ratio in word problems

6,000 pounds of concrete consists of cement, sand and gravel in the ratio of 2:3:5. How many pounds of each are in the concrete?

To find the answer to the problem and other 9 similar problems, please visit here to get the worksheet

how much does the jacket cost?

A pair of pants cost $75.00 and it costs 2/3 as much as a jacket. How much does the jacket cost?

Matthew weighs 48 pounds. If he 3 /8 as much as his dad, how much does his dad weigh?

The purpose of these problems is to prepare students with standardized testing. To be able to find the amount in 1 is the key to solve all the fraction word problems.

To find the answers and a total of 10 word problems of this type, please visit here

 

 

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

Answer:

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

Answer to the question:

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?

To work on similar questions on your own, please click here

 

Answer:

 

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?

This was Lisa’s answer:

(60+40)÷2=50 miles per hour

 

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

This was Sarah’s answer:

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.