour is reached.
– We can count the minute up to 25, but not including 30. We don’t say 30 minutes to. Instead, we say half-past.
– According to the above diagram from 12 we can count 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and so on… up to 30 in the clockwise direction.
– In the diagram, the representation is 25 minutes past 2.

Fill in the blanks with the correct time.

Question 23.
18 minutes past 2 is ___________.
Answer: 2:18
– Each increment on the clock face is one minute.
– Looking at the right-hand side of the clock, moving clockwise from 12, each number is multiple of 5 minutes to the next hour.
– So, from 12 we can count in fives to find out how many minutes there are until the next hour is reached.
– We can count the minute up to 25, but not including 30. We don’t say 30 minutes to. Instead, we say half-past.
– According to the above diagram from 12 we can count 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and so on… up to 30 in the clockwise direction.

– In the diagram, the representation is 18 minutes past 2.

Question 24.
15 minutes to 1 is __________.
Answer: 12:45

The actual time is 12:45.
1 hour is equal to 60 minutes.
12:45 can be written as 12 hours 45 minutes.
If we subtract 55 from 60: 60-45=15.
So what is this mean, 15 minutes left to the next hour.
The next hour is 1. So I wrote 15 minutes to 1.

Question 25.
8:25 is __________ minutes past __________.
Answer: 25 minutes past 8

– Each increment on the clock face is one minute.
– Looking at the right-hand side of the clock, moving clockwise from 12, each number is multiple of 5 minutes to the next hour.
– So, from 12 we can count in fives to find out how many minutes there are until the next hour is reached.
– We can count the minute up to 25, but not including 30. We don’t say 30 minutes to. Instead, we say half-past.
– According to the above diagram from 12 we can count 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and so on… up to 30 in the clockwise direction.

Question 26.
6:50 is __________ minutes to ___________.
Answer: 10 minutes to 7
The actual time is 6:50.
1 hour is equal to 60 minutes.
6:50 can be written as 6 hours 50 minutes.
If we subtract 50 from 60: 60-50=10.
So what is this mean, 10 minutes left to the next hour.
The next hour is 7. So I wrote 10 minutes to 7.