General terms related to spherical mirrors: A mirror with the shape of a portion cut out of a spherical surface or substance is known as a...

General Terms Related to Spherical Mirrors

April 11, 2024**Fun with Numbers: **Numbers play a vital role in mathematics and in our life too. We use numbers to count things, money, etc., and we use numbers in date and time, calendar, solving puzzles, brain teasers and many more. Numbers help us to understand which collection of objects is larger or smaller and arrange them in order. Counting items is easy for us now.

We will learn what a number is in this article. Also, about ones, tens, and hundreds, we will perform a fun prime number activity. We will also cover dot multiplication, repeated addition, regrouping, the standard multiplication algorithm, and Lattice multiplication.

Math is nothing without numbers, which are the foundation of the subject. The pattern of writing a number in words is referred to as a number name. For example, \(1\) is written as one in words. Now let us take a look at some numbers and the names that go with them.

\(0=\,\text {Zero}\), \(1=\,\text {One}\), \(2=\,\text {Two}\), \(3=\,\text {Three}\), \(4=\,\text {Four}\), \(5=\,\text {Five}\),

\(6=\operatorname{Six}\), \(7=\,\text {Seven}\), \(8=\,\text {Eight}\), \(9=\,\text {Nine}\).

The numbers mentioned above are the fundamental numbers from which \(2\)-digit, \(3\)-digit, \(4\)-digit, and \(n\)-digit numbers can be formed. Understanding the place value of numbers is important to write bigger numbers in words or vice versa.

Place values in India are divided into four categories: ones, thousands, lakhs, and crores. Ones [ones, tens, and hundreds], thousands [thousands and ten thousand], lakhs [lakhs and ten lakhs], and crores [crores and ten crores] are the nine place values for these four periods.

With the help of the figure below, we can observe how numbers are represented in both the international and Indian numeration systems.

For example, write one hundred fifty-two in figures.

One hundred fifty-two \(=100+50+2=152\)

For example, write the smallest \(2\)-digit number.

The smallest \(2\)-digit number is \(10\).

Example: The number \(256\) is read in the Indian system in words as two hundred and fifty-six.

Example: We can read \(33,501,580\) in words as thirty-three million five hundred one thousand five hundred eighty.

**Using Ones, Tens & Hundreds**

Let us go shopping at the Lazy Crazy store.

This is where you will find the jungle store. Things are only given out in packages of tens, hundreds, and loose objects by Lazy Crazy.

Determine how many tens, hundreds, and loose things each animal will consume?

Rabbit wants \(143\) carrots.

Lazy Crazy will give him one packet of \(100, 4\) packets of \(10\) and \(3\) loose carrots.

i.e., \(100+4 \times 10+3=100+40+3\)

\(=143\)

Elephant wants \(210\) sugarcanes.

Lazy Crazy will give him two packets of \(100, 1\) packet of \(10\) sugarcanes

i.e., \(2 \times 100+1 \times 10=200+10\)

\(=210\)

Monkey wants \(242\) bananas.

Lazy Crazy will give him two packets of \(100, 4\) packets of \(10\) and \(2\) loose bananas.

i.e., \(2 \times 100+4 \times 10+2=200+40+2\)

\(=242\)

Deer wants \(552\) grass.

Lazy Crazy will give him five packets of \(100, 5\) packets of \(10\) and \(2\) loose grass.

i.e., \(5 \times 100+5 \times 10+2=500+50+2\)

\(=552\)

The process of comparison shows us which items have similar properties. When comparing two numbers, this is the primary concept in mathematics that helps us express whether the numbers are equal or if one is bigger than or less than the other.

When comparing numbers in mathematics, three specific symbols are used. The following are the fundamental symbols for comparing numbers:

- Greater than \((>)\)
- Less than
- Equals to \((=)\)

We may compare two numbers of any sort, such as natural numbers, whole numbers, integers, and decimal numbers, using the symbols above. As a result, the process of comparing and examining the differences between numbers is known as the Comparison of Numbers.

\(=\) | When two values are equal, we use the “equals” sign | example: \(3+2=5\) |

\(<\) | When one value is smaller than another, we can use a “less than” sign. | example: \(2<7\) |

\(>\) | When one value is bigger than another, we can use a “greater than” sign | example: \(10>5\) |

The “less than” sign and the “greater than” sign look like a “V” on its side, don’t they? To remember which way around the “\(<\)” and “\(>\)” signs go, just remember:

- BIG \(>\) small
- small \(<\) BIG

Greater Than Symbol: BIG \(>\) small

**Example:**

\(9>3\)*“*\(9\) is greater than* *\(3\).*“*

Make a prime number chart of your own!

When you click on a number, it will turn dark blue (indicating that it is a possible prime number), and all of its multiples will turn light blue (definitely composite numbers).

Continue to highlight numbers until you get a list of:

- prime number, and
- composite numbers

You cannot mark \(1\) because it’s neither prime nor composite.

Multiplication is adding the same number to a specified number of times.

Example: \(4+4+4=12\)

Here, we add \(4\) three times, and the answer is \(12\)

This can be written as \(4 \times 3=12\).

Multiplication is a quicker way to add the number occurring repeatedly.

We use the symbol \(\times\) to represent multiplication.

\(4\) Trees in \(5\) groups is \(20\)

This can be written as \(4×5=20\)

Multiplication of a number with other numbers can be done in the following ways.

(i) Dot multiplication

(ii) Repeated addition

(iii) Regrouping

(iv) Standard multiplication algorithm

(v) Lattice multiplication

We can find the total number of flowers as follows.

\(3+3+3=9\)

\(3\) groups of \(3\) flowers make \(9\)

\(3 \times 3=9\)

This method can be used by multiplying a two-digit number. Consider the following multiplication.

\(53 \times 7\)

\(53\) can be regrouped into \(5\) tens and \(3\) ones.

Hence, \(53 \times 7\) can be written as \((50+3) \times 7\)

\(=(50 \times 7)+(3 \times 7)\)

\(=350+21\)

\(=371\)

Multiply using the multiplication table

**Step 1**: Multiply Ones.

**Step 2**: Multiply Tens

Product \(=14×2=28\)

Lattice multiplication is helpful while dealing with numbers with more than two digits. We follow the following steps in Lattice multiplication.

**Step 1:** Write the numbers to be multiplied as follows.

(i) \(52×36\)

**Step 2**: Draw diagonals of the square.

**Step 3**: Multiply the numbers and write them in the cells as shown below.

**Step 4**: Find the sum of each diagonal and write as follows.

**Step 5**: Arrange the sum to get the answer as follows.

Answer: \(1872\)

**Q.1. Multiply using the lattice multiplication **893 × 25**Ans:** **Step 1:** Write the numbers to be multiplied as follows.

**Step 2:** Draw diagonals of the square.

**Step 3:** Multiply the numbers and write them in the cells as shown below.

**Step 4:** Find the sum of each diagonal and write as follows.

**Step 5:** Arrange the sum to get the answer as follows.

**Answer:** \((1+1)(1+1)(2+1) 2+5\)

\(22325\)

**Q.2. If the cost of one eraser is **₹ 4**, what will be the cost of **2** erasers?****Ans:**

\(4+4=8\)

\(2 \times 4=8\)

The cost of two erasers \(=2 \times 4=8\)

**Q.3. Multiply.** \(23 \times 4\)**Ans:** **Step 1:** Multiply Ones.

**Step 2: **Multiply Tens.

Product \(=23 \times 4=92\)

**Q.4. If there are **4** toys in a box, how many toys will be there in **5** boxes?**

**Ans:** Given: Number of toys in a box \(=4\)

Total number of boxes \(=5\)

Hence, the number of toys in \(5\) boxes \(=4 \times 5=20\) toys

**Q.5. Jazzy and friends are picking some apples. Jazzy picked 7 apples, Jaleigne picked 8 apples, Jared picked 10 apples, and Jamel picked 8.**

1. **Who picked more apples?**

2. **Who picked less apples?**

3. **Who among them has the same or the equal number of apples picked?**

**Ans:** Given, Jazzy picked \(7\) apples, Jaleigne picked \(8\) apples, Jared picked \(10\) apples, and Jamel picked \(8\).

Jared picked more apples.

Jazzy picked less apples.

Jaleigne and Jamel have the same or the equal number of apples picked.

**Q.6. Write the number in words (in the Indian number system)****(i) 24527 (ii) 9745326****Ans: **(i) \(24527 =\) Twenty four thousand five hundred and twenty-seven

(ii) \(9745326 =\) Ninety-seven lakhs forty-five thousand three hundred and twenty-six

We learned what a number is in this article. Then we went to a lazy crazy store to learn about tens and hundreds, and then we performed a fun prime number activity. We also covered dot multiplication, repeated addition, regrouping, the standard multiplication algorithm, and Lattice multiplication and some solved examples and frequently asked questions.

**Q.1. What is a number?****Ans:** Numbers are the values that we use for representing the quantity and in making the calculations. We have the digits \(0,1,2,3,4,5,6,7,8,9\) to make or form all the other numbers.

**Q.2. Which number is neither prime nor composite?****Ans:** \(1\) is neither prime nor composite.

**Q.3. What is the standard form of **12**?****Ans: **The standard form of \(12\) is \(1×10+2\).

**Q.4. What is the example of repeated addition?****Ans**: For example, \(3+3+3+3\)

\(3\) is repeated \(4\) times, we can write this addition as \(4×3=12\)

Similarly, to solve a multiplication problem through repeated addition, we repetitively group and add the same number repeatedly to find the answer.

**Q.5. How many ones are there in **100** tens?****Ans:** We can write \(100\) as \(100×10=1000\).

Therefore, there are \(1000\) ones in \(100\) tens.