# cooking rice

A cook bought 100 pounds of rice. If he used 4/5 of it in cooking, how many pounds of rice did he use?

Similar problems worksheets

From “used 4/5  of it in cooking” the word after “used 4/5  of” is “it” or “100 pounds of rice” so the amount rice bought is the amount in 1 (whole).

4/5 of 100 pounds of rice were used in cooking so we multiply the amount in 1 ( whole ), 100 pounds, with the fractional part used,4/5  , to find the amount in this part, the amount of rice used:

4/5x 100=80 pounds

# the greatest common factor—question and answer

Three  ropes  are  120  inches  long,  90  inches  long  and  150 inches  long.  They are cut into sections with no remaining parts.  If each section has the same length, what is the largest possible length for each section?  How  many  sections  can  we  get  altogether?

Worksheets for this type of questions

Since each section has the same length, that means we need to find the common factors of 120, 90 and 150. Since we need to find the largest possible length of each section, we need to find the greatest common factor. That is 30. So the largest possible length of each section is 30 inches.

The  rope  that  is  120  inches  long  is  cut  into  4  sections. The  rope  that  is  90  inches  long  is  cut  into  3  sections. The  rope  that  is  150  inches  long  is  cut  into  5  sections. Therefore, all the ropes are cut into a total of 12  sections.

# parenthesis and multiplication in one expression: which operation should be taken care of first?

Order of operations ( in order to make the explanation easy to understand, simple numbers are used)

Without any other operations in an expression: Addition and subtraction are equal operations in the way that is “first come, first served” from left to right:

12+3-9-5

=15-9-5

=6-5

=1

Without any other operations in an expression: multiplication and division are equal operations in the way that is “first come, first served” from left to right:

12 ÷6×3

= 2 ×3

=6

When an expression has addition and (or) subtractions with multiplication and (or) divisions in it, multiplications and ( or divisions) should be done first; additions and (or) subtractions should be done afterwards.

34- 9×3

=34- 27

=7

2+ 4 ×5 – 3×7

=2+ 20- 21

=22-21

=1

When an expression has parenthesis first, the operations in the parenthesis should be done first and other operations need to follow the rules above.

2+ 4 × (5 – 3) ×7 (operation in the parenthesis is done first)

=2+4 × 2×7 (multiplication is done before addition)

=2+ 8 × 7 (first multiplication is done , now let’s do the second multiplication)

=2+56

=58

Worksheets for similar problems

# the least common multiple and the greatest common factor

The  product  of  two  natural  numbers  is  420.  If  their greatest  common  factor  is  12,what  is  their  least  common multiple?

According  to  this  rule:  The  product  of  the  greatest  common factor  and  the  least  common  multiple  of  the  two  numbers  equals to  the  product  of  the  two  numbers

The  least  common  multiple  of  the  two  numbers  is:  420÷12=35

# Order of operations

Many teachers do not emphasize “order of operation”, but “order of operations” is very important. Without knowing order of operations well, you do not know how to solve a math problem.

Some examples are given in the following, There are also worksheets for you to work on after you understand the examples.

Order of operations ( in order to make the explanation easy to understand, simple numbers are used)

Without any other operations in an expression: Addition and subtraction are equal operations in the way that is “first come, first served” from left to right:

12+3-9-5

=15-9-5

=6-5

=1

Without any other operations in an expression: multiplication and division are equal operations in the way that is “first come, first served” from left to right:

12 ÷6×3

= 2 ×3

=6

When an expression has addition and (or) subtractions with multiplication and (or) divisions in it, multiplications and ( or divisions) should be done first; additions and (or) subtractions should be done afterwards.

34- 9×3

=34- 27

=7

2+ 4 ×5 – 3×7

=2+ 20- 21

=22-21

=1

When an expression has parenthesis first, the operations in the parenthesis should be done first and other operations need to follow the rules above.

2+ 4 × (5 – 3) ×7 (operation in the parenthesis is done first)

=2+4 × 2×7 (multiplication is done before addition)

=2+ 8 × 7 (first multiplication is done , now let’s do the second multiplication)

=2+56

=58

Worksheets for you to work on

# Average Speed

Lisa and Sarah were given a word problem to work on:

The distance between City A and City B is 360 miles. A car was going at 60 miles per hour from City A to City B; on the way back, the car was going at  40 miles  per hour because it was raining really hard so that driver could not see very well. What was the average speed of the car for the round trip?

(60+40)÷2=50 miles per hour

Sarah said: “No, you cannot solve the problem like that. This is how to solve it.”

The total distance for the round trip: 360×2=720 miles

The amount of time the car used to travel from City A to City B:

360÷60=6 hours

The amount of time the car used to travel back to City A from City B:

360÷40=9 hours

The total amount of time for the round trip:

6+9=15 hours

The average speed for the round trip= the total distance for the round trip÷ the total amount of time spent on the round trip= 720÷15=48 miles per hour

Friends, I believe that you all think that Sarah is right and she is. Remember: when you solve a word problem on travelling, finding the average speed is not the same as finding the average age, the average height, etc.

# cutting a stick

A stick is 1 yard long. If 1/5 is cut off at first, 1/6 of the remaining section is cut off secondly, 1/7 of the last remaining section is cut off thirdly and the cutting keeps on until 1/10 of the last remaining section is cut off finally, what is the length of the remaining stick?
The solution to this type of question usually has a pattern:

When 1/5 is cut off, 4/5 yard is left;

When 1/6 of the remaining section is cut off, 5/6 of 4/5 yard is left:

4/5 yard × 5/6 =4/6 yard

When 1/7 of the last remaining section is cut off, 6/7 of 4/6 yard is left:

6/7  × 4/6 = 4/7 yard

In this pattern, when 1/10 of the last remaining part is cut off, the amount left should be:

4/10 yard= 2/5 yard ( simplest term)

# the 3 elements you need to find to solve a word problem

To solve a whole number or a decimal word problem, 3 elements are essential: the number of groups (days, hours, rows, lines, etc.), the amount in each group, and the total amount in all groups.

To solve for one element, you need to determine what the other two elements are.

If the amount in each group is NOT the same, use addition or subtraction to solve for one of the 3 elements.

Examples:

1. Tom has \$2.00; Peter has \$5.00. How much do they have altogether?

In this example, there are two people (groups) and each person does not have the same amount of money. To find the total amount of money they have, we need to use addition. Therefore, the total amount of money they have is : 2+5=\$7.00

If the amount in each group is the SAME, use one of the following 3 elements formulas to solve for one of the 3 elements:

1. Tom has \$2.00; Peter also has \$2.00. How much do they have altogether?

In this example, there are two people (groups) and each person has the same amount of money.

To find the total amount of money they have, we can use addition but we can also use the following 3 elements formulas for whole number and decimal word problems: Total amount in all groups= the number of groups x the amount in each group

To find more on how to use 3 elements formulas to solve word problems with multiplication and division, please purchase word problems; detailed explanations of reasoning and solving strategies (volumes 3volume 4, volume 5volume 6, volume 7, volume 8, volume 9volume 10, volume 11 and volume 12)

# a math problem from SAT

The following is a problem from a SAT practice test:

If 6x + 1/x = 5, then x = ?

1. -1/6
2. 1/6
3. 1/4
4. 1/2
5. 2

You can try each number but you can also solve the problem on your own first and find the match for your answers.

How is how to solve it:

Multiply both sides of the equal sign with x so the equation becomes:

6x+1=5x

6x2-5x+1=0

Factor:

(2x-1)(3x-1)=0

X can be either ½ or 1/3.

The following is a question from a SAT practice test:

The average (arithmetic mean) of 3 numbers is 22 and the smallest of these numbers is 2. If the two remaining numbers are equal, what is the value of each of the remaining numbers?

1. 22
2. 32
3. 40
4. 64
5. 66

Here is how to solve for the answer:

The average of the 3 numbers is 22 so the sum of them should be:

22 x 3=66

One of the numbers is 2 so the sum of the other two numbers should be:

66-2=64

Since the other two numbers have the same value the value of each number should be:

64÷2=32