Mukhlis Tanveer Jan writer.

Mathematics With Tanveer

Welcome to class!

In today’s class, we will be learning the whole numbers counting and writing. Enjoy the class!

Whole Numbers Counting and Writing

In your previous classes that is primary 5 and 6 Book, you all have learnt how to count in thousands and millions. Such that, when reading numbers with more than seven digits, breaking the number into groups of threes (3s) starting from the unit digits, we then read from the leftmost group.

Counting and writing

Counting numbers in millions:

Example 1: Read the following numbers aloud.

10 000 000 = Ten million

25 000 000 = Twenty-five million

40 000 000 = Forty million

50 000 000 = Fifty million

70 000 000 = Seventy million

75 000 000 = Seventy-five million

90 000 000 = Ninety million

Example 2: Read the following aloud.

100 000 000 = One hundred million

250 000 000 = Two hundred and fifty million

400 000 000 = Four hundred million

500 000 000 = Five hundred million

700 000 000 = Seven hundred million

750000 000 = Seven hundred and fifty million

900 000 000 = Nine hundred million

Example 3: Read and write the following numbers in words.

(a) 2538476

(b) 45 832 647

(c) 170609 345

(d) 85000 000

(a) Two million, five hundred and thirty-eight thousand, four hundred and seventy-six.

(b) Forty-five million, eight hundred and thirty-two thousand, six hundred and forty-seven

(C) One hundred and seventy million, six hundred and nine thousand, three hundred and forty-five.

(d) Eight hundred and fifty million.

Note: We can also write in numerals, numbers that are written in words.

Example 4: Write the following in numerals.

(a) Six million, one hundred and twenty-eight thousand and thirty-five.

(b) Seventy-two million, four hundred and thirteen thousand, eight hundred and twenty.

(c) Three hundred and forty-four million, one hundred and fifty thousand, seven hundred and eight.

(a) 6 128 035

(b) 72413 820

(c) 344 150 708

Counting up to 1 billion:

Note: This contained up to nine-digit numbers.

Read the following aloud:

900 000 000 = Nine hundred million

910 000 000 = Nine hundred and ten million

920 000 000 = Nine hundred and twenty million

930 000 000 = Nine hundred and thirty million

940 000 000 = Nine hundred and forty million

950 000 000 = Nine hundred and fifty million

960 000 000 = Nine hundred and sixty million

970 000 000 = Nine hundred and seventy million

980 000 000 = Nine hundred and eighty million

990 000 000 = Nine hundred and ninety million

1 000 000 000 = One billion

Counting numbers in billions

Example 5: Read the following aloud.

5 000 000 000 = five billion

10 000 000 000 = ten billion

20 000 000 000 = twenty billion

50 000 000 000 = fifty billion

100 000 000 000 = one hundred billion

200 000 000 000 = two hundred billion

Examples 6:

1 125 000 000 reads one billion, one hundred and twenty-five million.

21 752 052 363 reads twenty-one billion, seven hundred and fifty-two million, fifty-two thousand, three hundred and sixty-three.

1 000 000 032 reads one billion and thirty-two

3 103 000 190 reads three billion, one hundred and three million, one hundred and ninety

Counting numbers up to 1 trillion

Example 7: Read aloud the following numbers.

1 000 000 000 = one billion

10 000 000 000 = ten billion

20 000 000 000 = twenty billion

30 000 000 000 = thirty billion

60 000 000 000 = sixty billion

80 000 000 000 = eighty billion

100 000 000 000 = one hundred billion

300 000 000 000 = three hundred billion

600 000 000 000 = six hundred billion

900 000 000 000 = nine hundred billion

1 000 000 000 000 = one trillion

Counting numbers in trillions

Examples 8:

3 000 000 000 000 = three trillion

5 000 000 000 000 = five trillion

10 000 000 000 000 = ten trillion

20 000 000 000 000 = twenty trillion

50 000 000 000 000 = fifty trillion

90 000 000 000 000 = ninety trillion

Examples 9: Read aloud the following numbers

100 000 000 000 000 = one hundred trillion

200 000 000 000 000 = two hundred trillion

300 000 000 000 000 = three hundred trillion

500 000 000 000 000 = five hundred trillion

700 000 000 000 000 = seven hundred trillion

900 000 000 000 000 = nine hundred trillion.

Examples 10: Read and write the following in words.

800 000 000 000

15 608 000 000 000

240 509 000 000 000

765 423 154 628 450

Eight hundred billion

Fifteen trillion, six hundred and eight billion

Two hundred and forty trillion, five hundred and nine billion

Seven hundred and sixty-five trillion, four hundred and twenty-three billion, one hundred and fifty-four million, six hundred and twenty-eight thousand, four hundred and fifty.

In our next class, we will be talking about the Lowest Common Multiple (LCM) and the Highest Common Factor (HCF) of Whole Numbers. We hope you enjoyed the class.

Welcome to class!

In today’s class, we will be talking about the lowest common multiple (LCM) and the highest common factor (HCF) of whole numbers. Enjoy the class!

Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of Whole Numbers

Highest common factor (H.C.F):

The highest common factor of the two given numbers is the highest of the factors common to both numbers.

Example 1

Find the H.C.F. of 20 and 32.

20 = 2 x 2 x 5

32 = 2 x 2 x 2 x 2 x 2

The H.C.E of 20 and 32 is the product of the prime factors common to both numbers.

That is 2 X 2 = 4

Example 2

Find the H.C.F. of 42 and 70.

42 = 2 x 3 x 7

70 = 2 x 5 x 7

The H.C.F. of 42 and 70 = 2 x 7 = 14

Example 3

Find the H.C.F of 2³ x 3² x 5², 2⁴ x 3 x 5³, 3³ x 5 x 7, 2² x 3³ x 5 x 7

2³ x 3² x 5² = 2 x 2 x 2 x 3 x 3 x 5 x 5

2⁴ x 3 x 5³ = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5

2² x 3³ x 5 x 7 = 3 x 3 x 3 x 5 x 7

H.C.F =3 x 5 = 15

Activity 1

Find the H.C.F of the following:

60 and 48,

38 and 95,

60 and 96, by:

(a) the method of listing common factors;

(b) the method of expressing the numbers as products of prime factors. Which of the two methods are less laborious?

Multiples of a Given Whole Number

The 1st multiple of number 7 is 1 X 7 = 7

The 3rd multiple of number 7 is 3 x 7 = 21

The 6th multiple of number 7 is 6 x 7 = 42

The 11th multiple of number 7 is 11 x 7 = 77

The multiple of number 7 may now be listed as 1 x 7, 2 x 7, 3 x 7, 4 x 7…

Note: The three dots… are used to indicate that some multiples in the list have not to be written down. The dots… may be read and so on.

If we list the first six counting numbers, we get, 1, 2, 3, 4, 5, 6. If we multiply each of them by any number, say 7 we get

1 x 7 = 7 2 x 7 = 14

3 x 7 = 21 4 X 7 = 28

5 x 7 = 35 6 x 7 = 42

We say the numbers 7, 14, 21, 28, 35, 42, are multiples of 7.

Activity 2

Complete the following table

Number

Order of Multiple

Multiple Number

Required

23 8th

15

12th

6 42nd

320

5th

18

50th

List the first thirty-one multiples of 9 omitting those from the 4th to the 29th.

List the first twenty multiples of 6.

What is the 10th multiple of 12?

List the multiples of 8. How many?

What is the 25th multiple of 24?

What is the 60th multiple of 19?

In our next class, we will be talking more about the Lowest Common Multiple (Lcm) and Highest Common Factor (HCF) of Whole Numbers. We hope you enjoyed the class.

i

elcome to class!

In today’s class, we will be talking more about the lowest common multiple (LCM) and the highest common factor (HCF) of whole numbers. Enjoy the class!

Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of Whole Numbers

The lowest common multiples (LCM) of two whole numbers

From the list of multiples of two whole numbers, we can find the list of their common multiples. We pick from the list, the lowest or least common multiples which is usually called L.C.M

Let us consider the following examples.

The multiples of 12 are:

12, 24, 36, 48, 60, 72, 84, 96, ….

The multiples of 18 are:

18, 36, 54, 72, 90, 108, …

The common multiples of 12 and 18 are 36, 72, 108, …

The L.C.M of 12 and 18 is 36.

The result may be obtained by expressing 12 and 18 as products of prime factors:

12 = 2 X 2 x 3

18 = 2 x 2 x 3

The L.C.M. of 12 and 118 = 2 x 2 x 3 x 3 = 30.

Note: that each prime factor in 12 and 18 is taken for their L.C.M. and from where it occurs most; the two’s in rather than the only one in 18 and the two 3’s in 18 rather than the only one in 12.

Example 1

Find the L.C.M. of 42 and 96.

42 = 2 x 3 x 7

96 = 2 x 2 x 2 x 2 x 2 x 3

The L.C.M. of 42 and 96 is 2 x 2 x 2 x 2 x 2 x 3 x 7 = 672

Note that 3 occurs once for both 42 and 96 and so we take 3 once for the L.C.M. 7 occurs in 42 and not in 96, so we take 7 once for the L.C.M.

Activity 1

Find the L.C.M. of (i) 16 and 30, (ii) 18 and 12, by the method of listing common multiples and by the method of prime factors. Which method do you prefer? Give reasons.

Example 2

Find the L.C.M of 6, 5 and 4.

6 = 2 x 3

5 = 5 x 1

4 = 2 x 2

: · L.C.M = 2 x 2 x 3 x 5 = 60

Example 3

Find the H.C.F of 13 and 39.

13 = 1 x 13

39 = 3 x 13

H.C.F = 13

Example 4

Find the L.C.M of 2² X 3² X 5, 2 x 3² x 5² and 2³ x 3 x 5³

2² x 3² x 5 = 2 x 2 x 3 x 3 x 5

2 x 3² x 5² = 2 x 3 x 3 x 5 x 5

2³ x 3 x 5³ = 2 x 2 x 2 x 3 x 5 x 5 x 5

L.C.M = 2 x 2 x 2 x 3 x 3 x 5 x 5 x 5

= 2³ x 3² x 5³

= 9000

Example 5

What is the H.C.F of 21, 45 and 105?

21 = 3 x 7

45 = 5 x 3 x 3

105 = 3 x 5 x 7

: · H.C.F = 3

In our next class, we will be talking about Fractions. We hope you enjoyed the class.

Should you have any further question, feel free to ask i

Welcome to class!

In today’s class, we will be talking about fractions. Enjoy the class!

Fractions

What Is a Fraction?

Fractions give some people nightmares, but this doesn’t have to be you. Keep watching this video lesson, and you will come out with a better understanding of fractions. And hopefully, you won’t feel so afraid of them.

We begin with a definition of what fractions are. A fraction simply tells us how many parts of a whole we have. You can recognize a fraction by the s***h that is written between the two numbers. We have a top number, the numerator, and a bottom number, the denominator. For example, 1/2 is a fraction. You can write it with a slanted s***h like we have or you can write the 1 on top of the 2 with the s***h between the two numbers. The 1 is the numerator, and the 2 is the denominator.

Proper fraction:

Fractions whose numerators are less than the denominators are called proper fractions. (Numerator denominator)

Fractions like 5/4, 17/5, 5/2 etc. are not proper fractions. These are improper fractions. The fraction 7/7 is an improper fraction.

Fractions 5/4, 3/2, 8/3, 6/5, 10/3, 13/10, 15/4, 9/9, 20/13, 12/12, 13/11, 14/11, 17/17 are examples of improper fractions. The top number (numerator) is greater than the bottom number (denominator). Such type of fraction is called an improper fraction.

Notes:

(i) Every natural number can be written as a fraction in which 1 is its denominator. For example, 2 = 2/1, 25 = 25/1, 53 = 53/1, etc. So, every natural number is an improper fraction.

(ii) The value of an improper fraction is always equal to or greater than 1.

Mixed fraction:

A combination of a proper fraction and a whole number is called a mixed fraction.

1 1/3, 2 1/3, 3 2/5, 4 2/5, 11 1/10, 9 13/15 and 12 3/5 are examples of mixed fraction.

In other words, A fraction which contains two parts: (i) a natural number and (ii) a proper fraction, is called a mixed fraction, e.g., 3 2/5, 7 3/4, etc.

For the number; 3frac{2}{5} , 3 is the natural number part and 2/5 is the proper fraction part.

In Fact, 3frac{2}{5} means 3 + 2/5.

Note: A mixed number is formed with a whole number and a fraction.

Property 1:

A mixed fraction may always be converted into an improper fraction. Multiply the natural number by the denominator and add to the numerator. This new numerator over the denominator is the required fraction.

Property 2:

An important fraction can be always be converted into a mixed fraction.

Divide the numerator by the denominator to get the quotient and remainder. Then the quotient is the natural number part and the remainder over the denominator is the proper fraction part of the required mixed fraction.

In our next class, we will be talking more about Fractions. We hope you enjoyed the class.

Equivalent fractions

Summary: Equivalent fractions are different fractions that name the same number. The numerator and the denominator of a fraction must be multiplied by the same nonzero whole number to have equivalent fractions.

Definition: Equivalent fractions are different fractions that name the same number.

Example 1

The fraction in example 1 represents the same number. These are equivalent fractions.

Two-thirds is equivalent to four-sixths i.e. frac{2}{3}=frac{4}6{}

Example 2

The fractions three-fourths frac{3}{4}, six-eighths frac{6}{8}, and nine-twelfths frac{9}{12} are equivalent.

Procedure: To find equivalent fractions (multiply the numerator AND denominator by the same nonzero whole number).

You can multiply the numerator and the denominator of a fraction by any nonzero whole number, as long as you multiply both by the same whole number! For example, you can multiply the numerator and the denominator by 3. But you cannot multiply the numerator by 3 and the denominator by 5. You can multiply the numerator and the denominator by 4. But you cannot multiply the numerator by 4 and the denominator by 2.

The numerator and the denominator of a fraction must be multiplied by the same nonzero whole number to have equivalent fractions. You may be wondering why this is so.

In the last lesson, we learned that a fraction that has the same numerator and denominator is equal to one. This is shown below.

2/2 = 1 (Two-halves)

3/3 = 1 (Three-thirds)

4/4 = 1 (Four-fourths)

5/5 = 1 (Five-fifths)

6/6 = 1 (Six-sixths)

So, multiplying a fraction by one does not change its value. Multiplying the numerator and the denominator of a fraction by the same nonzero whole number will change that fraction into an equivalent fraction, but it will not change its value. Equivalent fractions may look different, but they have the same value.

In our next class, we will be talking more about Fractions. We hope you enjoyed the class.

Fractions

Conversion of fractions to percentages classnotes.ng

Conversion of fractions to percentages

To convert a fraction to a percent, first, divide the numerator by the denominator. Then multiply the decimal by 100. That is, the fraction 48 can be converted to a decimal by dividing 4 by 8. It can be converted to percent by multiplying the decimal by 100.

Remember that a percent is just a special way of expressing a fraction as a number out of 100100.

To convert a fraction to a percent, first divide the numerator by the denominator. Then multiply the decimal by 100/100.

That is, the fraction 4/8 can be converted to decimal by dividing 4 by 8 . It can be converted to percent by multiplying the decimal by 100/100.

Example 1:

Write 2/25 as a percent.

Since 25 is larger than 2, to divide, we must add a decimal point and some zeroes after the 22. We may not know how many zeroes to add but it doesn’t matter. If we add too many, we can erase the extras; if we don’t add enough, we can add more.

So,

2/25 = 0.08 × 100, 0.08×100=8

Therefore, the fraction 225 is equivalent to 8%

Look at the image below, it shows that the fraction 225 is same as 8 out of 100, that is 8%.

Example 2:

Write 7/4 as a percent.

Divide 7 by 4.

So,

7/4 = 1.75×100, 1.75×100=175

Therefore, the fraction 7/4 is equivalent to 175%

Example 3:

Write 1/8 as a percent.

Divide 1 by.

So,

1/8=0.1250, 125×100=12.518 = 12.5

Therefore, the fraction 1/8 is equivalent to 12.5%.

Conversion of percentages to fractions

To convert a Percent to a Fraction, follow these steps:

Step 1: Write down the percent divided by 100 like this: percent 100

Step 2: If the percent is not a whole number, then multiply both top and bottom by 10 for every number after the decimal point. (For example, if there is one number after the decimal, then use 10, if there are two then use 100, etc.)

Step 3: Simplify (or reduce) the fraction

Example 1:

Convert 11% to a fraction

Step 1: Write down:

11/100

Step 2: A percent is a whole number, go straight to step 3.

Step 3: The fraction cannot be simplified further.

Answer = 11100

Example 2:

Convert 75% to a fraction

Step 1: Write down:

75/100

Step 2: A percent is a whole number, go straight to step 3.

Step 3: Simplify the fraction (this took me two steps, you may be able to do it one!):

75/100

÷5 = 15/20 ÷ 5 = 3/4

Answer = 3/4

Note: 75/100 is called a decimal fraction and 34 is called a common fraction!

Example 3:

Convert 62.5% to a fraction

Step 1: Write down:

62.5/100

Step 2: Multiply both top and bottom by 10 (because there is 1 digit after the decimal place)

62.5/100

× 10 = 625/1000

(See how this neatly makes the top a whole number?)

Step 3: Simplify the fraction (this took me two steps, you may be able to do it one!) :

625/1000 ÷ 25 = 25/40

÷ 5 = 5/8

Answer = 5/8

Example 4:

Convert 150% to a fraction

Step 1: Write down:

150/100

Step 2: The percent is a whole number, go straight to step 3.

Step 3: Simplify the fraction (I did it one step):

150/100

÷ 50 = 3/2

Answer = 3/2

In our next class, we will be talking more about Fractions. We hope you enjoyed the class.

Conversion of fractions to decimals

To convert fractions to decimals, look at the fraction as a division problem. Take the top number, or the numerator, of the fraction and divide it by the bottom number, or the denominator. You can do this in your head, by using a calculator, or by doing long division. For example, ¼ is just 1 divided by 4, or 0.25.

Just divide the top of the fraction by the bottom, and read off the answer!

Example 1:

What is 5/8 as a decimal

get your calculator and type in 5 / 8 = 0.625

Example 2:

here is what long division of 5/8 looks like:

0.625

8)5.000

0

5.0

4.8

20

16

40

40

0

In that case, we inserted extra zeros and did 5.000/8 to get 0.625

Another method

Yet another method you may like is to follow these steps:

Step 1: Find a number you can multiply by the bottom of the fraction to make it 10, or 100, or 1000, or any 1 followed by 0.

Step 2: Multiply both top and bottom by that number.

Step 3. Then write down just the top number, putting the decimal point in the correct spot (one space from the right-hand side for every zero in the bottom number)

Example 3:

Convert 3/4 to a Decimal

Step 1: We can multiply 4 by 25 to become 100

Step 2: Multiply top and bottom by 25:

3/4 ×25

= 75/100

Step 3: Write down 75 with the decimal point 2 spaces from the right (because 100 has 2 zeros);

Answer = 0.75

Example 4:

Convert 3/6 to a Decimal

Step 1: We have to multiply 16 by 625 to become 10,000

Step 2: Multiply top and bottom by 625:

3/6 ×625

= 1,875/10,000

Step 3: Write down 1875 with the decimal point 4 spaces from the right (because 10,000 has 4 zeros);

Answer = 0.1875

Example 5:

Convert 1/3 to a Decimal

Step 1: There is no way to multiply 3 to become 10 or 100 or any “1 followed by 0s”, but we can calculate an approximate decimal by choosing to multiply by, say, 333

Step 2: Multiply top and bottom by 333:

1/3 ×333

= 333/999

Step 3: Now, 999 is nearly 1,000, so let us write down 333 with the decimal point 3 spaces from the right (because 1,000 has 3 zeros):

Answer = 0.333 (accurate to only 3 decimal places !!)

To convert a decimal to a fraction

To convert a Decimal to a Fraction, follow these steps:

Step 1: Write down the decimal divided by 1, like this: decimal/1

Step 2: Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)

Step 3: Simplify (or reduce) the fraction

Example 1:

Convert 0.75 to a fraction

Step 1: Write down 0.75 divided by 1:

0.75/1

Step 2: Multiply both top and bottom by 100 (because there are 2 digits after the decimal point so that is 10×10=100):

0.75/1 × 100 = 75/100

(Do you see how it turns the top number into a whole number?)

Step 3: Simplify the fraction (this took me two steps):

75/100 ÷5= 15/20 ÷ 5 = 3/4

Answer = 3/4

Note: 75/100 is called a decimal fraction and 3/4 is called a common fraction!

Example 2:

Convert 0.625 to a fraction

Step 1: write down:

0.625/1

Step 2: multiply both top and bottom by 1,000 (3 digits after the decimal point, so 10×10×10=1,000)

625/1000

Step 3: Simplify the fraction (it took me two steps here):

625/1000 ÷ 25= 25/40 ÷ 5= 5/8

Answer = 5/8

When there is a whole number part, put the whole number aside and bring it back at the end.

Example 3:

Convert 2.35 to a fraction

Put the 2 aside and just work on 0.35

Step 1: write down:

0.35/1

Step 2: multiply both top and bottom by 100 (2 digits after the decimal point so that is 10×10=100):

35/100

Step 3: Simplify the fraction:

35/100 ÷ 5 = 7/20

Bring back the 2 (to make a mixed fraction):

Answer = 2 7/20

Example 4:

Convert 0.333 to a fraction

Step 1: Write down:

0.333/1

Step 2: Multiply both top and bottom by 1,000 (3 digits after the decimal point so that is 10×10×10=1,000)

333/1000

Step 3: Simplify Fraction:

Can’t get any simpler!

Answer = 333/1000

In our next class, we will be talking more about Fractions. We hope you enjoyed the class.

Addition and subtraction of fractions

Adding and subtracting fractions may seem tricky at first, but if you follow a few simple steps and work a lot of practice problems, you will have the hang of it in no time.

Here are some steps to follow:

Check to see if the fractions have the same denominator.

If they don’t have the same denominator, then convert them to equivalent fractions with the same denominator.

Once they have the same denominator, add or subtract the numbers in the numerator.

Write your answer with the new numerator over the denominator.

Note:

The denominator may have changed when you converted the fractions to the same common denominator.

Example 1:

A simple example is when the denominators are already the same:fraction

Since the denominators are the same in each question, you just add or subtract the numerators to get the answers.

Example 2:

Here we will try a problem where the denominators are not the same. fraction

As you can see, these fractions do not have the same denominator. Before we can add the fractions together, we must first create equivalent fractions that have common denominators.

Find the Common Denominator:

To find a common denominator, we must multiply each fraction by the other fraction’s denominator (the one the bottom). If we multiply both the top and the bottom of the fraction by the same number, it’s just like multiplying it by 1, so the value of the fraction stays the same. See the example below: fraction

Add the Numerators

fraction

Now that the denominators are the same, you can add the numerators and put the answer over the same denominator.

Subtracting Fractions Example:

Here is an example of subtracting fractions where only one denominator needs to be changed:

fraction

Reduce Your Final Answer: Sometimes the answer will need to be reduced. Here is an example:

The initial answer after adding the numerators was 10/15, however, this fraction can be further reduced to 2/3 as shown in the last step.

Fractions

Always make sure that the denominators are the same before you add or subtract.

If you multiply the top and the bottom of a fraction by the same number, the value stays the same.

Be sure to practice converting fractions to common denominators. This is the hardest part of adding and subtracting fractions.

You may need to simplify your answer after you are done adding and subtracting. Sometimes the answer can be reduced even though the original fractions could not be reduced.

The same process is used for both adding and subtracting if you can add fractions, you can subtract them.

If there are mixed numbers that you are adding or subtracting be sure to convert them to improper fractions before you start the proces.ultiplication and division of fractions

Multiplying fractions:

Three simple steps are required to multiply two fractions:

Step 1: Multiply the numerators from each fraction by each other (the numbers on top). The result is the numerator of the answer.

Step 2: Multiply the denominators of each fraction by each other (the numbers on the bottom). The result is the denominator of the answer.

fraction

In the first example, you can see that we multiply the numerators 2 x 6 to get the numerator for the answer, 12. We also multiply the denominators 5 x 7 to get the denominator for the answer, 35. In the second example, we use the same method. In this problem, the answer we get is 2/12 which can be further reduced to 1/6.

Multiplying different types of fractions:

The examples above multiplied proper fractions. The same process is used to multiply improper fractions and mixed numbers. There are a couple of things to watch out for with these other types of fractions.

Improper fractions – With improper fractions (where the numerator is greater than the denominator) you may need to change the answer into a mixed number. For example, if the answer you get is 17/4, your teacher may want you to change this to the mixed number 4 ¼.

Mixed numbers – Mixed numbers are numbers that have a whole number and a fraction, like 2 ½.