# Let me solve your Math Problems

## MATHS PROBLEMS EXPLAINED

I have created this site to benefit adolescent teenagers in their quest to achieve maximum grades in maths and to help others conquer their fear of maths. I hope to be able to bring understanding and simplification of mathematical problems to all people that enquire. As I have a daughter who did her GCSE maths higher tier exam under my careful eye I can understand the frustrations felt by the student let alone the parent, what is significant in the above sentence is that my girl has dyslexia and dyspraxia which added to the frustration. My daughter achieved a grade C in her higher tier maths which was a big achievement with regards to her disabilities. If my daughter can accomplish this with my help I can also help you.

**PERCENTAGES**

**Q1**: In a classroom there are 40 pupils. 26 of these pupils are female, **the rest of the class are male.(highlighted part of sentence holds important information)** What percentage of the class are male?

**A1:** First we must establish how many are male.

There are 40 pupils - 26 females = 14 males.

So now we must establish what % of 40 is 14

which means 14 / 40 which is 14 divided by 40 = 0.35 ( do this on your calculator)

Now we must change this decimal into a percentage, to do so multiply by 100

0.35 x 100 = **35 % **

**(Answer) 35%**

Therefore 35% of the class are male

**Q2: **What is 40% of £3600?

**A2:** It is important to remember 40% means 40 / 100 ( 40 divided by 100)

So what we have to find is 40 / 100 **of** £3600

To do this we must replace the word **of **with a multiplication sign **X**

Therefore we have **40 / 100 X 3600 ( this can be simplified by cancelling zeros on the bottom with zeros on the top e.g. the 100 has (2) zeros and the 3600 has (2) zeros.**

Now by cancelling out the zeros we end up with **40 /1 X 36 = 1440**

Therefore **40% of £3600 = £1440 **

**(Answer) £1440**

**Q3:** Find the simple Interest on £4000 invested for 3 years at 8% per year?

**A3: **If simple interest is 8% per year then we must find

8% of £4000

To do this we must replace the word **of **with a multiplication sign **X**

This is 8 / 100 X 4000 (**this can be simplified by cancelling zeros on the bottom with zeros on the top )**

Now by cancelling out the zeros we end up with 8 X 40 = £320

So therefore the simple interest per year is £320

Simple Interest means that £320 will be added on to the £4000 at the end of each year. Therefore to find 3 years interest we must multiply the

£320 X 3 = £960

Thus the simple Interest on £4000 after 3 years is £960

**(Answer) £960**

**Q4:** Gary bought a new motorbike for £9000. At the end of each year his motorbike depreciates by 10%.

What is the value of Gary's motorbike 3 years later?

It's important to remember that 10% means 10 / 100( 10 divided by 100) which is 1 / 10,

so therefore Gary's motorbike loses 1 / 10 (one tenth) of its value at the end of each year.

We will carry out this equation in 3 steps.

__STEP 1(year one)__

**Starting value £9000**

**9000 / 10 = 900 - 900 ( 1/10 of 9000)**

**£8100 (value at end of first year)**

__STEP 2(year two)__

**Value after 1st year £8100 **

**8100 / 10 = 810 - 810 (1/10 of 8100)**

**£7290 (value at end of second year)**

**STEP 3(year three)**

**Value after 2nd year £7290**

**7290 / 10 = 729 - 729 (1/10 of 7290)**

**£6561 (value at end of third year)**

Therefore the value of Gary's motorbike three years later is £6561

**(Answer) £6561**

Now I will move on to ratio

**RATIO:**

A ratio is a comparision of quantities **3 : 6** three is to six.

This can be written as a fraction **3 / 6** (3 divided by 6) which breaks down to **1 / 2 **

**Therefore 3 : 6** can also be written **as 1 : 2**

This is an example of an equivelant ratio

Now lets simplify some ratios the first one is;

**10 : 15 **When we look at these two numbers we need to find a number that will divide into both, that number is **5**

So **10 / 5 = 2**

**15 / 5 = 3 **

therefore the simplified ratio in this equation is** 2 : 3**

**OK** we'll do another

**8 : 4** To simplify this equation we need to divide by **4**

So **8 / 4 = 2**

**4 / 4 = 1**

therefore the simplified ratio in this equation is** 2 : 1**

**One** more before we move on;

**9 : 15 : 12** Im doing this equation to show ratio isn't always about two numbers. To simplify this equation we will need to divide by **3 **

So **9 / 3 = 3**

**15 / 3 = 5**

**12 / 3 = 4**

therefore the simplified ratio in this equation is** 3 : 5 : 4**

#### Next we will move on to making sure the ratio equations have the same units:

**Simplify these fully:**

**15cm : 1m**

**Finding Same Units:- **there is 100 cm in 1 metre, therefore we multiply the **1 X 100 to change from metres to cm, **our equation now becomes **15cm : 100cm**

**Now** we need to simplify the equation;

**15cm : 100cm** The number we are looking to divide by is **5 **

**15 / 5 = 3**

**100 / 5 = 20 **our equation is now;

**3 : 20** This is the ratio simplified and note we don't use the cm's or units in our answer.

**Next **

**1hr : 40mins **

**Finding Same Units:-** there is 60mins in 1 hour so this would be the easiest option. **1 x 60 to change into minutes, **our equation now becomes **60Min's : 40Min's**

**Now** we need to simplify the equation;

**60mins : 40mins **The number we are looking to divide by is **20 **(this is to take the equation to its simplest form)

**60 / 20 = 3**

**40 / 20 = 2 **our equation is now;

**3 : 2** This is the ratio simplified and note we don't use hours or minutes in the answer.

#### Now as ratio should only have whole numbers we will do some with fractions and sort out a denominator:

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