Read Online How to Pass Numerical Reasoning by Heidi Smith - Free Book Online
Authors: Heidi Smith
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at the end of the term is £63.75, after how many years has Katie redeemed the bond?
Q4 Max bought a house for £40,000. The value of his house increased over 6 years, so that by the end of the term it had seen a 40% increase on the original price. The same amount invested in a bank account yields 9% per annum simple interest over the same period. Which is the more profitable investment option?
Q5 If Paul invests £385 in National Savings Certificates, which currently yield annual compound interest of 2.8%, what will his certificates be worth at the end of 3 years (to the nearest penny?) Answers to Chapter 4
Percentage converter drill
Convert to percentage
Convert to decimal
Convert to fraction
Q1
0.25 = 25%
1 ⁄ 100 = 0.01
87.5% = 7 ⁄ 8
Q2
0.75 = 75%
1 ⁄ 25 = 0.04
0.5% = 1 ⁄ 200
Q3
0.1 = 10%
5 ⁄ 6 = 0.83 r
0.125% = 1 ⁄ 800
Q4
0.0047 = 0.47%
3 ⁄ 8 = 0.375
60% = 3 ⁄ 5
Q5
0.063 = 6.3%
3 ⁄ 9 = 0.3 r
250% = 2½
Q6
½ = 50%
0.1% = 0.001
0.625 = 5 ⁄ 8
Q7
7 ⁄ 8 = 87.5%
0.043% = 0.00043
2.75 = 2¾
Q8
5 ⁄ 3 = 166.6% r
8.3% = 0.083
0.006 = 6 ⁄ 1000
Q9
1 ⁄ 200 = ½%
430% = 4.3
0.125 = 1 ⁄ 8
Q10
4 ⁄ 400 = 1%
5 ⁄ 3 % = 0.16 r
6.002 = 6 1 ⁄ 500
Percentage formulae practice questions: explanations
In the following explanations, only one method is given. You may prefer to use another method to check your answers.
Q1 Answer = 18
Convert 50% to its decimal equivalent and multiply the whole number by the decimal:
50% = 0.5
0.5 × 36 = 18
Q2 Answer = 120
Convert 75% to its decimal equivalent and multiply the whole number by the decimal:
75% = 0.75
0.75 × 160 = 120
Q3 Answer = 39
To find 10% of 130, move the decimal place one place to the left of the whole number:
10% = 13
30% = 3 × 10% = 39
Q4 Answer = 5.76
24% is approximately equal to ¼ (25%) so your answer will be approximately ¼ × 24 = 6. Express the percentage as a fraction over 100 and multiply by the whole number (24):
Q5 Answer = 2
Both percentages are recognizable as common fractions, so express both as fractions and multiply by the whole number (80). (You can also find 20% of 12.5% (= 2.5%) and multiply by the whole number, 80.)
Q6 Answer = 60
25% = ¼, so you know that 15 = ¼ x (where x = the whole number). To solve the equation for a whole number, multiply both sides by the inverse of the fraction.
Q7 Answer = 200
To solve the equation for a whole number, multiply both sides by the inverse of the fraction:
Reduce the equation to its simplest terms:
Q8 Answer = 32
Convert the percentage to its decimal equivalent: 32% = 0.32. Multiply by the whole number (60) to find the percentage to find the part:
Percentage
×
Whole
=
Part
0.32
×
60
=
19.2
So you know that 19.2 = 60% of a new whole number x . Solve for x by setting up the percentage as a fraction over 100 and cross-multiply:
60x = 19.2 × 100 = 1920. Divide both sides by 60:
Q9 Answer = 150
To solve the equation for a whole number, multiply both sides by the inverse of the fraction:
Q10 Answer = 128
To solve the equation for a whole number, multiply both sides by the inverse of the fraction:
Reduce the equation to its simplest terms:
Q11 Answer = 37.5%
Plug in the numbers and solve for x:
Recall from the converter table that 3 ⁄ 8 = 37.5%.
Q12 Answer = 2.5%
Plug in the numbers to the formula:
Reduce the fraction to its lowest terms:
You know from the converter table that 1 ⁄ 20 = 5% and therefore 1 ⁄ 40 = 2.5%.
Q13 Answer = 6%
12 ÷ 200 = 0.06 = 6%
Q14 Answer = 24
First find 12.5% of the whole number (512):
Next find 37.5% of the new whole number:
Q15 Answer = 0.75%.
Percentage
×
Whole
=
Part
x %
×
320
=
2.4
Divide both sides by 320:
Percentage increase and decrease practice questions
Q1 13.5
Q2 33 1 ⁄ 3 %
Q3 23%
Q4 Year 3
Q5 £28,222.50
Q6 P = Q ⁄ 6
Q7 £85
Q8 £867
Q9 £61.86
Q10 49 litres
Percentage increase and decrease practice questions explanations
Q1 Answer = 13.5
First find 25% of
Q4 Max bought a house for £40,000. The value of his house increased over 6 years, so that by the end of the term it had seen a 40% increase on the original price. The same amount invested in a bank account yields 9% per annum simple interest over the same period. Which is the more profitable investment option?
Q5 If Paul invests £385 in National Savings Certificates, which currently yield annual compound interest of 2.8%, what will his certificates be worth at the end of 3 years (to the nearest penny?) Answers to Chapter 4
Percentage converter drill
Convert to percentage
Convert to decimal
Convert to fraction
Q1
0.25 = 25%
1 ⁄ 100 = 0.01
87.5% = 7 ⁄ 8
Q2
0.75 = 75%
1 ⁄ 25 = 0.04
0.5% = 1 ⁄ 200
Q3
0.1 = 10%
5 ⁄ 6 = 0.83 r
0.125% = 1 ⁄ 800
Q4
0.0047 = 0.47%
3 ⁄ 8 = 0.375
60% = 3 ⁄ 5
Q5
0.063 = 6.3%
3 ⁄ 9 = 0.3 r
250% = 2½
Q6
½ = 50%
0.1% = 0.001
0.625 = 5 ⁄ 8
Q7
7 ⁄ 8 = 87.5%
0.043% = 0.00043
2.75 = 2¾
Q8
5 ⁄ 3 = 166.6% r
8.3% = 0.083
0.006 = 6 ⁄ 1000
Q9
1 ⁄ 200 = ½%
430% = 4.3
0.125 = 1 ⁄ 8
Q10
4 ⁄ 400 = 1%
5 ⁄ 3 % = 0.16 r
6.002 = 6 1 ⁄ 500
Percentage formulae practice questions: explanations
In the following explanations, only one method is given. You may prefer to use another method to check your answers.
Q1 Answer = 18
Convert 50% to its decimal equivalent and multiply the whole number by the decimal:
50% = 0.5
0.5 × 36 = 18
Q2 Answer = 120
Convert 75% to its decimal equivalent and multiply the whole number by the decimal:
75% = 0.75
0.75 × 160 = 120
Q3 Answer = 39
To find 10% of 130, move the decimal place one place to the left of the whole number:
10% = 13
30% = 3 × 10% = 39
Q4 Answer = 5.76
24% is approximately equal to ¼ (25%) so your answer will be approximately ¼ × 24 = 6. Express the percentage as a fraction over 100 and multiply by the whole number (24):
Q5 Answer = 2
Both percentages are recognizable as common fractions, so express both as fractions and multiply by the whole number (80). (You can also find 20% of 12.5% (= 2.5%) and multiply by the whole number, 80.)
Q6 Answer = 60
25% = ¼, so you know that 15 = ¼ x (where x = the whole number). To solve the equation for a whole number, multiply both sides by the inverse of the fraction.
Q7 Answer = 200
To solve the equation for a whole number, multiply both sides by the inverse of the fraction:
Reduce the equation to its simplest terms:
Q8 Answer = 32
Convert the percentage to its decimal equivalent: 32% = 0.32. Multiply by the whole number (60) to find the percentage to find the part:
Percentage
×
Whole
=
Part
0.32
×
60
=
19.2
So you know that 19.2 = 60% of a new whole number x . Solve for x by setting up the percentage as a fraction over 100 and cross-multiply:
60x = 19.2 × 100 = 1920. Divide both sides by 60:
Q9 Answer = 150
To solve the equation for a whole number, multiply both sides by the inverse of the fraction:
Q10 Answer = 128
To solve the equation for a whole number, multiply both sides by the inverse of the fraction:
Reduce the equation to its simplest terms:
Q11 Answer = 37.5%
Plug in the numbers and solve for x:
Recall from the converter table that 3 ⁄ 8 = 37.5%.
Q12 Answer = 2.5%
Plug in the numbers to the formula:
Reduce the fraction to its lowest terms:
You know from the converter table that 1 ⁄ 20 = 5% and therefore 1 ⁄ 40 = 2.5%.
Q13 Answer = 6%
12 ÷ 200 = 0.06 = 6%
Q14 Answer = 24
First find 12.5% of the whole number (512):
Next find 37.5% of the new whole number:
Q15 Answer = 0.75%.
Percentage
×
Whole
=
Part
x %
×
320
=
2.4
Divide both sides by 320:
Percentage increase and decrease practice questions
Q1 13.5
Q2 33 1 ⁄ 3 %
Q3 23%
Q4 Year 3
Q5 £28,222.50
Q6 P = Q ⁄ 6
Q7 £85
Q8 £867
Q9 £61.86
Q10 49 litres
Percentage increase and decrease practice questions explanations
Q1 Answer = 13.5
First find 25% of
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