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Summary Manhattan GMAT - Fractions, decimals and percents
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Fractions, decimals & percent’s1 Digits & Decimals
Rounding tot the nearest place value
3.681 wordt afgerond naar 3.7. Er wordt alleen gekeken naar de eerste twee cijfers na de
komma. De rest wordt buiten beschouwing gelaten.
Powers of 10: shifting the decimals
In words thousand hundreds tens ones tenths hundredths thous
In numbers 1,000 100 10 1 0,1 0,01 0,001
In powers of ten 103 102 101 100 10-1 10-2 10-3
Multiplication
In the factors, count all the digitis to the right of the decimal point, then put that many digitis
to the right of the decimal point in the product.
0.002 x 1.4 = 2 x 14 = 28 = 0.028
When multiplying a very large number and a very small number than move the decimals in
the opposite direction:
0.0003 x 40000 = 3 x 4 = 12
Je verplaatst ze beide 4 plekken.
Divison
Divide by whole numbers.
You can always simplify division problems by shifting the decimals point in the same
direction.
Powers and roots
(0.54) = ?
0.5 = 0.5 x 10-1
(0.5 x 10-1)4 = 54 x 10-4
54 = 252 = 625
625 x 10-4 = 0,0625
A square roots is a number raised to the ½ power, a cub root is a number raised tot the 1/3
power etc.
3
√ 0.000027 = ?
0.000027 = 27 x 10-6
(0.000027)1/3 = (273 x 10-6)-2
(27)1/3 x (10-6)1/3 = (27)1/3 x 10-2
(27)1/3 = 3 (33 = 27)
3 x 10-2 = 0.03
Short cut
Shortcut by counting decimal places.
The number places in the result of a cubed decimal is 3 times the number of decimals places
in the original decimal.
The number of decimal place in a cube root is 1/3 the number of decimal places in the
original decimal
, 2 Fractions
Proper fractions are those that fall between 0 and 1. In proper fractions, the numerator is
always smaller than the denominator: ¼
Improper fractions are those that are greater than 1. The numerator is greater than the
denominator: 5/s
Improper fractions can be rewritten as mixed numbers.
Numerator and denominator rules
Rules who only apply to positive fractions:
As the numerator goes up, the fraction increases. 10/8 9/8 8/8
As the denominator goes up, the fraction decreases. 3/2 3/3
Adding the same number to both the number and the denominator brings the fraction
closer to 1, regardless of the fractions value.
The multiplication shortcut
8 35 8(35) 1(7) 7
− x − = − = − = −
15 72 15(72) 3(9) 27
8 en 72 zijn beide deelbaar door 8, dus wordt dan 1 en 9
15 en 35 zijn beide deelbaar door 5, dus wordt dan 3 en 7
No addition or subtraction shortcuts
In order to add or subtract fractions, you must:
1. Find a common denominator
2. Change each fraction so that it is expressed using this common denominator
3. Add up the numerators only.
Dividing fractions: use the reciprocal
The reciprocal is the fraction flipped upside down:
¾ = 4/3
To check if you have found the reciprocal of a number, use this rule: the product of a number
and it’s reciprocal always equal 1. Example:
¾ x 4/3 = 12/12 = 1
In order to divide fraction:
1. Change the divisor into its reciprocal, and then
2. Multiply the fractions. Note that the divisor is the second number.
Comparing fractions: cross-multiply
There is a shortcut to comparing fractions called cross-multiplications. This is a process that
involves multiplying the numerator of one fraction with the denominator of the other fraction,
and vice versa.
7 4
− x − = 7x5 en 4x9
9 5
Cross multiply the fractions and put each answer by the corresponding numerator (not the
denominator)
Never split the denominator
Three examples of complex fractions are:
15+ en +10
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