fractions, decimals and percentages · 5/8/2020 · section 2: convert fractions to decimals there...

$: Fractions, Decimals and Percentages · 5/8/2020 · Section 2: Convert fractions to decimals There are three kinds of fractions to convert 1. The denominator is a power of 10 (eg$
Fractions, Decimals and Percentages Write your name in this box __________________________________________________________________________ How to use this workbook Where to write your answers You will see on each question there are one or more grey boxes. These are for you to type the answer in. Eg: 6 + 4 = In the box you write your answer. The layout keeps changing One problem is that the grey boxes are a different size when empty, to when full. This means that questions take up a different amount of space when empty. You will see this means the pages will change as you fill them in. Unfortunately there is nothing I can do about that. Why are you asking me questions about my answers? You will also see that on some questions you are asked to write what has changed from one question to the next. Most questions are in a specific order and only one thing has changed from one question to the next. By looking at what changes from one question to the next, you can see what affect that change has on the answer. That should help you to understand what is going on. You are also asked to say what the affect this had on the answer. Did it double it? Did it increase it by 3, reduce it by a power of x? Once again, by looking at what impact the change had on the answer, it will help you understand what is going on in the question.

Section 1: Converting a decimal to a fraction Example 1: Tenths 0.4

T U ● 110

1100

1

1000

0 ● 4 0.4 = #

$%. We can simplify #

$% by dividing both numerator and denominator by 2 = &

'

Example 2: Hundredths 0.04

T U ● 110

1100

1

1000

0 ● 0 4 0.04 = #

$%%. We can simplify #

$%% by dividing both numerator and denominator by 4 = $

&'

Example 3: Thousandths (single digit) 0.004

T U ● 110

1100

1

1000

0 ● 0 0 4 0.004 = #

$%%%. We can simplify #

$%%% by dividing both numerator and denominator by 4 = $

&'%

Example 4: Hundredths (2 digits) 0.24

T U ● 110

1100

1

1000

0 ● 2 4 0.24 = &#

$%%. We can simplify &#

$%% by dividing both numerator and denominator by 4 = (

&'

Example 5: Thousandths (2 digits) 0.024

T U ● 110

1100

1

1000

0 ● 0 2 4 0.024 = &#

$%%%. We can simplify &#

$%%% by dividing both numerator and denominator by 4 = (

&'%

Example 6: Thousandths (3 digits) 0.424

T U ● 110

1100

1

1000

0 ● 4 2 4 0.424 = #&#

$%%%. We can simplify #&#

$%%% by dividing both numerator and denominator by 8 = ')

$&'.

Worksheet 1: Express the following decimal as fractions in their simplest form Q1 0.6

T U ● 110

1100

1

1000

0 ● 6

0.6 = ($%=

'

Q2 0.06

T U ● 110

1100

1

1000

0 ● 0 6 0.06 = (

$%%= )

What changed between Q1 and Q2? How did this affect the answer? Q3 0.66

T U ● 110

1100

1

1000

0 ● 6 6

0.66 = (($%%

=

What has changed between Q2 and Q3? How did this affect the answer?

Q4 0.65 T U ● 1

10

1100

1

1000

0 ● 6 5

0.65 = ('

=

What has changed between Q3 and Q4? How did this affect the answer? Q5 0.56 T U ● 1

10

1100

1

1000

0 ● 5 6

0.56 =

=


10

1100

1

1000

0 ●

0.55 =

=


Q7 0.006 T U ● 1

10

1100

1

1000

0 ●

0.006 =

=

Q8 0.055

T U ● 110

1100

1

1000

0 ●

0.055 =

=

What has changed between Q8 and Q7? How did this affect the answer? Q9 0.065

T U ● 110

1100

1

1000

0 ●

0.065 =

=


Q10 0.605 T U ● 1

10

1100

1

1000

0 ●

0.605 =

=


10

1100

1

1000

6 ● 5

6.5 = ('$%=


10

1100

1

1000

6 ● 0 5

6.05 = $%%

=


Q14 6.005 T U ● 1

10

1100

1

1000

6 ● 0 0 5

6.005 =

=


T U ● 110

1100

1

1000

●

5.06 =

=


T U ● 110

1100

1

1000

●

5.006 =

=


Section 2: Convert fractions to decimals There are three kinds of fractions to convert 1. The denominator is a power of 10 (eg 10, 100, 1000). This is the easiest case. Using the place headings, simply write the value of the numerator in the appropriate column Example 1: 𝟕

𝟏𝟎: Denominator = 10

U ● 110

1100

1

1000

0 ● 7 = 0.7 Example 2 𝟕

𝟏𝟎𝟎: Denominator = 100

U ● 110

1100

1

1000

0 ● 0 7 = 0.07 2. The denominator is a multiple or factor of a power of 10. Either multiply or divide the denominator by an integer to make it a power of 10. Then multiply or divide the numerator by the same amount. Note: You must have an integer for a numerator. You cannot have a fraction with a non-integer numerator. Example 3 𝟖

𝟐𝟓: Denominator is a factor of 10, 100, 1000 𝟖

𝟐𝟓

25 × 4 = 100 So 8 × 4 = 32 825 =

32100

U ● 1

10

1100

1

1000

0 ● 3 2 = 0.32 Example 4 𝟖

𝟐𝟎𝟎: Denominator is a multiple of 10, 100, 1000

200 ÷ 2 = 100 So 8 ÷ 2 = 4 8200 =

4100

U ● 1

10

1100

1

1000

0 ● 0 4 = 0.04

3. The denominator is not a factor, or multiple, of a power of 10. In this case divide the numerator by the denominator Example 5 𝟖

𝟑𝟐: Denominator is not a factor of 10, 100, 1000

Where possible, simplify the fraction 832 =

416 =

28 =

14

______ 4 )1.00 : 4 into 1 doesn’t go 0 .2___ 4 )0. 0$ 0 : carry the 1. 4 into 10 goes 2, remainder 2 0 .25__ 4 )0. 0$ 0& : 4 into 20 is 5, so the answer is 0.25 Example 5 𝟖

𝟑𝟕 : Denominator is not a factor of 10, 100, 1000

The fraction cannot be simplified. Use a calculator. 8 ÷ 37 = 0.22 (2 dp)

Worksheet 2: Convert these fractions to decimals Q1. 𝟏

𝟓

Is 5 a factor or multiple of 10, 100, 1000? Yes 5 × 2 = 10 1 × 2 = 2 15 =

210

= 0. Q2. 𝟐

𝟓

Is 5 a factor or multiple of 10, 100, 1000? Yes 5 × 2 = 10 2 × 2 = 25 =

10

= 0. What has changed between Q1 and Q2? How did this affect the answer? Q3. 𝟑

𝟓

Is 5 a factor or multiple of 10, 100, 1000? Yes 5 × 2 = × 2 = 35 =

10

= 0. What has changed between Q2 and Q3? How did this affect the answer?

Q4. 𝟐𝟓𝟎

Is 50 a factor or multiple of 10, 100, 1000? Yes 50 × = 100 2 × = 250 =

100

= 0. What has changed between Q3 and Q4? How did this affect the answer? Q5. 𝟑𝟎

𝟓𝟎

Is 50 a factor or multiple of 10, 100, 1000? Yes 50 ÷ = 10 30 ÷ = 3050 =

10

= 0. What has changed between Q4 and Q5? How did this affect the answer? Q6. 𝟑

𝟓𝟎𝟎

Is 50 a factor or multiple of 10, 100, 1000? Yes 500 × = 1000 3 × = 3500 =

1000

= 0. What has changed between Q5 and Q6? How did this affect the answer?

Q7. 𝟏𝟔

Is 6 a factor or multiple of 10, 100, 1000? No 16 = 1 ÷ 6 =

= 0. (2 dp) What has changed between Q6 and Q7? How did this affect the answer? Q8. 𝟐

𝟔

Is 6 a factor or multiple of 10, 100, 1000? No 26 = 2 ÷ =

= 0. (2 sf) What has changed between Q7 and Q8? How did this affect the answer? Q9. 𝟐

𝟔𝟎

Is 60 a factor or multiple of 10, 100, 1000? No 260 = ÷ =

= 0. (2 sf) What has changed between Q8 and Q9? How did this affect the answer?

Q10. 𝟐𝟔𝟎𝟎

Is 600 a factor or multiple of 10, 100, 1000? Yes 600 ÷ 100 = 6 But 2 ÷ 6 is not an integer. So have to do it the division route. 2600 = ÷ =

= 0. (2 dp) What has changed between Q9 and Q10? How did this affect the answer? Q11. 𝟐𝟎

𝟔𝟎


= 0. (2 sf) What has changed between Q10 and Q11? How did this affect the answer? Q12. 𝟑

𝟔𝟎


= 0. (2 sf) What has changed between Q11 and Q12? How did this affect the answer?

Section 3: Converting a decimal to a percentage Remember, percent means out of 100. To convert a decimal to a percentage, we simply express it as a number out of 100. Example 1: Express 0.3 as a percentage

0.3 = 310 =

30100

0.3 = 30% Example 2: Express 0.03 as a percentage

0.03 = 3100


0.03 = 3

1000 = 0.3100

0.003 = 0.3% Example 4: Express 3 as a percentage

3 = 300100

3 = 300% Example 5: Express 30 as a percentage

30 = 3000100

30 = 3000% Example 6: Express 0.33 as a percentage

0.33 = 33100


0.033 = 331000 =

3.3100

0.033 = 3.3% Example 8: Express 3.033 as a percentage

3.033 = 303.3100

3.033 = 303.3%

Worksheet 3: Express the following decimals as percentages Q1. 0.48 48100 = %

Q2. 0.49 100 = %

Q3. 0.50

= %

Q4. 0.5

= %

Q5. 0.05

= %

What has changed between Q4 and Q5? How did this affect the answer? Q6. 0.005

= %


Q7. 0.085

= %


= %


= %


= %


Q11. 2.085

= %


= %


= %


Q14. 2.5

= %

What has changed between Q13 and Q14? How did this affect the answer? Q15. 2

= %


= %


Section 4: Converting fractions to percentages Remember, percent means out of 100. This is essentially the same skill as converting a fraction to a decimal. The only difference is that to express the value as a percentage, the denominator must be 100. Example 1: Express 𝟐

𝟏𝟎 as a percentage

210 =

20100

= 20% Example 2: Express 𝟐

𝟏𝟎𝟎 as a percentage

&$%% is already a fraction with a denominator of 100, so &

$%% = 2%

Example 3: Express 𝟐

𝟏𝟎𝟎𝟎 as a percentage

&$%%%

= %.&$%%

(to get the denominator = 100, divide by 10, so divide the numerator by 10) = 0.2% Example 4: Express 𝟐

𝟕 as a percentage

We cannot simply multiply or divide 7 by another value to equal 100. So first convert the fraction to a decimal, and then convert the decimal to a per centage 2 ÷ 7 = 0.29 (2 sf). 0.29 = &=

$%%. So 𝟐

𝟕 is 29% (2 sf)

Example 4: Express 𝟑

𝟕𝟏 as a percentage

We cannot simply multiply or divide 71 by another value to equal 100. So first convert the fraction to a decimal, and then convert the decimal to a per centage 3 ÷ 71 = 0.29 (2 dp). 0.042 = #.&

$%%. So 𝟑

𝟕𝟏 is 4.2% (2 sf)

Worksheet 4: Express the following fractions as a percentage Q1. 𝟕

𝟏𝟎

10 × 10 = 100 7 × 10 = 70 710 =

70100 = %

Q2. 𝟕

𝟓𝟎

50 × 2 = 100 7 × 2 = 750 =

100 = %

Q3. 𝟑𝟓

𝟓𝟎

50 × = 100 35 × = 3550 =

100 = %

What has changed between Q2 and Q3? How did this affect the answer? Q4. 𝟑𝟓

𝟓𝟎𝟎

500 ÷ 5 = 100 35 ÷ 5 = 35500 =

100 = %


Q5. 𝟑𝟓𝟎

𝟓𝟎𝟎

500 ÷ = 100 350 ÷ = 350500 =

100 = %

What has changed between Q4 and Q5? How did this affect the answer? Q6. 𝟏𝟕𝟓

𝟓𝟎𝟎

÷ = 100 175 ÷ = 175500 =

100 = %


Q7. 𝟑𝟏𝟎

× = 100 × = 310 =

100 = %

Q8. 𝟑

𝟓

× = 100 × = 35 =

100 = %

What has changed between Q7 and Q8? How did this affect the answer? Q9. 𝟑

𝟐𝟎

× = 100 × = 320 =

100 = %

What has changed between Q8 and Q9? How did this affect the answer? Q10. 𝟑𝟎

𝟐𝟎

× = 100 × = 3020 =

100 = %


Q11. 𝟑𝟎𝟒𝟎

40 × = 100 (or 100 ÷ 40 = ) 30 × = 3040 =

100 = %

What has changed between Q10 and Q11? How did this affect the answer? Q12. 𝟑𝟎

𝟖𝟎

× = 100 (or 100 ÷ 80 = ) × = 3080 =

100 = %

What has changed between Q11 and Q12? How did this affect the answer? Q13. 𝟔𝟎

𝟖𝟎

× = 100 (or 100 ÷ 80 = ) × = 6080 =

100 = %


Q14. 𝟔𝟎𝟖𝟎𝟎

÷ = 100 ÷ = 60800 =

100 = %

What has changed between Q14 and Q15? How did this affect the answer? Q15. 𝟔

𝟖𝟎𝟎

÷ = 100 ÷ = 6800 =

100 = %

What has changed between Q14 and Q15? How did this affect the answer? Q16. 𝟖𝟎𝟎

𝟔

× = 100 (or 100 ÷ 6 = ) × = 8006 =

100 = %


Section 5: Number as a percentage of another Very often, we have to express one number as a percentage of another. For example if you got 30 out of 40 marks in a test, what is that as percentage? This is, in fact, exactly the same skill as the previous exercise. The fraction )%

#% is just another

way of saying 30 out of 40, or 30 ÷ 40. These are all equivalent. Example 1: What is 15 out of 20 as a percentage? 15 out of 20 can be written as $'

&%

20 × 5 = 100 15 × 5 = 75 1520 =

75100 = 75%

Example 2: What is 20 out of 15 as a percentage? 20 out of 15 can be written as &%

$'

15 × 6.7 = 100 (or 100 ÷ 15 = 6.7) 20 × 6.7 = 133 2015 =

133100 = 133%

Worksheet 5: Write one number as a percentage of another Q1 Write 5 as a percentage of 20 20 × 5 = 100 5 × 5 = 75 520 =

25100 = %

Q2 Write 50 as a percentage of 200 200 ÷ 2 = 100 50 ÷ 2 = 25 50200 =

100 = %

Q3 Write 150 as a percentage of 200 200 ÷ 2 = 100 150 ÷ 2 = 150200 =

100 = %

Q4 Write 15 as a percentage of 20 20 × = 100 15 × = 1520 =

100 = %

Q5 Write 5 as a percentage of 40 40 × = 100 (or 100 ÷ 40 = ) 5 × = 540 =

100 = %

Q6 Write 50 as a percentage of 400 400 ÷ = 100 50 ÷ = 50400 =

100 = %

Q7 Write 150 as a percentage of 400 ÷ = 100 ÷ = 150400 =

100 = %

Q8 Write 15 as a percentage of 40 40 × = 100 (or 100 ÷ 40 = ) 15 × = 1540 =

100 = %

Q9 Write 150 as a percentage of 40 × = 100 (or 100 ÷ 40 = ) × = 15040 =

100 = %

Section 6: Finding 10% of a number If you remember, percent means “out of 100”. So 10% is $%

$%%= $

$%= 0.1. To find 10% of a

number we simply divide it by 10. Example 1: 10% of a multiple of 10 Find 10% of 60 60 ÷ 10 = 6 Example 2: 10% of a number not a multiple of 10 Find 10% of 55 55 ÷ 10 = 5.5 Example 3: 10% of an integer less than 10 Find 10% of 6 6 ÷ 10 = 0.6 Example 4: 10% of a decimal less than 10 Find 10% of 5.5 5.5 ÷ 10 = 0.55

Worksheet 6: Find 10% of the following Q1. Find 10% of 30 30 ÷ 10 = Q2. Find 10% of 40 40 ÷ = Q3. Find 10% of 120 ÷ = Q4. Calculate 10% of 120 ÷ = Q5. Calculate 10% of 74 ÷ = Q6. Calculate 10% of 98 ÷ = Q7. Calculate 10% of 178 ÷ = Q8. Calculate 10% of 356 ÷ = Q9. Work out 10% of 356 ÷ = Q10. Work out 10% of 286 ÷ = Q11. Work out 10% of 28 ÷ = Q12. 10% × 28 ÷ = Q13. 28 × 10% ÷ = Q14. 14 × 10% ÷ = Q15. 10% × 14 ÷ =

Q16. 10% × 897 ÷ = Q17. 897 × 10% ÷ = Q18. 897 × 0.1 ÷ =

Section 7: Percentage increase or decrease You are very often required to increase or decrease an amount by a given percentage. The easiest way is to work out what 10% of the amount is (divide by 10) and use that. Next year you will be taught another method. Example 1: Increase £14 by 10% 10% is the same as $

$% which is 0.1

10% of £14 = £14 × 0.1 = £1.40 To increase £14 by 10% add £1.40 £14.00 + £1.40 = £15.40 Example 2: Decrease £14 by 10% 10% is the same as $

$% which is 0.1

10% of £14 = £14 × 0.1 = £1.40 To decrease £14 by 10% subtract £1.40 £14.00 - £1.40 = £12.60 Example 3: Increase £14 by 8% 10% is the same as $

$% which is 0.1

10% of £14 = £14 × 0.1 = £1.40 If 10% = £1.40, then 1% = £0.14 So 8% = 8 × £0.14 = £1.12 To increase £14 by 8% add £1.12 £14.00 + £1.12 = £15.12 Example 4: Decrease £14 by 8% 10% is the same as $

$% which is 0.1

10% of £14 = £14 × 0.1 = £1.40 If 10% = £1.40, then 1% = £0.14 So 8% = 8 × £0.14 = £1.12 To decrease £14 by 8% subtract £1.12 £14.00 - £1.12 = £12.88 Example 5: Increase £14 by 28% 10% is the same as $

$% which is 0.1

10% of £14 = £14 × 0.1 = £1.40 If 10% = £1.40, then 20% = £2.80 If 10% = £1.40, then 1% = £0.14 So 8% = 8 × £0.14 = £1.12 28% = 20% + 8% 28% = £2.80 + £1.12 = £3.92 To increase £14 by 8% add £3.92 £14.00 + £3.92= £17.92

Worksheet 7: Percentage increase or decrease Q1. Increase 30 by 10% 10% of 30 = )%

$%= 3

30 + 3 = Q2. Increase 30 by 20% 10% of 30 = )%

$%= 3

20% = 2 × 10% 20% of 30 = 2 × 30 + = Q3. Increase 60 by 20% 10% of 60 = (%

$%=

20% = 2 × 10% 20% of 60 = 2 ×

60 + = Q4. Increase 60 by 10%

10% of 60 = $%=

60 + = What has changed between Q3 and Q4? How did this affect the answer? Q5. Increase 74 by 10%

10% of 74 = $%=

74 + = What has changed between Q4 and Q5? How did this affect the answer?

Q6. Increase 74 by 50%

10% of 74 = $%=

50% = 5 × 10% 50% of 74 = 5 × 74 + = What has changed between Q5 and Q6? How did this affect the answer? Q7. Increase 84 by 50%

10% of 84 =

=

50% = × 10% 50% of 84 = 5 × + = What has changed between Q6 and Q7? How did this affect the answer? Q8. Increase 84 by 10%

10% of 84 =

=

+ = What has changed between Q7 and Q8? How did this affect the answer?


10% of 84 =

=

5% = 0.5 × 10% 5% of 84 = × + = What has changed between Q8 and Q9? How did this affect the answer? Q10. Increase 44 by 5%

10% of 44 =

=

5% = × 10% 5% of 44 = × + = What has changed between Q9 and Q10? How did this affect the answer? Q11. Increase 44 by 20%

10% of 44 =

=

20% = × 10% 20% of 44 = × + = What has changed between Q10 and Q11? How did this affect the answer?


10% of 44 =

=

50% = × 10% 50% of 44 = × + = What has changed between Q11 and Q12? How did this affect the answer? Q13. Increase 44 by15%

10% of 44 =

=

5% = × 10% 5% of 44 = × 15% = 10% + 5% 15% of 44 = + + = What has changed between Q12 and Q13? How did this affect the answer? Q14. Increase 44 by 85%

10% of 44 =

=

80% = × 10% 80% of 44 = × 5% = × 10% 5% of 44 = × 85% = % + 5% 85% of 44 = + + = What has changed between Q13 and Q14? How did this affect the answer?

Section 8: Ordering fractions, decimals and percentages A very common task is to be given a list of numbers as decimals, percentages and fractions, and be asked to put them in order, either ascending (getting larger) or descending (getting smaller). Put these in descending order Example 1: All decimals 0.03 0.3 0.45 0.451 0.303 Step 1: Find the longest number (greatest number of digits) – 0.451, 0,.303 – 3 digits Step 2: Add zeros to the other numbers 0.030 0.300 0.450 0.451 0.303 Step 3: Ignore the decimal point, treat them as if they were integers 30 300 450 451 303 Step 4: Put these in order 451 450 303 300 030 Step 5: Re-write them in their original format 0.451, 0.45, 0.303, 0.3, 0.03 Example 2: All fractions

12132516

915

Step 1: Find the lowest common denominator (30) Step 2: Re-write all the fractions with a common denominator

1530

1030

1230

530

1830

Step3: Put them in order by numerator 530

1030

1230

1530

1830

Example 3: Mixture of fractions, decimals and percentages

0.61930 55%

1115 0.7

712

815

Step 1: Convert all to decimals (use 2dp) : 0.60, 0.63, 0.55, 0.73, 0.70, 0.58, 0.53 Step 2: Ignore the decimal point. Put these in order: 53, 55, 58, 60, 63, 70, 73 Step 3: Re-write them in their original format

815 55%

712 0.6

1930 0.7

1115

Worksheet 8: Put the following in ASCENDING order Q1 0.45, 0.55, 0.3, 0.18, 0.058 Step 1: 0.058 Step 2: 0.450, 0.550, 0.300, 0.180, 0.058 Step 3: 450, 550, 300, 180, 058 Step 4: 058, 180, 300, 450, 550 Step 5: , , , , Q2 0.451, 0.55, 0.3, 0.18, 0.058 Step 1: 0.058, 0.451 Step 2: 0.451, 0.550, 0.300, 0.180, 0.058 Step 3: 451, 550, 300, 180, 058 Step 4: , , 300, 451, 550 Step 5: , , , , Q3 0.451, 0.55, 0.3, 0.18, 0.558 Step 1: 0.558, 0.451 Step 2: 0.451, 0.550, 0.300, 0.180, 0.558 Step 3: 451, 550, 300, 180, 558 Step 4: , , , , Step 5: , , , , Q4 0.451, 0.859, 0.3, 0.18, 0.558 Step 1: 0.558, 0.451, 0.859 Step 2: 0.451, 0.859, 0.300, 0.180, 0.558 Step 3: , , , , Step 4: , , , , Step 5: , , , ,

Q5 0.451, 0.859, 0.3, 0.18, 0.0558 Step 1: 0.0558 Step 2: 0.4510, 0.8590, 0.3000, 0.1800, 0.0558 Step 3: , , , , Step 4: , , , , Step 5: , , , , Q6 0.45, 0.86, 30%, 0.18, 0.05 Step 1: 0.45, 0.86, 0.30, 0.18, 0.05 Step 2: 0.05, 0.18, 0.30, 0.45, 0.86 Step 3: , , , , Q7 𝟗𝟐𝟎

, 0.86, 30%, 0.18, 0.05 Step 1: , , , , Step 2: , , , , Step 3: , , , ,

Q8 𝟗𝟐𝟎

, 0.86, 30%, 𝟗𝟏𝟎

, 0.05 Step 1: , , , , Step 2: , , , , Step 3: , , , , Q9 𝟗𝟐𝟎

, 0.865, 30%, 𝟗𝟏𝟎

, 0.05 Step 1: , , , , Step 2: , , , , Step 3: , , , , Q10 𝟗𝟐𝟎

, 0.865, 30%, 𝟗𝟏𝟎

, 0.95 Step 1: , , , , Step 2: , , , , Step 3: , , , ,

Q11 𝟏𝟕𝟐𝟎

, 0.865, 30%, 𝟗𝟏𝟎

, 0.95 Step 1: , , , , Step 2: , , , , Step 3: , , , , Q12 𝟏𝟕𝟐𝟎

, 𝟏𝟕𝟑𝟐𝟎𝟎

, 30%, 𝟗𝟏𝟎

, 0.95 Step 1: , , , , Step 2: , , , , Step 3: , , , ,

fractions, decimals and percentages · 5/8/2020 · section 2: convert fractions to decimals there...

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