MATHS EXERCISES

On this exercise we will explain 3 of the exercises we made some time ago on a math exam. For that we will explain these one by one and then solve the exercises.

1- Round these numbers to their tenths To solve this exercise we must round some decimal numbers to their tenths. To solve these exercises we must look to hundredths and if this is greater or equal to five we will increase the tenth in one. Let's take as example the first exercise:

a) 6,27 In this case the hundredth number is 7 that is greater than 5. For this reason we will increase the tenth (2) by one. The result of this exercise will be: 6,3

 And now, let's solve all the exercises:

b) 3,84 Here, the hundredth (4) is lower than 5, so the tenth will stay as it is (8): 3,8

c) 2,99 Here, the hundredth (9) is greater than 5, so the tenth (9) will be increased by 1, and that will affect the units that will be increased by 1 as well, so the result is: 3

d) 0,094 here the hundredth (9) is greater than 5, so the tenth (0) will be increased by 1: 0,1

e) 0,852 here the hundredth (5) is equal than 5, so the tenth (8) will be increased by 1: 0,9

2- Reduce to one power On this exercise we must solve some powers problems and reduce them to just one power. For that we must know first some things:

Any number raised to the power of one equals the number itself (a^1=a) Any number raised to the power of zero, except zero, equals one (a^0=1 )

When multiplying two powers with the same base, we can simply add the exponents (a^b • a^c = a^b+c)

When dividing two powers with the same base, we can simply substract the exponents (a^b : a^c = a^b-c)

To raise a power to a power, keep the base and multiply the exponents. ((x^m)^n = x^m•n)

Knowing this basic rules we will solve some exercises:

a) 10^5 : 10^2 Here we have a division, so we will take the exponents and make a substraction, so: 10^5 : 10^2 = 10^5-2 = 10^3

 b) 10^4 • 10^2 Here we have a multiplication so we will add the exponents, and then we will have: 10^4 • 10^2 = 10^4+2 = 10^6

c) a^4 • a^6 Here we will follow the same base than in the previous exercise so: a^4 • a^6 = a^4+6 = a^10

d) m^2•m^4•m^5 We will continue with the same base, we will add the exponents: m^2•m^4•m^5 = m^2+4+5 = m^11

e) (10^3)^3 Here we must multiply the exponents so: (10^3)^3 = 10^3•3 = 10^9 f) k^6 : k^2 Here we must substract the exponents: k^6 : k^2 = k^6-2 = k^4

3- Greatest Common Divisor The greatest common divisor is the way to operate different fractions, for that we will reduce the divisors to their factors.

 a)3 + 5 + 4/7 + 3/4 here 3 and 5 are equal to 3/1 and 5/1 so the Common Divisor will be (7 • 4 (2^2) • 1) and we will multiply the factors by the new numbers so: ((3 • 28)/28) + ((5 • 28)/28) + ((4 • 4)/28) + ((3 • 7)/28) = 84/28 + 140/28 + 16/28 + 21/28 = 261/28

b) 5(3/4) here we have a multiply for that we will multiply the factors with the factors and the divisor with the divisors, so we have: 5/1 • 3/4 = 5•3 / 1•4 = 15/4

c)7/5 : 3/8 Here we will multiply the first factor with the second divisor and it will be the solution factor, and the first divisor with the second factor and it will be the solution divisor so: 7/5 : 3/8 = 7•8/5•3 = 56/15

d)(7/5)^3 We must expose the factor and the divisor so: (7/5)^3 = 7^3/5^3