Try to simplify the problem

When dealing with a difficult equation, one of the basic instructions is to try and see if the problem can be divided into smaller pieces.

Example:

23 x 5 = ……

Divide into smaller pieces

20 x 5 = 100 3 x 5 = 15

Add up the outcomes of both pieces

100 + 15 = 115

Number of digits after the decimal point

When calculating with small numbers in a mathematical equation that needs dividing it may be easier to reduce the amount of numbers after the decimal point. Example given: 0,0003 ÷ 0,0006

When you move the decimal point in both numbers, the sum remains the same. In the sum above it is possible to move the decimal point 4 times to the right:

3 ÷ 6 = 0,5

An exact calculation is not always necessary. Sometimes, analytical reasoning will get you there. 

Sometimes it is sufficient to rule out certain answer options by using analytical reasoning, instead of knowing the exact solution.

Example:

Moving everything to one side of the “=” sign

When asked for the first or second number in front of the “=” sign, it may be useful to move the entire equation to one side of the “=” sign. The general rules for dividing and multiplying in this case are as follows:

X x Y=Z: 2 x 3 = 6,

Z ÷ X=Y: 6 / 2 = 3,

Z ÷ Y=X: 6 / 3 = 2

An example could be for instance:

2 x ….. = 6

6 ÷ 2 = 3

The general rules for adding and subtracting in this case are as follows:

X+Y=Z: 2+3=5

Z-X=Y: 5-2=3

Z-Y=X: 5-3=2

Example:

5 – … = 3

5 – 3 = 2

Minus and Minus equals Plus

+ – is the same as –

Example given:

5 +- 3 = 2

5 – 3 = 2 –

- – is the same as +

Example:

5 – - 3 = 8

5 + 3 = 8

Dividing and Multiplying negative numbers

Remember the following:

positive x positive = positive, positive ÷ positive = positive

positive x negative = negative, positive ÷ negative = negative

negative x positive = negative, negative ÷ negative = negative

negative x negative = positive, negative ÷ negative = positive

Converting fractions into numbers

A fraction can be turned into a number by performing the fraction as a dividing sum.

Example:

2/5 2 ÷ 5 = 0.4

Equalizing fractions

Sometimes when you are working with fractions it may be useful to equalize them. You will need to find a number that suits both of the lower numbers. The upper number has to be multiplied with the amount of times the lower number fits into the new suitable number.

Example given:

2/5 + 3/10

2/5 = 4/10

4/10 + 3/10 = 7/10

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