## Math Helper

Homework Helper: Frequently asked questions:

I need a place chart

I need a Customary Common Measurement Chart

I need a number line.I need a coordinate grid.

I need a copy of the Integer Card.

How do I change a fraction to a decimal?

To change a fraction to a decimal, you need to divide the numerator (top number) by the denominator (bottom number). For example, to change 1/2 to a decimal you need to divide 1 by 2. 1 divided by 2 = .5

How do I change a fraction to a percent?

To change a fraction to a percent, you need to use a proportion. Remember that percent means "of 100." For example, 1/2= ?/100

How do I change a decimal to a fraction?

To change a decimal to a fraction simply read it aloud, write it as a fraction, then simply when possible. For example, .4 would be read "four tenths." Write 4/10 then simplify to 2/5.

How do I change a decimal to a percent?

You can change a decimal to a percent several ways. I encourage you to use the short cut that we used in class. Simply move the decimal two places to the right and add a percent sign. For example, .75 would equal 75%.

How do I change a percent to a decimal?

You can change a percent to a decimal several ways. I encourage you to use the short cut that we used in class. Simply drop the percent sign and move the decimal two places to the left. For example, 80% would equal .8.

How do I change a percent to a fraction?

To change a percent to a fraction, remember that percent means "of 100." For example, 25% would be written 25/100, then just simplify.

What are the Order of Operations?

The order of operation are

1st: Grouping Symbols (parenthesis, braces, brackets and fraction bars) from left to right

2nd: Exponents (from left to right)

3rd: Multiplication and Division (from left to right)

4th: Addition and Subtraction (from left to right)

In class, I ask the students to underline the expression they are working on during each step so that they can keep track of what they have done.

For example: 2³ - 8/4 + (3+4) - 2 x 3 (1st step is grouping symbols)

2³ - 8/4 + 7 - 2 x 3 (2nd step is exponents)

8 - 8/4 + 7 - 2 x 3 (3rd step is multiplication and division from left to right)

8 - 2 + 7 - 2 x 3

8 - 2 + 7 - 6 (4th step is addition and subtraction from left to right)

6 + 7 - 6

13 - 6

7

How do I find the GCF of numbers?

To find the Greatest Common Factor of two or more numbers, list all the factors of the numbers and find the largest one that they have in common.

Example: GCF (20,25)

20: 1, 2, 4,5, 10, 20

25: 1, 5, 25

GCF (20, 25)= 5

How do I find the LCM of numbers?

To find the Least Common Multiple of two or more numbers, list the multiples of the numbers until you find a common multiple.

Example: LCM (20,25)

20: 20, 40, 60, 80, 100

25: 25, 50, 75, 100

LCM (20,25)=100

How do I find the prime factorization of a number?

To find the prime factorization of a number, we use a factor tree.

Examples:

12 10 50

/ \ / \ / \

2 x 6 2 x 5 2 x 25

/ \ / \

2 x 3 5 x 5

12 = 2² x 3 10 = 2 x 5 50 = 2 x 5²

How do I multiply decimals numbers?

To multiply decimal numbers, simply multiply as if you were multiplying numbers without decimals. When you are done, count how many "decimal places" you have in the problem. You need that many decimal places in your answer.

Example:

123.45

x 12.345

61725

493800

3703500

24690000

+ 123450000

1523.99025

How do I divide by a decimal number?

We never really divide by the decimal. We rewrite the problem so that the divisor is a whole number. For example: 75.874 / .25 would be rewritten to 7587.4 / 25. We had to move the decimal two places to the right (or multiply by 100) to move it out of the divisor (.25), so we had to move it two places to the right (or multiply by 100) in the dividend, also.

I'm not sure how to use an exponent.

It is important to know the difference between a base and an exponent in order to use an exponent. Look at the following expression: 8² The 8 is the base and will be multiplied. The 2 is the exponent and tells us how many bases to multiply. To solve this problem you must multiply 8 x 8 which is 64.

Examples:

2³ = 2 x 2 x 2 = 8

9² = 9 x 9 = 81

How do I find mean, median, mode and range?

To find the mean, you simply add all of your digits, then divide by how many digits you had.

For example: Find the mean of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55

55 / 10 = 5.5

The mean is 5.5

To find the median, you must put them in numerical order, then find the middle number. If there are an even number of digits, then you will have 2 in the middle and must find the average of the 2 digit in the middle.

For example: Find the median of 4, 56, 73, 82, 92, 6, 75, 83.

(first list in numerical order) 4, 6, 56, 73, 75, 82, 83, 92

The two "middle numbers" are 73 and 75. The average of the middle numbers is 74.

The median is 74.

To find the mode, you need to see which digit occurs the most. If no digit occurs more than once, then you have "no mode." If two or digits have the same number (or tie) then you can have more than one mode.

For example: Find the mode of 2, 5, 6, 3, 4, 3, 2, 5, 5, 4, 4.

The digits 4 and 5 occur the most with 3 each.

The mode is 4 and 5.

To find the range, you need to find the difference of the highest and lowest digits.

For example: Find the range for 45, 7, 43, 24, 35, 17, 28.

The highest digit is 45 and the lowest digit is 7. Their difference is 45-7=38

The range is 38.

How do I solve 1-Step Equations?

To solve 1-step equations, you need to isolate the variable (get it alone on one side.) To do that, you need undo whatever is done to the variable. Here are some examples.

Example 1: A + 5 = 7 Since 5 is added to the variable, you need to subtract 5 from both sides of the equation.

A + 5 - 5 = 7 - 5

A = 2

Example 2: A - 4 = 10 Since 4 is subtracted from your variable, you need to add 4 to both sides of the equation.

A - 4 + 4 = 10 + 4

A = 14

Example 3: A x 3 = 18 Since 3 is multiplied by the variable, you need to divide each side by 3.

A x 3 = 18

3 3

A = 6

Example 4: A/2 = 8 Since the variable is divided by 2, you need to multiply each side by 2.

A/2 x 2 = 8 x 2

A = 16

How do I use the formulas on my mathematics chart?

The first step to using a formula is to use the correct one. Make sure that you read carefully and use the formula that works with your problem. Then, you must write the formula exactly as it is written on the mathematics chart. Then replace the variables with "known information." The last step is to simplify as much as you can. Here are two examples.

1) Find the volume of a rectangular prism that is 2 feet wide, 3 feet tall and 4 feet long.

You need the volume formula for a rectangular prism.

V = lwh (lwh means length x width x height)

V = 3 ft x 2 ft x 4 ft

V = 24 ft³

2) Find the length of a rectangle whose area is 36 in² and width is 4 in.

A = lw (lw means length x width)

36 in² = l x 4 in. In order to solve, you must divide each side of the equation by 4 in.

36 in² = l x 4 in.

4 in. 4 in.

9 in.= l

How do I add fractions?

Here are the steps to adding fractions. Example: 3 1/5 + 2 7/8

1. First, the fractions must have a common denominator. If they do not already have one, you must find one and change the fractions. You can use 40 as a common denominator for this problem. So rewrite the problem with the new denominator. Remember, if you change the denominator, you must change the numerator proportionately.

3 1/5 = 3 8/40

+ 2 7/8 = 2 35/40

2. Now add the numerators, then the whole numbers. The denominator will stay the same.

3 8/40

+ 2 35/40

5 43/40

3. If your sum is an improper fraction, change it to a mixed fraction. If it can be simplified, do so.

5 43/40 = 6 3/40

How do I subtract fractions?

Here are the steps to subtracting fractions. Example: 3 1/2 - 1 3/4

1. First, you must have a common denominator. If you do not, find one and rewrite the fractions with a common denominator.

3 1/2 = 3 2/4

- 1 3/4 = 1 3/4

2. In some problems, you may need to "borrow" or "rename" the fractions in order to borrow.

3 2/4 = 2 2/4+4/4 = 2 6/4

3. Subtract the numerators, then the whole numbers. The denominator will stay the same.

2 6/4

- 1 3/4

1 3/4

4. Simplify your answers if necessary.

How do I multiply fractions?Here are the steps to multiplying fractions. Example: 2 1/2 x 3 3/4

1. If you have any mixed numbers, or whole numbers, make them improper.

For example: 2 1/2 = 5/2 and 3 3/4 = 15/4, so rewrite the problem as 5/2 x 15/4

2. Multiply the numerators, then the denominators. 5/2 x 15/4 = 75/8

3. Change improper fractions to mixed numbers and simplify if possible.

75/8 = 9 3/8 (This fraction can not be simplified.

Here are a few more examples:

1/2 x 7/9 4 x 1/3 1 1/4 x 2/3

7/18 4/1 x 1/3 5/4 x 2/3

4/3 10/12 "Simplify"

5/6

How do I divide fractions?Here are the steps to dividing fractions.

1. Make any mixed fractions or whole numbers improper.

2/3 ÷ 1 1/4 = 2/3 ÷ 5/4

2. Rather than dividing by the divisor, you need to rewrite the problem as a multiplication problem using the reciprocal of the divisor. 2/3 x 4/5

3. Multiply the numerators, then multiply the denominators.

2/3 x 4/5 = 8/15

4. Change improper fractions to mixed numbers and simplify if necessary.

More Examples:

2 1/4 ÷ 1 5/8 3 ÷ 1 1/2 2 1/5 ÷ 5

9/4 ÷ 13/8 3/1 ÷ 3/2 11/5 ÷ 5/1

9/4 x 8/13 3/1 x 2/3 11/5 x 1/5

72/52 6/3 11/25

1 20/52 2

1 5/13

How do I use a protractor?Place the center of the protractor on the vertex of the angle. Then line up one side (or ray) of the angle with the 0˚ mark on the protractor. Follow the scale around to the other side (or ray) of the angle and read the measure. You should always consider the size of the angle with the measurement to make sure that it is reasonable. Protractor Examples

I need a place chart

I need a Customary Common Measurement Chart

I need a number line.I need a coordinate grid.

I need a copy of the Integer Card.

How do I change a fraction to a decimal?

To change a fraction to a decimal, you need to divide the numerator (top number) by the denominator (bottom number). For example, to change 1/2 to a decimal you need to divide 1 by 2. 1 divided by 2 = .5

How do I change a fraction to a percent?

To change a fraction to a percent, you need to use a proportion. Remember that percent means "of 100." For example, 1/2= ?/100

How do I change a decimal to a fraction?

To change a decimal to a fraction simply read it aloud, write it as a fraction, then simply when possible. For example, .4 would be read "four tenths." Write 4/10 then simplify to 2/5.

How do I change a decimal to a percent?

You can change a decimal to a percent several ways. I encourage you to use the short cut that we used in class. Simply move the decimal two places to the right and add a percent sign. For example, .75 would equal 75%.

How do I change a percent to a decimal?

You can change a percent to a decimal several ways. I encourage you to use the short cut that we used in class. Simply drop the percent sign and move the decimal two places to the left. For example, 80% would equal .8.

How do I change a percent to a fraction?

To change a percent to a fraction, remember that percent means "of 100." For example, 25% would be written 25/100, then just simplify.

What are the Order of Operations?

The order of operation are

1st: Grouping Symbols (parenthesis, braces, brackets and fraction bars) from left to right

2nd: Exponents (from left to right)

3rd: Multiplication and Division (from left to right)

4th: Addition and Subtraction (from left to right)

In class, I ask the students to underline the expression they are working on during each step so that they can keep track of what they have done.

For example: 2³ - 8/4 + (3+4) - 2 x 3 (1st step is grouping symbols)

2³ - 8/4 + 7 - 2 x 3 (2nd step is exponents)

8 - 8/4 + 7 - 2 x 3 (3rd step is multiplication and division from left to right)

8 - 2 + 7 - 2 x 3

8 - 2 + 7 - 6 (4th step is addition and subtraction from left to right)

6 + 7 - 6

13 - 6

7

How do I find the GCF of numbers?

To find the Greatest Common Factor of two or more numbers, list all the factors of the numbers and find the largest one that they have in common.

Example: GCF (20,25)

20: 1, 2, 4,5, 10, 20

25: 1, 5, 25

GCF (20, 25)= 5

How do I find the LCM of numbers?

To find the Least Common Multiple of two or more numbers, list the multiples of the numbers until you find a common multiple.

Example: LCM (20,25)

20: 20, 40, 60, 80, 100

25: 25, 50, 75, 100

LCM (20,25)=100

How do I find the prime factorization of a number?

To find the prime factorization of a number, we use a factor tree.

Examples:

12 10 50

/ \ / \ / \

2 x 6 2 x 5 2 x 25

/ \ / \

2 x 3 5 x 5

12 = 2² x 3 10 = 2 x 5 50 = 2 x 5²

How do I multiply decimals numbers?

To multiply decimal numbers, simply multiply as if you were multiplying numbers without decimals. When you are done, count how many "decimal places" you have in the problem. You need that many decimal places in your answer.

Example:

123.45

x 12.345

61725

493800

3703500

24690000

+ 123450000

1523.99025

How do I divide by a decimal number?

We never really divide by the decimal. We rewrite the problem so that the divisor is a whole number. For example: 75.874 / .25 would be rewritten to 7587.4 / 25. We had to move the decimal two places to the right (or multiply by 100) to move it out of the divisor (.25), so we had to move it two places to the right (or multiply by 100) in the dividend, also.

I'm not sure how to use an exponent.

It is important to know the difference between a base and an exponent in order to use an exponent. Look at the following expression: 8² The 8 is the base and will be multiplied. The 2 is the exponent and tells us how many bases to multiply. To solve this problem you must multiply 8 x 8 which is 64.

Examples:

2³ = 2 x 2 x 2 = 8

9² = 9 x 9 = 81

How do I find mean, median, mode and range?

To find the mean, you simply add all of your digits, then divide by how many digits you had.

For example: Find the mean of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55

55 / 10 = 5.5

The mean is 5.5

To find the median, you must put them in numerical order, then find the middle number. If there are an even number of digits, then you will have 2 in the middle and must find the average of the 2 digit in the middle.

For example: Find the median of 4, 56, 73, 82, 92, 6, 75, 83.

(first list in numerical order) 4, 6, 56, 73, 75, 82, 83, 92

The two "middle numbers" are 73 and 75. The average of the middle numbers is 74.

The median is 74.

To find the mode, you need to see which digit occurs the most. If no digit occurs more than once, then you have "no mode." If two or digits have the same number (or tie) then you can have more than one mode.

For example: Find the mode of 2, 5, 6, 3, 4, 3, 2, 5, 5, 4, 4.

The digits 4 and 5 occur the most with 3 each.

The mode is 4 and 5.

To find the range, you need to find the difference of the highest and lowest digits.

For example: Find the range for 45, 7, 43, 24, 35, 17, 28.

The highest digit is 45 and the lowest digit is 7. Their difference is 45-7=38

The range is 38.

How do I solve 1-Step Equations?

To solve 1-step equations, you need to isolate the variable (get it alone on one side.) To do that, you need undo whatever is done to the variable. Here are some examples.

Example 1: A + 5 = 7 Since 5 is added to the variable, you need to subtract 5 from both sides of the equation.

A + 5 - 5 = 7 - 5

A = 2

Example 2: A - 4 = 10 Since 4 is subtracted from your variable, you need to add 4 to both sides of the equation.

A - 4 + 4 = 10 + 4

A = 14

Example 3: A x 3 = 18 Since 3 is multiplied by the variable, you need to divide each side by 3.

A x 3 = 18

3 3

A = 6

Example 4: A/2 = 8 Since the variable is divided by 2, you need to multiply each side by 2.

A/2 x 2 = 8 x 2

A = 16

How do I use the formulas on my mathematics chart?

The first step to using a formula is to use the correct one. Make sure that you read carefully and use the formula that works with your problem. Then, you must write the formula exactly as it is written on the mathematics chart. Then replace the variables with "known information." The last step is to simplify as much as you can. Here are two examples.

1) Find the volume of a rectangular prism that is 2 feet wide, 3 feet tall and 4 feet long.

You need the volume formula for a rectangular prism.

V = lwh (lwh means length x width x height)

V = 3 ft x 2 ft x 4 ft

V = 24 ft³

2) Find the length of a rectangle whose area is 36 in² and width is 4 in.

A = lw (lw means length x width)

36 in² = l x 4 in. In order to solve, you must divide each side of the equation by 4 in.

36 in² = l x 4 in.

4 in. 4 in.

9 in.= l

How do I add fractions?

Here are the steps to adding fractions. Example: 3 1/5 + 2 7/8

1. First, the fractions must have a common denominator. If they do not already have one, you must find one and change the fractions. You can use 40 as a common denominator for this problem. So rewrite the problem with the new denominator. Remember, if you change the denominator, you must change the numerator proportionately.

3 1/5 = 3 8/40

+ 2 7/8 = 2 35/40

2. Now add the numerators, then the whole numbers. The denominator will stay the same.

3 8/40

+ 2 35/40

5 43/40

3. If your sum is an improper fraction, change it to a mixed fraction. If it can be simplified, do so.

5 43/40 = 6 3/40

How do I subtract fractions?

Here are the steps to subtracting fractions. Example: 3 1/2 - 1 3/4

1. First, you must have a common denominator. If you do not, find one and rewrite the fractions with a common denominator.

3 1/2 = 3 2/4

- 1 3/4 = 1 3/4

2. In some problems, you may need to "borrow" or "rename" the fractions in order to borrow.

3 2/4 = 2 2/4+4/4 = 2 6/4

3. Subtract the numerators, then the whole numbers. The denominator will stay the same.

2 6/4

- 1 3/4

1 3/4

4. Simplify your answers if necessary.

How do I multiply fractions?Here are the steps to multiplying fractions. Example: 2 1/2 x 3 3/4

1. If you have any mixed numbers, or whole numbers, make them improper.

For example: 2 1/2 = 5/2 and 3 3/4 = 15/4, so rewrite the problem as 5/2 x 15/4

2. Multiply the numerators, then the denominators. 5/2 x 15/4 = 75/8

3. Change improper fractions to mixed numbers and simplify if possible.

75/8 = 9 3/8 (This fraction can not be simplified.

Here are a few more examples:

1/2 x 7/9 4 x 1/3 1 1/4 x 2/3

7/18 4/1 x 1/3 5/4 x 2/3

4/3 10/12 "Simplify"

5/6

How do I divide fractions?Here are the steps to dividing fractions.

1. Make any mixed fractions or whole numbers improper.

2/3 ÷ 1 1/4 = 2/3 ÷ 5/4

2. Rather than dividing by the divisor, you need to rewrite the problem as a multiplication problem using the reciprocal of the divisor. 2/3 x 4/5

3. Multiply the numerators, then multiply the denominators.

2/3 x 4/5 = 8/15

4. Change improper fractions to mixed numbers and simplify if necessary.

More Examples:

2 1/4 ÷ 1 5/8 3 ÷ 1 1/2 2 1/5 ÷ 5

9/4 ÷ 13/8 3/1 ÷ 3/2 11/5 ÷ 5/1

9/4 x 8/13 3/1 x 2/3 11/5 x 1/5

72/52 6/3 11/25

1 20/52 2

1 5/13

How do I use a protractor?Place the center of the protractor on the vertex of the angle. Then line up one side (or ray) of the angle with the 0˚ mark on the protractor. Follow the scale around to the other side (or ray) of the angle and read the measure. You should always consider the size of the angle with the measurement to make sure that it is reasonable. Protractor Examples