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Our expert and friendly tutors can help you learn pre-algebra with ease! Please call us at 1.877.TUTOR18 or register online to get help with these topics.

  • Place value
  • Decimal numbers and their operations
  • Percent
  • Exponents
  • Square root
  • Order of operations
  • Integers and their operations
  • Ratios and proportions
  • Distance, time and speed
  • Factors and multiples
  • Greatest common factor
  • Least common multiple
  • Fractions and their operations  
Our proven 4-step learning approach enables students to understand mathematical concepts and apply these concepts to successfully solve practical problems. We equip you with tips for tricky questions, and teach shortcuts to improve testing speed and mental calculations.

Our examples below illustrate our comprehensive explanations with all steps. This means: Better understanding and Greater success in Pre-Algebra topics for YOU           

1.

35 is what percent of 105?
   
Let us assume that 35 is x% of 105.
Then,
                
           
              
                      

2. During the summer months, one soft drink truck visits Maria's neighborhood every 4 days and another truck visits her neighborhood every 5 days. If both trucks visited today, when is the next time both trucks visit on the same day?

The first truck visits her neighborhood every 4 days. It has already visited today.

So the next visit will be on the 4th day, next will be on 8th day and so on

Here we can see that the visiting days of the truck is in multiples of 4

The second truck visits her neighborhood every 5 days. It has already visited today.

So the next visit will be on the 5th day, next will be on 10th day and so on

Here we can see that the visiting days of the truck is in multiples of 5

Multiples of 4 are 1, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, etc

Multiples of 5 are 1, 5, 10, 15, 20, 25, 30, 35, 40, 45, etc.

Both the trucks have already visited today, so the next day on which both trucks will visit is the 20th day.

(We know that 20 is the least common multiple of 4 and 5)

3.

The average speed of a train on the onward journey is 25% more than that on the return journey. The train stops for one hour on reaching the destination. The total time taken for the complete to and fro journey is 16 hours. The total distance covered is 800 miles. Find the speed of the train on the onward journey.
           
 Let us look at the given scenario. Here we are asked to find the speed of the train on the onward journey.
           
We have been given that; the average speed of the train on the onward journey is 25% more than that on the return journey.

Let us assume that speed of the train on the return journey be 'x' miles per hour.

Then speed of the train in the onward journey =
                                                                                   
                                                                                   

We know that, if an object covers a certain distance at 'x' miles per hour and an equal distance at 'y' miles per hour, then the average speed during the whole journey is

Therefore the average speed of the train

 

Also given that total distance covered = 800 miles, and
Time taken for the complete journey =16 hours.

Therefore,
                                               
                                                           
            So,                     

     Speed on onward journey