 # Solve Percentage and Decimal Problems

In this worksheet, students will be asked to solve worded problems using their knowledge of fractions, decimals and percentages. Key stage:  KS 2

Curriculum topic:   Number: Fractions, Decimals and Percentages

Curriculum subtopic:   Solve Percentage/Decimal Problems

Difficulty level:   ### QUESTION 1 of 10

In this activity, you will be asked to solve a range of questions using your knowledge of fractions, decimals and percentages.

Example 1:

Write the decimal number 0.456 in expanded form

Expanded form means to partition a number to see the place value of each digit clearly.

Because we are using a decimal number, we will write its expanded form using fractions.

0.456 = 4/10 + 5/100 + 6/1000

Example 2:

Francesca has completed 140 questions out of 200 in a huge quiz!

What is this as a decimal number?

Step 1:

Convert the numbers to a fraction: 140/200

Step 2:

Next, to convert a fraction into a decimal number, you need to divide the numerator by the denominator.

It's easiest to use a calculator or you can use the written method of long division.

140 ÷ 200 = 0.7

Francesca has completed 0.7 of her quiz.

Example 3:

Wayne has £85 from his savings.

He then spends 30% on a football ticket.

How much money does he have left?

Step 1: Find 1/5 of £85

85 ÷ 5 = £17

Wayne has spent £17 on a present for his Dad.

Step 2: Find 30% of £85

First find 10%

£85 ÷ 10 =£8.5

10% = £8.50

30% = £8.50 x 3

= £25.50

Step 3: Add both amounts together

£25.50 + £17 = £42.50

Step 4: Subtract the total spent from the original amount

£85 - £42.50 = £42.50

Wayne has £42.50 left.

Read the descriptions carefully and then match each one to the correct decimal number.

## Column B

This number has 7 tenths
3.2
This number has 3 hundredths
2.29
This number has 1 decimal place
2.71
This number has the same amount of ones and tenths
1.03

Look carefully, the decimal numbers have been written in their expanded form.

## Column B

0.29
2 tenths + 9 hundredths
0.19
3 tenths + 9 hundredths
0.09
1 tenth + 9 hundredths
0.39
0 tenths + 9 hundredths

Ashleigh says,

"0.602 in its expanded form is 6⁄10 + 2⁄100"

Is she correct?

Yes

No

I have placed some numbers in ascending order but one number is missing.

3.24

3 25⁄100

3.?

3.27

Can you write the missing fraction in the box below?

Yes

No

A group of children sat a quiz together.

Each child scored a result out of 100. The results are below.

 Name Score Percentage Bill 52 52% Kira 82 82% Mya 61 61%

How many more marks did each pupil need to score 100%?

Yes

No

Some children did a quiz together.

Each child scored a result out of 100. The results are below:

 Name Score Percentage Bill 52 52% Kira 82 82% Mya 61 61%

Another child, Charlotte, scored 1⁄4 of Bill's score.

What is Charlotte's result as a percentage?

Yes

No

Freya has read 240 pages of her book.

Her book has 400 pages.

How much of her book has she read as a decimal number?

0.6

0.65

0.4

0.06

Freddie has read 240 pages of his book.

His book has 600 pages.

How much of his book has he read as a decimal number?

George has a total of £45 that he has saved.

He decides to spend 3/5 of it on a game.

He also spends 10% of it on his lunch.

After his shopping trip, how much money does George have left?

Dylan has a total of £65 that he has saved.

He decides to spend 2/5 of it on toys.

He also spends 20% of it on magazines.

After his shopping trip, how much money does Dylan have left?

• Question 1

Read the descriptions carefully and then match each one to the correct decimal number.

## Column B

This number has 7 tenths
2.71
This number has 3 hundredths
1.03
This number has 1 decimal place
3.2
This number has the same amount o...
2.29
EDDIE SAYS
This question required that you use your place value knowledge of decimal numbers carefully. This number has 7 tenths = 2.71 This number has 3 hundredths = 1.03 This number has 1 decimal place = 3.2 This number has the same number of ones and tenths = 2.29
• Question 2

Look carefully, the decimal numbers have been written in their expanded form.

## Column B

0.29
2 tenths + 9 hundredths
0.19
1 tenth + 9 hundredths
0.09
0 tenths + 9 hundredths
0.39
3 tenths + 9 hundredths
EDDIE SAYS
How was your place value knowledge for this question? 0.29 = 2 tenths and 9 hundredths 0.19 = 1 tenth and 9 hundredths 0.09 = 0 tenths and 9 hundredths 0.39 = 3 tenths and 9 hundredths
• Question 3

Ashleigh says,

"0.602 in its expanded form is 6⁄10 + 2⁄100"

Is she correct?

No
EDDIE SAYS
Ashleigh is incorrect. 0.602 = 6/10 + 0/1000 + 2/1000 Remember, the use of the 0 digit shows that there's no value in that place of the number.
• Question 4

I have placed some numbers in ascending order but one number is missing.

3.24

3 25⁄100

3.?

3.27

Can you write the missing fraction in the box below?

EDDIE SAYS
Ascending order means to order the numbers from smallest to largest. The missing number is 3 26/100. Did you spot that?
• Question 5

A group of children sat a quiz together.

Each child scored a result out of 100. The results are below.

 Name Score Percentage Bill 52 52% Kira 82 82% Mya 61 61%

How many more marks did each pupil need to score 100%?

EDDIE SAYS
To achieve 100%, a pupil would need to score 100 marks. Therefore, Bill would need another 48 marks, Kira would need another 18 marks and Mya would need another 61 marks.
• Question 6

Some children did a quiz together.

Each child scored a result out of 100. The results are below:

 Name Score Percentage Bill 52 52% Kira 82 82% Mya 61 61%

Another child, Charlotte, scored 1⁄4 of Bill's score.

What is Charlotte's result as a percentage?

EDDIE SAYS
Charlotte scored 1/4 of Bill's score. To find 1/4 of 52, we divide by 4. 52 ÷ 4 = 13.
• Question 7

Freya has read 240 pages of her book.

Her book has 400 pages.

How much of her book has she read as a decimal number?

0.6
EDDIE SAYS
This is a 2 step problem to solve. Step 1. Find the fraction of the number of pages read: 240/400 Step 2. Convert the fraction into a decimal number by dividing the numerator by the denominator. 240 ÷ 400 = 0.6 Freya has read 0.6 of her book.
• Question 8

Freddie has read 240 pages of his book.

His book has 600 pages.

How much of his book has he read as a decimal number?

0.4
EDDIE SAYS
Again, this is a 2 step problem to solve. Step 1. Find the fraction of the number of pages read; 240/600 Step 2. Then, convert the fraction into a decimal number by dividing the numerator by the denominator. 240 ÷ 600 = 0.4 Freddie has read 0.4 of his book.
• Question 9

George has a total of £45 that he has saved.

He decides to spend 3/5 of it on a game.

He also spends 10% of it on his lunch.

After his shopping trip, how much money does George have left?

EDDIE SAYS
There were a few steps we had to take to solve this tricky one! Step 1: Work out how much George spent on the game. Find 1⁄5 of £45. £45 ÷ 5 = 9 1/5 = 9 3/5 = 9 x 3 = 27 George spent £27 on a game. Step 2: Work out how much George spent on lunch. £45 ÷ 10 = £4.50 10% = £4.50 George spent £4.50 on lunch. Step 3: Add the total spent together: £27 + £4.50 = £31.50 Step 4: Subtract the amount spent from the original total. £45 - £31.50 = £13.50 George has £13.50 left.
• Question 10

Dylan has a total of £65 that he has saved.

He decides to spend 2/5 of it on toys.

He also spends 20% of it on magazines.

After his shopping trip, how much money does Dylan have left?

EDDIE SAYS
Again, there were a few steps we had to take to solve this tricky one! Step 1: Work out how much Dylan spent on toys. Find 1/5 of £65. £65 ÷ 5 = 13 1/5 = 13 2/5 = 13 x 2 = 26 Dylan spent £26 on toys. Step 2: Work out how much Dylan spent on magazines. £65 ÷ 10 = £6.50 10% = £6.50 20% = £13 Dylan spent £13.00 on magazines. Step 3: Add the total spent together: £26 + £13 =£39 Step 4: Subtract the amount spent from the original total. £65 - £39 = £26 Dylan has £26 left. Great work, you've completed another activity! How about attempting another one so you feel super confident?
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