## Learn to Solve Math Problems Perfectly

Problem 1/1
Listen
0:30*
How many 7 dm pieces of ribbon can be cut from a spool of ribbon 50 meters long?

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 ^2 for (²), ^3 for (³), ^deg for (°).

## 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:

• 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. Review 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.

+12345678910
1234567891011
23456789101112
345678910111213
4567891011121314
56789101112131415
678910111213141516
7891011121314151617
89101112131415161718
910111213141516171819
1011121314151617181920
Multiplication Table
×12345678910
112345678910
22468101214161820
336912151821242730
4481216202428323640
55101520253035404550
66121824303642485460
77142128354249566370
88162432404856647280
99182736455463728190
10102030405060708090100

### 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.

## Good to Memorize

### Common Prefixes

• micro 1/1000000
• milli 1/1000
• centi 1/100
• deci 1/10
• deca 10
• hecto 100
• kilo 1000
• mega 1000000
• bi 2
• tri 3
• penta 5
• hexa 6
• hepta 7
• octa 8
• nona 9

### Standard Units

• mm millimeter
• cm centimeter
• dm decimeter
• m meter
• km kilometer
• mg milligram
• g gram
• kg kilogram
• s second
• min minute
• h/hr hour
• ml milliliter
• l liter
• ha hectare

### Conversion Factors

• 1 cm = 10 mm
• 1 dm = 10 cm
• 1 m = 10 dm or 100 cm
• 1 km = 1000 m
• 1 g = 1000 mg
• 1 kg = 1000 g
• 1 min = 60 s
• 1 h/hr = 60 min
• 1 ml = 1 cm³
• 1 l = 1000 ml or 1 dm³
• 1 ha = 10000 m²

### Formulas

Perimeter

• Triangle P = a + b + c
• Square P = 4s
• Rectangle P = 2(L + W)
• Circle C = 2πr or πD
Area
• Triangle A = ½bh
• Square A = s²
• Rectangle A = LW
• Trapezoid A = ½h(b1 + b2)
• Circle A = πr²
Volume
• Cube V = s³
• Rectangular Prism V = LWH
• Circular Prism V = πr²h
• Prism (any) V = Ah, where A is area of the base
• Cone V = ⅓πr²h
• Sphere V = 4⁄3πr³
• Pyramid V = ⅓Ah, where A is area of the base
Sum of Interior Angles of Triangle
• ∠A + ∠B + ∠C = 180°
Sum of Interior Angles of Regular Polygon with n Sides
• ∑ = (n - 2) × 180°
Simple Interest
• I = Prt
Sum of Consecutive Numbers (from n1 to n2)
• ∑ = ½(n1 + n2)(n2 - n1 + 1)
Sum of Consecutive Numbers (from 1 to n)
• ∑ = ½(n)(n + 1)
Sum of n Consecutive Even Numbers (starting from 2)
• ∑ = n(n + 1)
Sum of n Consecutive Odd Numbers (starting from 1)
• ∑ = n²