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All questions on Maths

Powers & Percentage Increase/Decrease

Hi, I'm revising for my gcse exam in June and struggling with these two topics.

Percentage Decrease: What is the new cost after a price of £56 is decreased by 15%? Work it out as 0.85 5g=£47.50 This is a question from a GCSE revision guide, I don't really get this. I have tried to find a way to understand but I really don't- I don't understand where the 0.85 came from. Multiplying powers- again this is a question from a rev guide- 48=32, but 48=2₂ 2₃=2₅ =32 I don't understand how 2 to the power of 3 is 8,

Percentage Decrease: Question from GCSE - 243 / 9 =7, but 243 / 9 = 3₅ / 3₂ = 3₃= 27

Can you please explain all these questions to me, sorry that I'm asking to many questions but please can you answer them, this is the only thing I'm struggling on. Thank You :D

Emma

Answers
The last question is diving powers, sorry
addycole_786
11 April 2012
If £56 is decreased by 15%, then it means that 15% of £56 is subtracted. Another way of looking at it is to say that you have 85% of it left. 85% is just another way of expressing the fraction 0.85 . To find out how much is 0.85 of £56 you just multiply the numbers together. The word "of" can almost always be replaced with a multiplication sign.
ianmoth
11 April 2012
Apparently 243 is 3 x 3 x 3 x 3 x 3 , ie, 3^5. 9 is 3 x 3 , or 3^2. So if you have a fraction where you have 3^5 on the top line and 3^2 on the bottom line, then you can cancel out two of the threes, to leave 3^3 on its own. This is the same as subtracting the power on the bottom line from the power on the top, ie, 5-2=3. 3^3 = 3 x 3 x 3 = 27
ianmoth
11 April 2012
Thank You, I understand it now :D
addycole_786
12 April 2012
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How to Find 1 Percent of a Number

Introduction

Have you ever seen a 5% discount in a shop or needed to calculate a 15% tip? All percentage calculations, no matter how complex, are built on one simple, core skill: finding 1 percent.

The word "percent" literally means "per hundred." So, 1% is simply one part out of one hundred.

Once you know how to find 1% of a number, you can easily find any other percentage.

  • To find 5%, you just find 1% and multiply it by 5.
  • To find 20%, you find 1% and multiply it by 20.
  • To find 72%, you find 1% and multiply it by 72.

This guide will show you the one simple trick to find 1% of any number instantly.

The Key Method: Finding 1%

Because 1% means "one out of one hundred" (£1/100£), finding 1% of a number is the same as dividing that number by 100.

The fastest way to divide any number by 100 is to move the decimal point two places to the left.

That's the entire trick.

Worked Example 1: A simple number

Find 1% of 300.

  • The number is 300. The decimal point is at the end: 300.
  • Move the decimal two places to the left: 3.00
  • Answer: 1% of 300 is 3.

Worked Example 2: A number with no zeros

Find 1% of 189.

  • The number is 189. The decimal point is at the end: 189.
  • Move the decimal two places to the left: 1.89
  • Answer: 1% of 189 is 1.89.

Worked Example 3: A number that already has a decimal

Find 1% of 84.5.

  • The number is 84.5.
  • Move the decimal two places to the left: 0.845
  • Answer: 1% of 84.5 is 0.845.

Worked Example 4: A very small decimal number

Find 1% of 0.7.

  • The number is 0.7.
  • Move the decimal two places to the left. We need to add zeros for the empty spaces: 0.007
  • Answer: 1% of 0.7 is 0.007.

Practice Questions & Solutions

1

Find 1% of 500.

Solution

To find 1% of 500, we move the decimal point two places to the left.

500. becomes 5.00

Answer: 5

2

Find 1% of 900.

Solution

To find 1% of 900, we move the decimal point two places to the left.

900. becomes 9.00

Answer: 9

3

Find 1% of 250.

Solution

o find 1% of 250, we move the decimal point two places to the left.

250. becomes 2.50

Answer: 2.5

4

Find 1% of 476.

Solution

To find 1% of 476, we move the decimal point two places to the left.

476. becomes 4.76

Answer: 4.76

5

Find 1% of 81.

Solution

To find 1% of 81, we move the decimal point two places to the left.

81. becomes 0.81

Answer: 0.81

6

A t-shirt costs £40. How much is 1% of its price?

Solution

To find 1% of £40, we move the decimal point two places to the left.

40. becomes 0.40

Answer: £0.40 (or 40p)

7

Find 1% of 15,200.

Solution

To find 1% of 15,200, we move the decimal point two places to the left.

15200. becomes 152.00

Answer: 152

8

Find 1% of 70.5.

Solution

To find 1% of 70.5, we move the decimal point two places to the left.

70.5 becomes 0.705

Answer: 0.705

9

Find 1% of 1.25.

Solution

To find 1% of 1.25, we move the decimal point two places to the left.

1.25 becomes 0.0125

Answer: 0.0125

10

A bank offers a 1% annual interest rate. If you deposit £5.50, how much interest would you earn in a year?

Solution

We need to find 1% of 5.50. We move the decimal point two places to the left.

5.50 becomes 0.0550

Answer: £0.055

Gianpiero Placidi