Thursday, October 23, 2025

Decimals chapter concept of 11 plus exam GL assessment examination

 Decimals chapter concept of 11 plus exam GL assessment examination 

#### **1. Understanding Place Value**

The key to decimals is understanding that each digit to the right of the decimal point represents a fraction with a denominator of 10, 100, 1000, etc.


*   **Tenths (0.1):** The first digit after the decimal. `1/10`

*   **Hundredths (0.01):** The second digit after the decimal. `1/100`

*   **Thousandths (0.001):** The third digit after the decimal. `1/1000`


**Example:** In the number 45.367

*   `4` is 4 tens (40)

*   `5` is 5 units (5)

*   `3` is 3 tenths (`3/10` or 0.3)

*   `6` is 6 hundredths (`6/100` or 0.06)

*   `7` is 7 thousandths (`7/1000` or 0.007)


So, 45.367 = 40 + 5 + 0.3 + 0.06 + 0.007


#### **2. Adding & Subtracting Decimals**

**Golden Rule:** **Line up the decimal points!** You can add zeroes to the right to help keep everything aligned.


**Example (Addition):** 12.45 + 3.8

```

  12.45

+  3.80

--------

  16.25

```


**Example (Subtraction):** 7.5 - 2.34

```

   7.50

-  2.34

--------

   5.16

```


#### **3. Multiplying Decimals**

1.  Multiply the numbers as if they were whole numbers (ignore the decimal points).

2.  Count the **total number of decimal places** in both of the original numbers.

3.  Place the decimal point in your answer so it has the same total number of decimal places.


**Example:** 1.3 × 0.25

1.  13 × 25 = 325

2.  1.3 has 1 decimal place, 0.25 has 2. Total = 3 decimal places.

3.  Answer: 0.325


#### **4. Dividing Decimals**

The easiest way is to make the divisor a whole number.


**Example:** 6.84 ÷ 0.4

1.  Multiply both numbers by 10 (to make the divisor, 0.4, a whole number): 68.4 ÷ 4

2.  Now do the division: `4 goes into 6 one time (1), remainder 2. Bring down 8, making 28. 4 goes into 28 seven times (7). Bring down 4. 4 goes into 4 one time (1).`

3.  The answer is 17.1


#### **5. Converting between Decimals, Fractions & Percentages**

*   **Decimal to Fraction:** Write the decimal as the numerator and use 1 followed by zeros (10, 100, 1000) as the denominator based on the place value. Then simplify.

    *   `0.7 = 7/10`

    *   `0.35 = 35/100 = 7/20`

    *   `0.125 = 125/1000 = 1/8`


*   **Fraction to Decimal:** Divide the numerator by the denominator.

    *   `3/4 = 3 ÷ 4 = 0.75`

    *   `1/8 = 1 ÷ 8 = 0.125`


*   **Decimal to Percentage:** Multiply by 100 and add the % sign.

    *   `0.89 = 0.89 × 100 = 89%`

    *   `0.04 = 4%`


*   **Percentage to Decimal:** Divide by 100 (or move the decimal point two places to the left).

    *   `75% = 75 ÷ 100 = 0.75`

    *   `5% = 0.05`


---


### **Part 2: 10 Practice Questions (Mixed Sub-topics)**


1.  What is the value of the 7 in the number 12.374?

2.  Calculate 5.67 + 12.3

3.  Calculate 8.4 - 2.57

4.  Calculate 3.5 × 0.6

5.  Calculate 9.1 ÷ 0.05

6.  Convert 0.65 to a fraction in its simplest form.

7.  Convert 3/8 to a decimal.

8.  Convert 0.08 to a percentage.

9.  Sarah buys a book for £5.75 and a pen for £1.20. How much change does she get from £10?

10. A piece of ribbon is 2.5m long. How many 0.4m lengths can be cut from it?


---


### **Part 3: 50+ Additional Practice Questions**


#### **Place Value & Ordering**

11. Write 15.068 in words.

12. What is the digit in the hundredths place in 203.951?

13. Arrange in ascending order: 0.6, 0.59, 0.608, 0.07

14. Which is larger: 4.099 or 4.1?

15. Round 12.478 to the nearest tenth.

16. Round 5.635 to 2 decimal places.

17. What number is half-way between 2.7 and 2.8?

18. Write down the smallest number you can make using the digits 4, 0, 9, and 1 and a decimal point.


#### **Addition & Subtraction**

19. 14.8 + 6.35

20. 22 + 3.07 + 0.9

21. 10.04 - 3.8

22. 5 - 2.76

23. 12.3 - 4.88

24. Alan is 1.45m tall. His sister is 1.3m tall. What is the difference in their heights?

25. The temperature was 5.8°C. It rose by 3.5°C. What is the new temperature?


#### **Multiplication**

26. 6.2 × 4

27. 1.5 × 0.7

28. 0.8 × 0.08

29. 12.5 × 1.1

30. 0.04 × 0.3

31. A pencil costs £0.35. How much do 6 pencils cost?

32. One litre of petrol costs £1.48. How much does 5 litres cost?

33. A square has a side length of 3.2cm. What is its perimeter?


#### **Division**

34. 15.6 ÷ 3

35. 9.1 ÷ 7

36. 4.5 ÷ 0.5

37. 6 ÷ 0.4

38. 0.81 ÷ 0.9

39. 2.4 ÷ 0.03

40. £10.50 is shared equally between 3 people. How much does each get?

41. A 2.5kg bag of flour is divided into 5 equal pots. How much flour is in each pot?


#### **Conversions & Mixed Applications**

42. Convert 3/5 to a decimal.

43. Convert 0.92 to a fraction in its simplest form.

44. Convert 7/20 to a percentage.

45. Convert 5% to a decimal.

46. Convert 0.375 to a fraction.

47. What is 25% of 3.6?

48. Find 1/4 of 8.4

49. A shirt costs £24. In a sale, there is a 15% discount. How much is the discount?

50. In a class of 30, 40% are girls. How many boys are there?

51. A recipe needs 0.3kg of flour. If you are making 1.5 times the recipe, how much flour do you need?

52. A car uses 0.12 litres of fuel for every kilometre. How much fuel is needed for a 45km journey?


---


### **Part 4: 10 Previous Year GL Assessment Style Questions with Solutions**

**1. Calculate 14.07 - 8.4**

   A) 6.67

   B) 5.67

   C) 6.47

   D) 5.87


**2. What is 3.25 × 0.6?**

   A) 1.95

   B) 19.5

   C) 0.195

   D) 195


**3. Convert the fraction 4/25 to a decimal.**

   A) 0.16

   B) 0.4

   C) 0.04

   D) 0.625


**4. A box of 12 yoghurts costs £4.80. What is the cost of one yoghurt?**

   A) £0.36

   B) £0.40

   C) £0.48

   D) £4.00


**5. Which of these numbers is the largest?**

   A) 5.099

   B) 5.9

   C) 5.91

   D) 5.1


**6. What is 4.56 ÷ 8?**

   A) 5.7

   B) 0.57

   C) 0.75

   D) 57


**7. In a sports day race, Ben's time was 14.8 seconds, Amy's was 15.02 seconds, and Tom's was 14.75 seconds. Who won the race?**

   A) Ben

   B) Amy

   C) Tom

   D) Cannot tell


**8. What is 15% written as a decimal?**

   A) 0.015

   B) 0.15

   C) 1.5

   D) 15.0


**9. A bag of sweets weighs 0.35kg. What is the total weight of 6 such bags?**

   A) 2.1kg

   B) 1.8kg

   C) 21kg

   D) 3.5kg


**10. Which calculation does NOT give the same answer as 0.4 × 12?**

    A) 4 × 1.2

    B) 40 × 0.12

    C) 0.04 × 120

    D) 0.2 × 24


---


### **Answer Key & Solutions**


#### **Part 2: 10 Practice Questions**

1.  **7 hundredths** or `7/100`

2.  **17.97** `(5.67 + 12.30)`

3.  **5.83** `(8.40 - 2.57)`

4.  **2.1** `(35 × 6 = 210, 2 total decimal places = 2.10 -> 2.1)`

5.  **182** `(9.1 ÷ 0.05 = 910 ÷ 5 = 182)`

6.  **13/20** `(0.65 = 65/100 = 13/20)`

7.  **0.375** `(3 ÷ 8 = 0.375)`

8.  **8%** `(0.08 × 100 = 8%)`

9.  **£3.05** `(Total = £5.75 + £1.20 = £6.95. Change = £10.00 - £6.95 = £3.05)`

10. **6 lengths** `(2.5 ÷ 0.4 = 6.25, so 6 full lengths can be cut)`


#### **Part 4: GL Style Questions**

1.  **B) 5.67**

    *Solution:*

    ```

      14.07

    -  8.40

    --------

       5.67

    ```


2.  **A) 1.95**

    *Solution: 325 × 6 = 1950. Total decimal places = 2 + 1 = 3. So, 1.950 -> 1.95*


3.  **A) 0.16**

    *Solution: 4 ÷ 25 = 0.16*


4.  **B) £0.40**

    *Solution: £4.80 ÷ 12 = £0.40*


5.  **C) 5.91**

    *Solution: Compare digit by digit from the left: Units: all 5. Tenths: 0 (A), 9 (B), 9 (C), 1 (D). Between B and C, compare hundredths: B is 5.90, C is 5.91. So C is largest.*


6.  **B) 0.57**

    *Solution: 4.56 ÷ 8 = 0.57*


7.  **C) Tom**

    *Solution: The smallest time wins. 14.75 (Tom) < 14.8 (Ben) < 15.02 (Amy).*


8.  **B) 0.15**

    *Solution: 15% = 15/100 = 0.15*


9.  **A) 2.1kg**

    *Solution: 0.35kg × 6 = 2.10kg*


10. **C) 0.04 × 120**

    *Solution: 0.4 × 12 = 4.8. Check each option: A) 4 × 1.2 = 4.8, B) 40 × 0.12 = 4.8, C) 0.04 × 120 = 4.8, D) 0.2 × 24 = 4.8. They ALL give 4.8. There is an error in the question. If this were a real exam, you would flag it. For practice, the intended answer is likely C, as the others are direct multiples of the original, while C changes the decimal place value more significantly. A better "NOT" question would be `0.4 x 12 = 4.8`, and `0.2 x 24 = 4.8`, `4 x 1.2 = 4.8`, `0.8 x 6 = 4.8`, `0.04 x 120 = 4.8`. They all give the same answer. The question is flawed.*

    ***Correction for a valid question:** Let's change option D to `0.2 × 2.4`. Now, `0.2 × 2.4 = 0.48`, which is NOT 4.8. So the correct answer would then be **D**.*


Good luck with your preparation! Consistent practice is the key to mastering decimals.

### **Section A: 10 More Questions on Place Value & Ordering**


1.  What is the value of the digit 8 in the number 24.083?

2.  Write the number seven and twenty-four thousandths in digits.

3.  Which number is exactly halfway between 4.7 and 4.8?

4.  Arrange in ascending order: 0.099, 0.9, 0.89, 0.0999.

5.  Round 6.4781 to the nearest hundredth.

6.  Which is larger: 5.060 or 5.006?

7.  Write 0.375 as a fraction in its simplest form.

8.  What is the next number in the sequence: 6.5, 6.45, 6.4, 6.35, ...?

9.  How many hundredths are there in 3.5?

10. Which number has the greatest value in the thousandths place: 8.235, 8.325, 8.532, 8.253?


---


### **Section B: 10 More Questions on Addition & Subtraction**


11. 15.8 + 4.67 + 0.3 =

12. 20.01 - 3.8 =

13. 7 - 2.345 =

14. 12.4 + 5.08 + 0.9 =

15. 8.5 - 4.67 =

16. 10.1 - 0.99 =

17. 6.7 + 12.35 + 1.002 =

18. 25.4 - 12.75 =

19. 4.2 + 3.05 + 0.8 =

20. 9.06 - 5.7 =


---


### **Section C: 10 More Questions on Multiplying & Dividing**


21. 4.5 × 0.8 =

22. 0.6 × 0.07 =

23. 12.5 × 1.2 =

24. 3.24 ÷ 6 =

25. 4.8 ÷ 0.4 =

26. 0.81 ÷ 0.9 =

27. 7.5 × 0.4 =

28. 6.3 ÷ 0.07 =

29. 0.125 × 8 =

30. 5.6 ÷ 0.08 =


---


### **Section D: 10 More Questions on Conversions & Mixed Applications**


31. Convert 0.88 to a fraction in its simplest form.

32. Convert 7/8 to a decimal.

33. Convert 0.03 to a percentage.

34. What is 30% of 8.5?

35. Express 19/20 as a decimal.

36. Write 0.075 as a fraction in its simplest form.

37. What is 15% of 4.0?

38. Convert 1.25 to a mixed number.

39. What is 1/5 of 7.5?

40. Convert 0.004 to a percentage.


---


### **Section E: 10 More Questions on Mixed Problem Solving**


41. A piece of string is 3.6m long. If I cut off 1.45m, how much is left?

42. One apple costs £0.28. How much do 6 apples cost?

43. A box of 24 pencils costs £7.20. What is the cost per pencil?

44. A car travels 84.5 miles on 6.5 gallons of petrol. How many miles per gallon does it do?

45. The perimeter of a square is 15.6cm. What is the length of one side?

46. A bag of sugar weighs 2.4kg. If I use 0.85kg in a recipe, how much is left?

47. A book has 240 pages. If I have read 0.65 of the book, how many pages have I read?

48. A bottle holds 2.25 litres of water. How many 0.25 litre glasses can be filled from it?

49. A rectangle has a length of 5.2cm and a width of 3.5cm. What is its area?

50. A packet of crisps weighs 0.35kg. How much would 8 packets weigh?


---


### **Section F: 15 More Questions on Mixed Word Problems & Multi-step**


51. Tom buys a magazine for £2.85 and a drink for £1.40. He pays with a £5 note. How much change does he get?

52. A piece of rope is 8m long. I cut off 3 pieces each of 1.25m. How much rope is left?

53. A box of 36 chocolates costs £12.60. What is the cost per chocolate?

54. A car uses 0.065 litres of fuel per kilometre. How much fuel is used for a 60km journey?

55. A shop reduces a £60 coat by 20%. What is the new price?

56. A recipe for 6 people requires 0.75kg of flour. How much flour is needed for 10 people?

57. A tank holds 120 litres. It is being filled at a rate of 7.5 litres per minute. How long will it take to fill?

58. A packet of biscuits contains 15 biscuits. Each biscuit weighs 0.032kg. What is the total weight of the packet?

59. A train travels at a constant speed of 90km/h. How far does it travel in 1 hour and 15 minutes?

60. A rectangle has a perimeter of 24.8cm. If its length is 7.5cm, what is its width?

61. A bag of potatoes weighs 5.6kg. I remove 4 potatoes with a combined weight of 1.25kg. What is the new weight of the bag?

62. A bottle of juice contains 1.75 litres. I pour out 0.4 litres. How much juice is left?

63. A book costs £8.50. How many books can I buy with £50?

64. A bus has 52 seats. 0.75 of the seats are occupied. How many seats are empty?

65. A piece of wood is 4.8m long. I need to cut it into 0.3m lengths. How many full pieces can I get?



### **Section G: Fictional "Previous Year Paper" (50 Questions)**

66.  Calculate 13.4 + 7.65

67.  What is 8.2 - 3.47?

68.  Multiply 4.5 by 0.6

69.  Divide 10.8 by 0.9

70.  Round 7.269 to one decimal place.

71.  Which is larger: 3.099 or 3.1?

72.  Write 0.625 as a fraction in its simplest form.

73.  Convert the fraction 3/5 to a decimal.

74.  What is 40% of 6.5?

75.  A box of 10 pencils costs £3.50. What is the cost of one pencil?

76.  A car travels 72km in 1.2 hours. What is its average speed in km/h?

77.  A rectangle measures 4.3cm by 6.2cm. What is its area?

78.  A bag of flour weighs 1.5kg. I use 450g. How much flour is left in kilograms?

79.  What is the perimeter of a square with a side length of 5.7cm?

80.  A train ticket costs £14.75. I buy 2 tickets. How much change do I get from £40?

81.  A bottle contains 2 litres of water. I drink 350ml. How much water is left in litres?

82.  A cake recipe requires 0.45kg of butter. I want to make 1.5 times the recipe. How much butter do I need?

83.  A packet of sweets costs £0.95. I buy 5 packets. How much change from a £10 note?

84.  A bus has 48 seats. 5/8 of the seats are occupied. How many seats are empty?

85.  A piece of ribbon is 5m long. I cut off 3 pieces, each 0.75m long. How much ribbon is left?

86.  A book has 180 pages. I have read 2/3 of the book. How many pages have I read?

87.  A box of 12 eggs costs £2.76. What is the cost per egg?

88.  A car uses 0.08 litres of fuel for every kilometre. How much fuel is needed for a 250km journey?

89.  A shirt costs £28.00. In a sale, it is reduced by 15%. What is the sale price?

90.  A triangle has a base of 8cm and a height of 5.5cm. What is its area?

91.  A bag of oranges weighs 3.2kg. I take out 3 oranges weighing 0.45kg in total. What is the new weight?

92.  A jug contains 1.8 litres of milk. I pour 0.55 litres into a bowl. How much milk remains in the jug?

93.  A pen costs £1.45. How many pens can I buy with £20?

94.  A cycling race is 30km long. A cyclist has completed 0.7 of the race. How far has she cycled?

95.  A plank of wood is 6m long. How many 0.4m lengths can be cut from it?

96.  What is the value of the 4 in 19.046?

97.  Write the number twelve and nine hundredths as a decimal.

98.  Put these in order from smallest to largest: 2.02, 2.2, 2.002, 2.202

99.  Calculate 0.1 × 0.1

100. Calculate 1.44 ÷ 1.2

101. Express 17/25 as a percentage.

102. Find 3/8 of 9.6

103. A TV programme starts at 7:35 pm and ends at 8:20 pm. How long does it last in hours?

104. A bag of 20 marbles weighs 0.5kg. What is the weight of one marble in grams?

105. A recipe needs 0.025kg of salt. How much salt is needed for 8 batches of the recipe?

106. 5.67 × 100 =

107. 34.8 ÷ 1000 =

108. 0.07 × 0.3 =

109. 4.5 + ? = 10

110. ? - 3.75 = 2.8

111. 6.3 ÷ ? = 9

112. ? × 0.4 = 1

113. A digital clock shows 14:25. What time is this in 12-hour format?

114. In a class of 30 children, 18 are girls. What fraction of the class are boys?

115. A bathtub has 120 litres of water. 45 litres are removed. What percentage of the water remains?


---


### **Section H: 50 More Questions from Previous Year GL Assessment Styles**


116. Calculate: 23.4 - 7.89

117. What is 6.7 × 0.5?

118. Divide 8.4 by 0.07

119. Round 12.3456 to three decimal places.

120. Which number is the smallest: 0.101, 0.011, 0.11, 0.0111?

121. Convert 22/1000 to a decimal.

122. What is 12.5% of £40?

123. A bag of 5 lemons costs £1.10. What is the cost of one lemon?

124. A cube has a side of length 2.5cm. What is its volume?

125. The sum of two numbers is 15.6. One number is 8.9. What is the other number?

126. Write 4.5% as a decimal.

127. A pizza is cut into 8 equal slices. I eat 3 slices. What decimal of the pizza did I eat?

128. A coat costs £85. Its price is increased by 20%. What is the new price?

129. 0.3 + 0.03 + 0.003 =

130. 1 - 0.007 =

131. 2.5 × 40 =

132. 4.8 ÷ 12 =

133. 7.07 ÷ 10 =

134. 0.9 × 1000 =

135. Find the difference between 10 and 6.54.

136. What is the product of 2.5 and 3.2?

137. A triangle has an area of 24cm² and a base of 8cm. What is its height?

138. A pen is 13.5cm long. A pencil is 8.7cm long. How much longer is the pen?

139. A bottle holds 1.5 litres. A glass holds 0.2 litres. How many full glasses can be poured from the bottle?

140. The temperature was -2°C. It rises by 5°C. What is the new temperature?

141. Which is heavier: 0.25kg or 350g?

142. A field is 40m long and 35.5m wide. What is the perimeter of the field?

143. 3/10 of a number is 9.3. What is the number?

144. A bus leaves at 10:15 am and arrives at 1:05 pm. How long is the journey?

145. A bag has 3 red, 5 blue, and 2 green balls. What is the probability of picking a blue ball?

146. Simplify the ratio 15:20.

147. A map scale is 1:25000. What is the actual distance if the map distance is 4cm?

148. A jacket was £60. It is in a sale with 1/3 off. What is the sale price?

149. 1.5 hours = ____ minutes.

150. 6500g = ____ kg.

151. 2.3km = ____ m.

152. 45mm = ____ cm.

153. 3/4 litre = ____ ml.

154. Find the mean of 4, 7, 5, 9, 5.

155. What is the range of the numbers in Q154?

156. (2.3 + 1.7) × 4 =

157. 5.6 - (2.1 + 0.9) =

158. 10 × (0.5 + 0.05) =

159. A number is multiplied by 10 and then 3 is added. The answer is 43. What was the original number?

160. The coordinates of a point are (3, 5). What are the coordinates after a reflection in the x-axis?

161. How many lines of symmetry does a square have?

162. What is the size of one interior angle of an equilateral triangle?

163. A roll of tape is 15m long. I use 7 pieces, each 0.85m long. How much tape is left?

164. A recipe for 4 people uses 2 eggs. How many eggs are needed for 10 people?

165. A number, when divided by 0.5, gives an answer of 16. What is the number?


---


### **Answer Key & Solutions**


#### **Section A: Place Value & Ordering**

1.  8 hundredths (0.08)

2.  7.024

3.  4.75

4.  0.099, 0.0999, 0.89, 0.9

5.  6.48

6.  5.060

7.  3/8

8.  6.3

9.  350 (3.5 = 350/100)

10. 8.532 (thousandths digit is 2)


#### **Section B: Addition & Subtraction**

11. 20.77

12. 16.21

13. 4.655

14. 18.38

15. 3.83

16. 9.11

17. 20.052

18. 12.65

19. 8.05

20. 3.36


#### **Section C: Multiplying & Dividing**

21. 3.6

22. 0.042

23. 15

24. 0.54

25. 12

26. 0.9

27. 3.0

28. 90

29. 1.000

30. 70


#### **Section D: Conversions & Mixed Applications**

31. 22/25

32. 0.875

33. 3%

34. 2.55

35. 0.95

36. 3/40

37. 0.6

38. 1 1/4

39. 1.5

40. 0.4%


*(Solutions for Sections E-H are provided below in a condensed format due to space)*


#### **Section E: Mixed Problem Solving (Condensed Answers)**

41. 2.15m | 42. £1.68 | 43. £0.30 | 44. 13 mpg | 45. 3.9cm | 46. 1.55kg | 47. 156 pages | 48. 9 glasses | 49. 18.2 cm² | 50. 2.8kg


#### **Section F: Mixed Word Problems (Condensed Answers)**

51. £0.75 | 52. 4.25m | 53. £0.35 | 54. 3.9 litres | 55. £48 | 56. 1.25kg | 57. 16 minutes | 58. 0.48kg | 59. 112.5km | 60. 4.9cm | 61. 4.35kg | 62. 1.35 litres | 63. 5 books | 64. 13 seats | 65. 16 pieces


#### **Section G: Fictional "Previous Year Paper" (Condensed Answers)**

66. 21.05 | 67. 4.73 | 68. 2.7 | 69. 12 | 70. 7.3 | 71. 3.1 | 72. 5/8 | 73. 0.6 | 74. 2.6 | 75. £0.35 | 76. 60 km/h | 77. 26.66 cm² | 78. 1.05kg | 79. 22.8cm | 80. £10.50 | 81. 1.65 litres | 82. 0.675kg | 83. £5.25 | 84. 18 seats | 85. 2.75m | 86. 120 pages | 87. £0.23 | 88. 20 litres | 89. £23.80 | 90. 22 cm² | 91. 2.75kg | 92. 1.25 litres | 93. 13 pens | 94. 21km | 95. 15 lengths | 96. 4 hundredths | 97. 12.09 | 98. 2.002, 2.02, 2.2, 2.202 | 99. 0.01 | 100. 1.2 | 101. 68% | 102. 3.6 | 103. 0.75 hours (or 45 mins) | 104. 25g | 105. 0.2kg | 106. 567 | 107. 0.0348 | 108. 0.021 | 109. 4.5 | 110. 6.55 | 111. 0.7 | 112. 2.5 | 113. 2:25 pm | 114. 2/5 | 115. 62.5%


#### **Section H: 50 More GL Styles (Condensed Answers)**

116. 15.51 | 117. 3.35 | 118. 120 | 119. 12.346 | 120. 0.011 | 121. 0.022 | 122. £5 | 123. £0.22 | 124. 15.625 cm³ | 125. 6.7 | 126. 0.045 | 127. 0.375 | 128. £102 | 129. 0.333 | 130. 0.993 | 131. 100 | 132. 0.4 | 133. 0.707 | 134. 900 | 135. 3.46 | 136. 8.0 | 137. 6cm | 138. 4.8cm | 139. 7 glasses | 140. 3°C | 141. 350g | 142. 151m | 143. 31 | 144. 2 hours 50 mins | 145. 1/2 | 146. 3:4 | 147. 1km | 148. £40 | 149. 90 | 150. 6.5 | 151. 2300 | 152. 4.5 | 153. 750 | 154. 6 | 155. 5 | 156. 16 | 157. 2.6 | 158. 5.5 | 159. 4 | 160. (3, -5) | 161. 4 | 162. 60° | 163. 9.05m | 164. 5 eggs | 165. 8

 Good luck

### Solutions with Explanations


#### **Money Problems**


**Q1. A chocolate bar costs £1.25. How much do 4 bars cost?**  

**Solution:** Multiply the cost per bar by the number of bars.  

£1.25 × 4 = £5.00  

**Answer:** £5.00


**Q2. A book costs £7.80. If you pay with a £10 note, how much change do you get?**  

**Solution:** Subtract the cost from the amount paid.  

£10.00 - £7.80 = £2.20  

**Answer:** £2.20


**Q3. A toy costs £12.45. How much do 3 toys cost?**  

**Solution:** Multiply the cost per toy by the number of toys.  

£12.45 × 3 = £37.35  

**Answer:** £37.35


**Q4. A pencil costs 35p. Write the cost in pounds.**  

**Solution:** Convert pence to pounds by dividing by 100.  

35p = £0.35  

**Answer:** £0.35


**Q5. A cinema ticket costs £6.50. How much do 5 tickets cost?**  

**Solution:** Multiply the cost per ticket by the number of tickets.  

£6.50 × 5 = £32.50  

**Answer:** £32.50


**Q6. A sandwich costs £2.75 and a drink costs £1.20. How much is the total?**  

**Solution:** Add the two costs together.  

£2.75 + £1.20 = £3.95  

**Answer:** £3.95


**Q7. A train ticket costs £14.60. You buy 2 tickets. How much do you spend?**  

**Solution:** Multiply the cost per ticket by the number of tickets.  

£14.60 × 2 = £29.20  

**Answer:** £29.20


**Q8. A book is reduced from £9.99 to £7.50. How much is the saving?**  

**Solution:** Subtract the sale price from the original price.  

£9.99 - £7.50 = £2.49  

**Answer:** £2.49


**Q9. A bag costs £3.45. How much for 10 bags?**  

**Solution:** Multiply the cost per bag by the number of bags.  

£3.45 × 10 = £34.50  

**Answer:** £34.50


**Q10. A child has £20 and spends £13.85. How much money is left?**  

**Solution:** Subtract the amount spent from the starting amount.  

£20.00 - £13.85 = £6.15  

**Answer:** £6.15


**Q5 (Word problem). A packet of biscuits costs £2.45. How much do 4 packets cost?**  

**Solution:** Multiply the cost per packet by the number of packets.  

£2.45 × 4 = £9.80  

**Answer:** £9.80


---


#### **Length Problems**


**Q1. A ribbon is 2.35 m long. Another is 1.8 m. What is their total length?**  

**Solution:** Add the two lengths.  

2.35 + 1.80 = 4.15 m  

**Answer:** 4.15 m


**Q2. A rope is 12.4 m long. If 3.75 m is cut off, how much remains?**  

**Solution:** Subtract the length cut off from the original length.  

12.40 - 3.75 = 8.65 m  

**Answer:** 8.65 m


**Q3. A stick is 1.25 m long. Write its length in centimetres.**  

**Solution:** Multiply by 100 (since 1 m = 100 cm).  

1.25 × 100 = 125 cm  

**Answer:** 125 cm


**Q4. A pencil is 18.6 cm long. Another is 24.3 cm long. How much longer is the second pencil?**  

**Solution:** Subtract the shorter length from the longer length.  

24.3 - 18.6 = 5.7 cm  

**Answer:** 5.7 cm


**Q5. A road is 3.45 km long. Another is 2.6 km. What is their total length?**  

**Solution:** Add the two lengths.  

3.45 + 2.60 = 6.05 km  

**Answer:** 6.05 km


**Q6. A plank is 2.75 m long. How many 0.5 m pieces can be cut from it?**  

**Solution:** Divide the total length by the length of each piece.  

2.75 ÷ 0.5 = 5.5 → 5 full pieces (since we can't have half a piece)  

**Answer:** 5 pieces


**Q7. A piece of wood is 1.38 m. Write this in millimetres.**  

**Solution:** Multiply by 1000 (since 1 m = 1000 mm).  

1.38 × 1000 = 1380 mm  

**Answer:** 1380 mm


**Q8. A child runs 1.25 km on Monday and 1.75 km on Tuesday. How far in total?**  

**Solution:** Add the two distances.  

1.25 + 1.75 = 3.00 km  

**Answer:** 3 km


**Q9. A garden path is 4.05 m long. A fence is 3.85 m. How much longer is the path?**  

**Solution:** Subtract the shorter length from the longer length.  

4.05 - 3.85 = 0.20 m  

**Answer:** 0.20 m


**Q10. A string is 0.95 m long. Add another 0.65 m. What is the total length?**  

**Solution:** Add the two lengths.  

0.95 + 0.65 = 1.60 m  

**Answer:** 1.60 m


---


#### **Weight Problems**


**Q1. A bag of sugar weighs 1.25 kg. How much do 4 bags weigh?**  

**Solution:** Multiply the weight per bag by the number of bags.  

1.25 × 4 = 5.00 kg  

**Answer:** 5 kg


**Q2. A melon weighs 2.8 kg. A pineapple weighs 1.35 kg. What is their total mass?**  

**Solution:** Add the two weights.  

2.80 + 1.35 = 4.15 kg  

**Answer:** 4.15 kg


**Q3. A loaf of bread weighs 750 g. Write this in kilograms.**  

**Solution:** Divide by 1000 (since 1 kg = 1000 g).  

750 ÷ 1000 = 0.75 kg  

**Answer:** 0.75 kg


**Q4. A packet weighs 3.45 kg. Another weighs 2.6 kg. How much heavier is the first?**  

**Solution:** Subtract the smaller weight from the larger weight.  

3.45 - 2.60 = 0.85 kg  

**Answer:** 0.85 kg


**Q5. A sack of potatoes is 12.5 kg. How much is left if 4.75 kg are used?**  

**Solution:** Subtract the amount used from the original weight.  

12.50 - 4.75 = 7.75 kg  

**Answer:** 7.75 kg


**Q6. A dog weighs 23.4 kg. A cat weighs 4.85 kg. What is the difference in weight?**  

**Solution:** Subtract the smaller weight from the larger weight.  

23.40 - 4.85 = 18.55 kg  

**Answer:** 18.55 kg


**Q7. A parcel weighs 1.205 kg. Write this in grams.**  

**Solution:** Multiply by 1000 (since 1 kg = 1000 g).  

1.205 × 1000 = 1205 g  

**Answer:** 1205 g


**Q8. A box weighs 2.35 kg. How many boxes weigh 7.05 kg?**  

**Solution:** Divide the total weight by the weight per box.  

7.05 ÷ 2.35 = 3  

**Answer:** 3 boxes


**Q9. An apple weighs 185 g. Write this in kilograms.**  

**Solution:** Divide by 1000 (since 1 kg = 1000 g).  

185 ÷ 1000 = 0.185 kg  

**Answer:** 0.185 kg


**Q10. A bag of flour weighs 1.65 kg. A bag of rice weighs 3.8 kg. What is their total weight?**  

**Solution:** Add the two weights.  

1.65 + 3.80 = 5.45 kg  

**Answer:** 5.45 kg


---


### **Key Tips for Decimal Problems**

1. **Line up decimal points** when adding or subtracting.

2. **Check units** - convert all measurements to the same unit before calculating.

3. **Money calculations** - always include two decimal places for pounds.

4. **Division** - if dividing by a decimal, multiply both numbers to make the divisor a whole number.

5. **Real-life context** - consider whether the answer needs to be a whole number (e.g., pieces of wood).

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