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).
