eMath Challenge

Practice makes perfect.

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Test History

Arithmetic Drills

Reference Guide

About eMathChallenge

Ready, Set, Solve!

Grade

Difficulty

Topic

Problem 1/1

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0:30

There are 32 red ballpens and 56 blue ballpens in a box. When the same numbers of red ballpens and blue ballpens were added in each respective box, the ratio of red ballpens to blue ballpens became 7:11. How many ballpens were added in all?

Instructions: Read each problem carefully and write your answer in the box. Click next to solve more problems (up to 10), then click submit to get the results.

Note: Type n^2 for n², n^3=n³, n^deg=n°

How eMath Challenge Works

eMath Challenge is a good resource for students who wish to learn and improve their problem-solving abilities. It offers a wide range of math challenge problems whose solution methods are within the scope of primary mathematics.

The strategy is for the learner to take a series of practice tests on his or her own, with only a pen and scratch paper. The result of every test will be discussed with the coach, who will explain the correct analysis and solution to each wrong answer.

The following are the criteria that can be applied as filters to problem selection:

Grade: Grade I/II, Grade III, Grade IV, Grade V, Grade VI
Difficulty: Easy, Average, Hard
Topic: Any, Fraction, Percent, Ratio, Age, Amount, Discount/Gain, Interest, Distance, Rate/Speed, Angle, Perimeter, Area, Volume

Problem-Solving Tips

1. Master your Arithmetic.

You can't solve a math challenge problem if you can't add, subtract, multiply, or divide. Make sure that you have memorized the multiplication and addition tables up to 10x10 and 10+10.

Doing Arithmetic calculations should be automatic and effortless. Subtraction and division are the inverse operations of addition and multiplication, respectively. So if you can add and multiply, you should also be able to subtract and divide.

Don't forget the rule of precedence by doing multiplication and division first before addition and subtraction. The order is from left to right, but the parenthesized expression always takes priority.

2. Understand the problem.

Identify what is asked, referred to as the "unknown," and which operation(s) to use by carefully reading the problem. Establish the relationships that exist between the given values and the unknown.

Read through the problem again to ensure nothing is missed. Interpret the problem based on real-life scenarios. A problem that is rightly understood is considered half-solved.

3. Formulate a solution.

Use a standard formula if applicable, or create your own equation by translating the problem statement into a mathematical sentence. Take a hint on the given unit of measure. Develop the simplest solution and avoid a complicated approach.

In some cases, there could be another unknown that may require a preliminary solution. Do not assume anything that is not given.

4. Provide the answer.

Perform the required operations step-by-step until you arrive at the answer. Use the appropriate conversion factor to conform the given unit of measure to what is asked.

Simplify your answer to the lowest terms, and, whenever applicable, don't forget to append the unit of measure.

5. Verify the answer.

This is done by reversing the process. The answer becomes a given; then one of the given becomes the unknown.

Another way to check the answer is to redo the process, i.e., to solve the problem all over again. The answer should be the same; if not, review the process again. As you do this, be mindful of the allowed time and try not to exceed it. Find the balance between speed and accuracy.