Math Grade 10 Study Guide

Math grade 10 study guide:

      In this article we are going to discuss math grade 10 study guide solving problems. Math grade 10 study guide solving problems are easy to understand and solve. Math grade 10 study guide solving problem involves a lot of  math concepts. The following topics are studied in the 10 grade,

Number systems
Measurements
Algebra
Geometry
Algebraic geometry
Trigonometry
Handling data
The math grade 10 study guide solving problems are given below.

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Math grade 10 study guide Example problems:


Example 1:

Find the sum of the entire element between 300 and 500 divisible by 11.

Solution:

The first element greater than 300 and divisible by 11 is 308. The last number less than 500 and divisible 11 is 495.

Series is 308 + 319 = … + 495

A = 308, d = 11, l = 495, tn = a+ (n-1) d = 495

308 + (n-1) 11 = 495

n = `(495-308)/11` +1 = 18

sn =` n/2` (a+l)

S18 = `18/2` (308+495) = 7227.

Example 2:

A solid metal cylinder is 20 cm in height and has a radius of 1.5 cm. This is melted down and cast into spheres each of radius 1.5 cm. How many spheres can be cast from the cylinder?

Solution:

Height of the cylinder = 20 cm; Radius of the cylinder = 1.5 cm

Volume of the cylinder = `pi`  * 1.5 * 1.5 * 20 cm3

Radius of the sphere = 1.5 cm

Volume of the sphere cast = `4/3` * `pi` * 1.5 * 1.5 * 1.5 cm3

Number of sphere cast = Volume of the cylinder melted/ Volume of a sphere cast

= `pi` * 1.5 * 1.5 * 20 * `3/ 4` * `pi` * 1.5 * 1.5 * 1.5 = 10

10 spheres can be cast from the cylinder

Example 3:

Simplify `(5x+20)/ (7x+20)`

Solution:

Given expression `(5x+20)/ (7x+20)`

`(5x+20)/ (7x+20)` = `5/7`

The simplify solution is `5/7`

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Math grade 10 study guide Practice problem:


Problem 1: Find the sum of n terms of an AP. whose nth term is an = 5-6n

Solution: 2n -3n2

Problem 2: A metallic sphere 3 cm in diameter is melted and made into 3 smaller spheres.

If the diameters of two of these smaller spheres are 1.5 cm and 2 cm, find the diameter of the third sphere.

Solution: The diameter of the 3rd sphere is 2.5 cm.

Problem 3: Simplify `(3x+9)/ (3x+15)`

Solution: `(x+3)/ (x+5)`

Math How to Divide

Introduction to math how to divide:

In mathematics, especially in elementary arithmetic, division (÷) is the arithmetic operation that is the inverse of multiplication. Teaching division usually leads to the concept of fractions being introduced to students. Unlike addition, subtraction, and multiplication, the set of all integers is not closed under division. Dividing two integers may result in a remainder. In this article we shall discuss about how to do divide in math.(Source: Wikipedia)

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Math how to divide example problem


Division is the process of equal distribution of number or repeated subtraction of same number by several times or is called as division. Zero divide by any number is zero.

Dividend = divisor x quotients + remainder

Example:

Divide 448 by 2

200 + 20 + 4
_____________

2      400 + 40 + 8

400 + 40 + 8
_____________

Now the quotient is 200 + 20 + 4 = 224.

Example:

Divide 668 by 2

300 + 30 + 4
_____________

2     600 + 60 + 8

600 + 60 + 8
_____________

Now the quotient is 300 + 30 + 4 = 334.

Example:

A shopkeeper made 352 chocolates. The shopkeeper packed 5 chocolates into each box. Find how many  number of boxes of chocolates he packed and how many chocolates unpacked?

Solution:

Total number of chocolates made by shopkeeper = 352

Each box contains 5 chocolates

Therefore 352/5 = 70 remainder 2

He packed 70 boxes of chocolates.

2 chocolates are unpacked.

Example:

A shopkeeper made 324 cakes. A shopkeeper packs 5 cakes into each box. Find how many boxes of cakes there and how many cakes are left over; Shopkeeper sold each box for `$` 2, Find how much money he receive?

Solution:

Number of box of cakes = Total cakes / Number cake in one box

324 / 5 = 64 remainder 4

There are 64 boxes of cakes. 4 cakes are remainder.

The number of box = 64

So multiply number of box x sold cost of each box

Receive money = 64 x 2 = `$` 128

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Math how to divide practice problem


Problem:

Divide 690 by 3

Answer:

230

Problem:

A shopkeeper made 340 cakes. He packed 6 cakes into each box. Find how many boxes of cake he packs and how many cakes unpacked?

Answer:

He packed 56 boxes of cakes.

4 cakes are unpacked.

20 of 50 in Math

Introduction to 20 of 50 in math:

This article is showing the 20 of 50 in math. Here, 20 of 50 is nothing but 20 × 50. In arithmetic, multiplication is one of the fundamental arithmetic procedures. There are a lot of ways of multiplying procedures similar to numeral multiplication, fraction multiplication, mixed fraction multiplications and etc. The symbol for multiplication is denoted as (×). Give us permission to observe a basic example for multiplication. For example, 20 × 5 = 20 + 20 + 20 + 20 + 20 `=>` 100

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Example problems based on how to simplify 20 of 50 in math:


The example problems based on how to simplify 20 of 50 in math is given below that,

Example 1:

How to simplify 20 of 50 in math?

Solution:

Step 1:

Here, 20 of 50 is nothing but 20 × 50.

Step 2:

The given problem is nothing but fundamental multiplication, at this time we require to multiply the digit 20 through 50.

Step 3:

Now, first multiply the digit 20 through second digit 0.

We obtain 20 × 0 = 00

Step 4:

Here we are going to multiply the digit 20 through first digit 5,

We obtain 20 × 5 = 100 (20 + 20 + 20 + 20 + 20 = 100)

Here add one zero to the answer. So, 1000

Step 5:

Now add these two values.

00

1000

1000

Step 7:

Another method is given below that.

20 × 50

00

1000

1000

Step 8:

The concluding answer for the on top of problem is 1000.

Example 2:

How to simplify 120 of 50 in math?

Solution:

Step 1:

Here, 120 of 50 is nothing but 120 × 50.

Step 2:

The given problem is nothing but fundamental multiplication, at this time we require to multiply the digit 120 through 50.

Step 3:

Now, first we have to multiply the digit 120 through Second digit 0

We obtain 120 × 0 = 000

Step 4:

Here we are going to multiply the digit 120 through first digit 5,

We obtain 120 × 5 = 600 (120 + 120 + 120 + 120 + 120 = 600)

Here add one zero to the answer. So, 6000

Step 5:

Now add these two values

000

6000

6000

Step 7:

Another method is given below that.

120 × 50

000

6000

6000

Step 8:

The concluding answer for the on top of problem is 6000.

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Practice problems based on how to simplify 20 of 50 in math:


The Practice problems based on how to simplify 20 of 50 in math is given below that,

Problem 1:

How to simplify 220 of 50 in math?

Answer: The concluding answer for the problem is 11000.

Problem 2:

How to simplify 1020 of 50 in math?

Answer: The concluding answer for the problem is 51000.

Problem 3:

How to simplify 2020 of 50 in math?

Answer: The concluding answer for the problem is 101000.

Free Online Math Games

Math games are very helpful to lot of children’s. Mostly many children’s do not interest to do math. So entertaining games have been introduced to kids. It helps the children to play and they learn math. Imagine that the kids are very busy to do math games. It is very helpful to the kids, because math is applicable in our practical life and all fields. The math is most powerful. Imagine the kids couldn’t stop to do math. This online math games are available for all categories of students, which includes: free online math games for kids, 1st graders to higher level and also for college students. There are also free online math games for adults. This free online math games make learning fun and interesting for students. The free online math games are useful not only for the students but also for the teachers and parents.

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SOME VARIETIES OF FREE ONLINE MATH GAMES


Free Math Games includes an Order Of Operations game, two "Secret Number" puzzles, and other fun ways to practice math facts and math principles.

Some of the free online math games include: Entrapment, Math Tutoring Service, One to Ten, Math Scramble, Side by Side, Secret Number, Subtraction Triangles, Magical Squares, Adders, Secret Numbers, Zap, Fraction Concentration, Fractional Hi-Lo, Guess It.



ENTRAPMENT

Trap the computer's red dots between our gray dots to solve this mind bender.  There are over two thousand puzzles under this category.

MATH TUTORING SERVICE

The Problem Site's administrator, Douglas Twitchell provides math-tutoring services for high school students.

ONE TO TEN

Use four single-digit integers and the standard arithmetic operations to create all the numbers from one to ten.

MATH SCRAMBLE

Fill in the blanks in an addition problem or a multiplication problem to obtain the correct solution!

SIDE BY SIDE

A set of three math puzzle games in which we are given a list of seven numbers in a row, and we must rearrange the numbers according to the rule of the game.

SECRET NUMBER

The computer picks a random number between 10 and 99. We must ask questions to determine what the secret number is.

SUBTRACTION TRIANGLES

This puzzle is a bit like a Pascal's Triangle, except the numbers subtract to the values above them, instead of adding to the numbers below.

MAGICAL SQUARES

Select an "Easy", "Moderate", or "Challenge" game, and then place numbers in the square grid so they add up to the right sum for each row and column.

ADDERS

Refresh our memory on basic math facts by racing a snake around the game, gobbling up correct answers and avoiding running into walls.

SECRET NUMBERS

A variation on 'My Secret Number'. The number has three digits, and the computer tells us all the information we need to determine the number.

ZAP

A math game that just might give us brain cramps. It's a sliding tile puzzle that forces us to do mental arithmetic while racing against the clock.

FRACTION CONCENTRATION

Test our memory while evaluating and reducing fractions to find equivalent fractions. This game can be played as a one-player game or a two-player game.

FRACTIONAL HI – LO

Similar to 'Hi-Lo', except that we are guessing fractions between 0 and 1. A bit more challenging, since we are dealing with both numerators and denominators!

GUESS IT!

Professor Puzzler helps young children learn about estimation by guessing amounts, and by recognizing more and less

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ADVANTAGES


Learn math in an fun and interestig way
Creates interest among students in maths
Loss of  fear of Math among students and parents
Helps students to learn Math very easily.
Loss of tension among parents regarding Math.

Math Fractions

Introduction to Math Fractions:
Fraction represents a part  of a whole. A fraction of material or thing is a piece or section of it. It is a quantity

which cannot be represented as a whole number.A fraction has two parts one is numerator and the  other is

denominator.

The rectangular  picture above can be divided into 8 equal parts.

4 parts of total   rectangle is painted  with Brown colour  .Hence brown colour constitutes 4/8 of total.

2 parts of total   rectangle is painted  with Black colour.Hence Black colour constitutes 2/8 of total.

1 part   of total   rectangle is painted  with Blue colour.Hence Blue colour constitutes 1/8 of total.

1 part   of total   rectangle is painted  with Red  colour.Hence Red  colour constitutes 1/8 of total.

MATH FRACTIONS IN DAILY LIFE:-

i)   Grades awarded to students for example (4/5, 5/5).

ii)  To represent  time such as  quarter past the hour.Quarter is nothing but a fraction equivalent to 1/4.

iii)  Percentages which are also fraction .50% is equivalent to 50/100 =1/2.


Math fractions description:

TYPES OF MATH  FRACTIONS :-

i)  Proper fractions:These are the fractions having numerator always less than the denominator

The value of a proper fraction is always less than 1.

Examples:-  1/3  ,5/6 ,7/9

ii)  Improper fractions:These are the fractions having numerator  greater  or equal to denominator

The  value of a improper fraction will be  always greater than or equal  to

Any   whole number can be transformed into a improper fraction.

Examples:-  8/3  , 6/6 , 9/2

iii)  Mixed fractions :Mixed fraction is whole number and fraction together. An improper

fraction  be rewritten as mixed fraction and vice versa.

Examples :-   2`(3)/(7)`,   4`(4)/(11)`

iv) Equivalent fractions :Fraction which  reduce to same number on simplification are called

equivalent fractions.

Examples :- the equivalent fraction of  10/25  is 2/5  as 5 is common factor

in numerator and denominator.

MATH FRACTIONS  OPERATIONS :

i)  Division : Fractions can be divided . Fraction in numerator is multiplied by reciprocal of fraction in

the denominator.

Example :  `(3)/(4)`   `-:`   `(5)/(7)`    =     `(3)/(4)`   `x`   `(5)/(7)`

=   `(15)/(28)`



ii) Subtraction  : Fractions can be subtracted provided the denominators of fractions  are same.For

fractions having unequal denominators ,denominators are to be made same for

subtraction.

Example1 :  `(2)/(9)`   `**`   `(1)/(9)`    =   `(1)/(9)`

Example2 : `(1)/(2)`     -    `(1)/(4)`        =   `(1*2)/(2*2)`   -    `(1)/(4)`      =        `(2)/(4)`  -  `(1)/(4)`      =   `(1)/(4)`



iii) Multiplication: Fractions can be multiplied directly ie numerators with numerators and

denominators with denominators.

Example : `(2)/(9)`   `xx`   `(1)/(9)`    =   `(2)/(81)`

iv) Addition :Fractions can be added provided the denominators of fractions  are same.For

fractions having unequal denominators ,denominators are to be made same for

addition.

Example1 :  `(2)/(9)`   +   `(1)/(9)`    =   `(3)/(9)`

Example2 : `(1)/(2)`     +  `(1)/(4)`        =   `(1*2)/(2*2)`   +    `(1)/(4)`      =        `(2)/(4)`  +  `(1)/(4)`      =   `(3)/(4)`

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More Examples for Math Fractions:


Ex1:

Multiply the fractions is `8/5` and `5/9`

Sol:

Here we can observe than there is a common factor in numerator and denominator which is 5.

so cancelling 5  we will be left with     `(8)/(9)`

Ex2:

Arrange  the following fractions in ascending order     `(3)/(4)`    `(2)/(3)` `(1)/(6)`

Sol:

To compare fractions their denominators should be equal .so least common multiple of 4,3,6 is

12 .So now we make denominators equal

`(3)/(4)`` = ` `(3xx3)/(4xx3) =9/12`

similarly

`(2)/(3)`` = ` `(8)/(12)`

`(1)/(6)``=``(2)/(12)`

Since denominators are equal and so numerators can be compared

so  1/6 ,2/3,3/4 is the required order.

Ex3:

Add the following mixed fractions

i)     `(1)/(3)`  + 5 `(1)/(3)`

`sol:`

`(1)/(3)`  + 5 `(1)/(3)`

=  1+5  +    (1/3)+ (1/3)

` =6 + ``(2)/(3)`

= 6`(2)/(3)`

Math Decimal System

Introduction to Math Decimal System:

The concept of decimal system  is also deals with the fractions whose denominators are 10, 100 or 1000 etc. In this section, a decimal can be expressed as a fraction and vice-versa. A math decimal system may contain a whole number part and a decimal part. In a decimal system, if whole number part is not given, we indicate it by writing a zero on the left of the decimal point.In math, decimal value is represented by the point.

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Decimal number system in math:


In math decimal number system, the value of a digit depends upon its place, or position, in the number.
Each place has some value of 10 times the place to its right.

To the left of  decimal point are:
Ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions, etc

To the right of the decimal point are:
Tenths, hundredths, thousandths, ten thousandths, hundred thousandths, and so on..

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Decimal Conversions math:


Fractions as decimals:
A  fraction with denominator 10 can be expressed  using decimals.here we are going to convert fractions into decimals
Let us try to find decimal representation.

Example 1:
Covert the  ` 22/10`  into decimal

Solution:
We know that
`22/10` =`20+ 2/10 `

= `20/10 +2/10`

= 2 +`2/10`

= 2.2

Therefore, `22/10` = 2.2 is the decimal form

Example 2:
Write the following as a decimal:
34+ `2/10+3/100`

Solution:
34+`2/10+3/100`

=34.23 is decimal form

Example 3:
Convert the following  72+`2/100+3/1000` into decimals

Solution:
72+ `0/10 +2/100+ 3/1000 `

=72.023

Decimals as fractions:
Till now we have to know, how to write fractions with denominators 10, 2 or 3 as decimals.  we  can write a decimal number  like 2.5 as  fraction.
Take numerator as the number obtained by removing the decimal point from the given decimal.
Take denominator as number obtained by inserting as many zeros with 1  ex. 10, 100 or 1000 ,etc. as there are
number of places in decimal  number part.

Example,    Let us see 1.2 = 1+`2/10`

Example 1:
Write the terms into fractions
7.02
Solution:
Here after point placed 2 digits so the fraction is 100
=`702/100`

Example 2:
Write the terms into fractions  0.81

Solution:
Here after point placed 2 digits so the fraction is 100
= `81/100`

Example 3:
Write the terms into fractions  0.125

Solution:
Here after point placed 3 digits so the fraction is 1000
0.123 = `123/1000`

Math Division Help

Introduction to division for kids:

Division is one of the mathematical operations. The process of splitting the whole part into equal parts is called as division. The division process is indicated by a symbol ‘÷’ or ‘/’.  The first term of division is termed as dividend and the second term is termed as divisor. The answer of the division process is termed as quotient. For example, 4 ÷ 2 or 4/2 means, we have to split 4 into 2 equal parts. Here, 4 is dividend and 2 is divisor. This division process is the opposite operation of multiplication. For example, a x b = c is the multiplication operation where as c/a = b or c/b = a are division operations. This article helps to teach the division process for kids by giving simple steps for division. We are also going to see some example problems for division which helps the kids to learn division easily. I like to share this what is the algebraic expression with you all through my article. I like to share this what is the algebraic expression with you all through my article.


Explanation to help the division for kids:


The general form of division is,

Dividend ÷ divisor = quotient

Step 1:

First, we have to subtract the divisor from the dividend. If we get the subtracted answer 0 then stop the process. Other wise, again we have to subtract the divisor from the previous subtracted answer.

Step 2:

Now, we have to count the number of subtraction operation. This count is equal to the quotient.

The above steps help the kids to easily understand the division.

Example:

Consider 6 balls. If we want to split it into 3 equal groups then we need to do division operation.

6 ÷ 3

Step 1:

First, we have to subtract 3 from 6.

6 – 3 = 3

The subtracted answer is 3. So, again we need to do subtraction of divisor 3 from the previous subtracted answer 3.

3 – 3 = 0

Step 2:

We get the subtracted answer 0. So, we can stop this process. The count of subtraction process is 2.

Therefore, 6 ÷ 3 = 2


We can split the 6 balls into 3 equal groups and each group has 2 balls.

Division by 1:

The division of any number by 1 results the same number.

a ÷ 1 = a

Example: 3 ÷ 1 = 3

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Example problems to division for kids help:


Example: 1

Divide: 10 ÷ 5

Solution:

Given: 10 ÷ 5

Step 1:

First, we need to subtract the divisor 5 from 10.

10 – 5 = 5

The answer of subtraction is 5. So, again we have to subtract the divisor 5 from the previous subtracted answer 5.

5 – 5 = 0

The subtracted answer is 0.

Step 2:

The number of steps of subtraction is 2. So, when we are dividing 10 by 5, we get 2.

10 ÷ 5 = 2

Example: 2

Ram has 20 chocolates. If he wants to share it for 5 members then how many chocolates each member has?

Solution:

Given:

Total number chocolates = 20

We have to split into 5 equal groups.

20 ÷ 5

Step 1:

First, we need to subtract the divisor 5 from 20.

20 – 5 = 15

The answer of subtraction is 15. So, again we have to subtract the divisor 5 from the subtracted answer 15.

15 – 5 = 10

Again, we need to subtract the divisor 5 from the previous answer 10.

10 – 5 = 5

Again, we need to subtract the divisor 5 from the previous answer 5.

5 – 5 = 0

The subtracted answer is 0.

Step 2:

The number of steps of subtraction is 4. So, when we are dividing 20 by 5, we get 4.

20 ÷ 5 = 4

So, Ram can share 30 chocolates to 5 members and each member has 4 chocolates.


Practice problems to helps kids for division:


Problem: 1

8 ÷ 4

Answer: 2

Problem: 2

4 ÷ 1

Answer: 4