Maths Answers
Summer Year 6 Week 1
Place value and rounding (page 1)
Y6 Sum Week 1 Day 1
1. 748,925
What is 7 worth in this number? 700,000
What is 8 worth in this number?8,000
2. Write digits to make these statements true.
5,> 2,
For example
25,432 > 24,321
5,< 5,
For example
51,555 56,222
3. Write four numbers between 300,000 and 400,000 in ascending order
For example
312,767
333,876
356,876
398,999
4. Write digits to make this statement true.
3,< 34, < 3,
For example
31,876 < 34,987 < 37,654
5. Circle the number that is closest to 500,000.
457,974 510,356 501,427 499,328
6. Circle the number that is closest to 800,000.
802,401 820,001 789,999 793,457
7. Write which numbers these arrows are pointing to.
Approximately 10,500 14,000 Approximately 17,500
8.Round 456,328 to:
a) the nearest multiple of 100,000:500,000
b) the nearest multiple of 10,000: 460,000
c) the nearest multiple of 1000: 456,000
d) the nearest multiple of 100: 456,300
e) the nearest multiple of 10: 456,330
Place value and rounding (page 2)
Y6 Sum Week 1 Day 1 E
1. 78,925
What is 7 worth in this number? 70,000
What is 8 worth in this number?8,000
2. Write digits to make these statements true.
5,,
For example
5,432 > 4,321
5,,
For example
53,555 55,222
3.Write three numbers between 30,000 and 40,000 in ascending order.
For example
31,546
35,487
39,765
4.Write digits to make this statement true.
,< 34, ,
For example
31,976 < 34,587 < 36,654
5.Circle the number that is closest to 50,000.
45,974 51,356 50,427 49,328
6. Circle the number that is closest to 800,000.
802,400 820,000 789,999 799,000
7. Write which numbers these arrows are pointing to.
10,500 14,000 17,500
8. Round 59,328 to:
a) the nearest multiple of 10,000: 60,000
b) the nearest multiple of 1000: 59,000
c) the nearest multiple of 100: 59,300
d) the nearest multiple of 10: 59,330
Multiplying and dividing by 10, 100 and 1000 (page 5)
Y6 Sum Week 1 Day 2 MH
1.
a) 456 ÷ 10 = 45.6 b) 456 ÷ 100 = 4.56 c) 456 ÷ 1000 = 0.456
2.
a) 456 × 10 = 4,560 b) 456 × 100 = 45,600 c) 456 × 1000 = 456,000
3.
3.25 x 10 = 32.5
4.
78,340 ÷ 10 = 7,834
5.
8.47 × 100 = 847
6.
2456 ÷ 100 = 24.56
7.
0.287 × 1000 = 287
8.
564,000 ÷ 1000 = 564
9.
45 x 10,000 = 450,000
10.
7.68 ÷ 10 = 0.768
11.
5672 ÷ 1000= 5.672
12.
346.213 × 1000 = 346,213
13.Convert 45 centimetres to:
a) 0.45 metres b) 450millimetres
14.Convert 1250 metres to kilometres
1.250 kilometres
15.Convert 0.327 kilograms to grams.
327 grams
16.Convert 2450 millilitres to litres.
2.45 litres
Negative numbers (page 6)
Y6 Sum Week 1 Day 3 EM
1. At noon, the temperature was 7°C. By midnight the temperature had fallen by 10°C. What was the temperature at midnight?
-3°C.
2.On Monday the temperature in London was 4°C. In Aberdeen the temperature was -4°C. What was the difference in temperature?
8°C.
3.On Tuesday, the temperature in Birmingham was 5°C. It was 8 degrees colder in Glasgow. What was the temperature in Glasgow?
-3°C.
4.
a) Which season has the lowest minimum temperature? Winter.
b) Which season has the lowest minimum temperature, autumn or spring? Spring.
c) What is the difference between the coldest and mildest temperatures in winter? 26°C.
d) What is the difference between the coldest and mildest temperatures in autumn? 16°C.
e) Which season has the biggest difference between maximum and minimum temperatures? Winter
f) What is the difference between the coldest temperature of the year and the warmest temperature of the year? 42°C.
5. What is the difference between -5 and 7?
12.
6. What is the difference between -10 and 6?
16.
7. What is the difference between -4 and 4?
8.
8.Write a pair of numbers, one negative and one positive with a difference of 5.
For example
-3 and2
9.Write a pair of numbers, one negative and one positive with a difference of 10.
For example
-5 and 5
10.Write a pair of numbers, one negative and one positive with a difference of 7.
For example
-4 and 3
Order of operations (page 7)
Y6 Sum Week 1 Day 4
1. 5 + 2 × 3 = 11
2. 7 × 2 – 4 = 10
3. 7 - 10 ÷ 5 = 5
4. 6 ÷ 2 + 4 = 7
5. 4 × 5 + 2 × 6 = 32
6. 12 ÷ 3 + 3 × 4 = 16
7. 10 + 8 ÷ 2 = 14
8. (9 + 7) ÷ 4 = 4
9. 6 × (9 - 4) = 30
10. 10 × (10 – 5) × 2 = 100
11. 10 × (10 - 5) ÷ 2 = 25
12. 7 + 2 × 5 + 5 = 22
13. 6 + 4 + 15 ÷ 3 = 15
14. 4² + 3 × 2 = 22
Addition and subtraction practice (Page 8)
Y6 Sum Week 1 Day 4
1. 534 + 279 = 813
2. 837 + 425 = 1,262
3. 985 - 426 = 559
4. 837 - 253 = 584
5. Write the missing digits to make the addition correct.
181
+ 619
800
6. Write the missing digits to make the addition correct.
181
+ 819
1000
7. 4357 + 1068 = 5,425
8. 8428 + 4623 = 13,051
9. 9347 - 4253 = 5,094
10. 8823 - 5378 = 3,445
11. Write the missing digits to make the addition correct.
5268
+ 2823
8091
12. Write the missing digits to make the addition correct.
6246
+3754
10000
13. Write an addition of two 4-digit numbers such that the total rounds to 8000 when rounded to the nearest multiple of 1000.
For example
3546 + 4537 = 8,083
14. Write a subtraction of two 4-digit numbers such that the answer rounds to 4000 when rounded to the nearest multiple of 1000.
For example
8,176 - 4,199 = 3,977
Addition and subtraction practice – continued. (page 8)
Y6 Sum Week 1 Day 4
15. 54,275 + 23,482 = 77, 757
16. 63,867 + 52,104 = 115,971
17. 85,372 - 41,825 = 43,547
18. 56,231 - 38,820 = 17,411
19. Write an addition of two 5-digit numbers such that the total rounds to 100,000 when rounded to the nearest multiple of 10,000.
For example
57,351 + 45,876 = 103,227
20. Write a subtraction of two 5-digit numbers such that the answer rounds to 50,000 when rounded to the nearest multiple of 10,000.
For example
97,354 - 45,673 = 51,681
Multi-step problems (page 9)
Y6 Sum Week 1 Day 5 MH
1. Jamie buys a bunch of flowers costing £12.49, a mug costing £4.75, two cards costing £2.79 each for his mum’s birthday as a present from him and his younger sister. How much did he have left over from £30?
£12.49 + £4.75 +£2.79 + £2.79 = £22.82
£30.00 - £22.82 =£7.18
2. Two children bake cakes for a charity cake sale. They spend £15.67 on ingredients and sell 108 cakes at 50p each. How much profit do they have to give to their chosen charity?
108 x £0.50 - £15.67 = £38.33
3. Samir bought four pens. She spent between £4 and £5 and bought both sorts of pens. How many of each type of pen might she have bought?
2 of each.
£0.79 x 2 + £1.49 x 2 = £4.56
4. Ruth ordered four identical books from an internet site for her grandchildren. The total cost including £4.75 postage was £30.75. What was the price of each book?
£6.50
£30.75 - £4.75 ÷ 4 = £6.50
5. A new internet site has 16,782 hits in week 1, 28,271 hits in week 2, and 32,143 hits in week 3. How many hits do they need to reach their monthly target of 100,000 hits?
16,782 + 28,271 + 32,143 = 77,196
100,000 - 77,196 = 22,804
6. A giant bamboo grows at a rate of 30cm a day. It begins the month at 1.45 metres tall. Will it reach 10 metres by the end of the month? (There are 31 days this month.)
Yes.
1.45 + 0.30 x 31 = 10.75
Multi-step problems (page 10)
Y6 Sum Week 1 Day 5 E
1. Jamie buys a bunch of flowers costing £12.50, a mug costing £4.75, and a card costing £2.79 for his mum’s birthday. How much did he have left over from £30?
£12.50 + £4.75 + £2.79 = £20.04
£30.00 - £20.04 = £9.96
2. Two children bake cakes for a charity cake sale. They spend £15.65 on ingredients and sell 100 cakes at 50p each. How much profit do they have to give to their chosen charity?
100 x £0.50 - £15.65 = £34.35
3. Samir bought four pens. She spent between £4 and £5 and bought both sorts of pens. How many of each type of pen might she have bought?
2 of each.
0.75 x 2 + £1.50 x 2 = £4.50
4. Ruth ordered four identical books from an internet site for her grandchildren. The total cost including £4.50 postage was £22.50. What was the price of each book?
£22.50 - £4.50 ÷ 4 = £4.50
5. A new internet site has 56,782 hits so far this month. How many hits do they need to reach their monthly target of 100,000 hits?
100,000 -56,782 = 43,218
6. A giant bamboo grows at a rate of 30cm a day. It begins the week at 1.45 metres tall. How tall will it be at the end of the week.
1.45m + 0.30 x 7 = 3.55metres
Week 2
Multiples, factors, multiplication and division (page 1)
Y6 Sum Week 2 Day 1
1. Write ALL the factors of 24.
1, 2, 3, 4, 6, 8, 12, 24.
2. If a number has 10 as a factor, what other three other factors must it have?
1, 2, 5.
3. If a number has 6 as a factor, what other three factors must it have?
1, 2, 3.
4. Write two common multiples of 4 and 5.
20, 40.
5. Write three common multiples of 2, 3 and 5.
30, 60, 90.
6.
2 x 6 x 5 = 60
7.
15 x 3 x 2 = 90
8.
4 x 5 x 6= 120
9.
7 x 10x 5 = 350
10.
720 x 4 = 2,880
11.
6x 80 = 480
12.
450 ÷ 90 = 5
13.
7 x 500 = 3500
14.
8 x 23 = 184
Multiples, factors, multiplication and division (page 1 - continued)
Y6 Sum Week 2 Day 1
15.
5 x 348 = 1,740
16.
25 x 36 = 900
17.
186 ÷ 5 = 37.2
18.
284 ÷ 20 = 14.2
Multiplication practice (page 3)
Y6 Sum Week 2 Day 2 MH
1.
6 × 378 = 2,268
2.
453 × 7 = 3,171
3.
3 × 7237 = 21,711
4.
3284 × 4 = 13,136
5. There are 678 people in the cinema. They each paid £7 for their ticket. How much did they pay altogether?
678 x £7 = £4746
6. 2364 people go to watch a hockey match. They each pay £8 for their ticket. How much did they pay altogether?
2364 x £8 = £18,912
7. Work out the perimeter of a regular hexagon where each side measures 23.4 centimetres. Write your answer in metres.
6 x 23.4 cm = 140.4 centimetres
140.4 centimetres = 1.404 metres
8. Find the total cost of seven hot chocolates costing £2.79 each.
7 x £2.79 = £19.53
9.
13 × 364 = 4,732
10.
724 × 16 = 11,584
11.
22 × 472 = 10,384
12.
783 × 23 = 18,009
13. Find the area of a poster measuring 123cm by 31cm.
123cm x 31cm = 3,813 cm2
14.
15 × 4312 = 64,680
15.
3752 × 16 = 60,032
Multiplication practice (page 3 - continued)
Y6 Sum Week 2 Day 2 MH
16.
23 × 2138 = 49,174
17.
8732 × 25 = 218,300
18. How many hours are in two years?
365 days x 2 = 730 days
One day = 24 hours
730 x 24 = 17,520 hours
Multiplication practice (page 4)
Y6 Sum Week 2 Day 2 E
1.
6 × 378 = 2,268
2.
453 × 7 = 3,171
3.
5 × 845 = 4,225
4.
967 × 8 = 7,736
5.
3 × 7237 = 21,711
6.
3284 × 4 = 13,136
7. There are 678 people in the cinema. They each paid £7 for their ticket. How much did they pay altogether?
678 x £7 = £4746
8. 2364 people go to watch a hockey match. They each pay £8 for their ticket. How much did they pay altogether?
2364 x £8 = £18,912
9.
13 × 364 = 4,732
10.
22 × 472 = 10,384
11.
783 × 23 = 18,009
12. Find the area of a poster measuring 123cm by 31cm.
123cm x 31cm = 3,813 cm2
Long Division (page 5)
Y6 Sum Week 2 Day 4 MH
1. Divide these numbers by 13: 339, 315, 453. Write the answers with remainders.
339 ÷ 13 = 26 remainder 1
315 ÷ 13 = 24 remainder 3
453 ÷ 13 = 34 remainder 11
2. Divide these numbers by 16: 568, 388, 444. Write your answers as decimals.
568 ÷ 16 = 35.5
388 ÷ 16 = 24.25
444 ÷ 16 = 27.75
3. Write a division which has half the answer to 756 ÷ 18.
756 ÷ 18 = 42
42 ÷ 2 = 21
4. Divide these numbers by 25: 970, 3550, 2890. Write the remainders as fractions.
970 ÷ 25 = 38 4⁄5
3550 ÷ 25 = 142
2890 ÷ 25 = 115 3⁄5
5. How many bananas costing 24p each could you buy with £6.50?
£6.50 ÷ £0.24 = 27(remainder 2p)
6. How many 18cm pieces of wire can be cut from a roll of 5 metres?
5 metres = 500 cm
500 ÷ 18 = 27 (remainder 14 cm)
Multiplication arithmagon (page 6)
Y6 Sum Week 2 Day 5
Solving number puzzles (page7)
Y6 Sum Week 2 Day 5
1. Vikesh has chosen two numbers. He divides the total by 2 and gets the answer 18. One of the numbers he chose was 15. What was the other number?
15 + 21÷ 2 = 18
21.
2. Katya chooses two numbers. They have a product of 36 and a difference of 5. What numbers did she choose?
4 x 9 = 36
4 and 9
3. Lauren thinks of three consecutive numbers. They have a product of 120. What are they? × × = 120
4 x 5 x 6 = 120
4, 5 and 6
4. Jordan thinks of two consecutive numbers. He halves the product. He gets an answer of 21. What were his numbers?
6 x 7÷ 2 = 21
6 and 7
5. Seth thinks of two even single-digit numbers. He doubles the product. He gets an answer of 48. What numbers did he choose?
4 x 6 x 2 = 48
4 and 6
6. Work out the missing numbers in these multiplication arithmagons.
a)
Solving number puzzles (page7 Continued)
Y6 Sum Week 2 Day 5
b)
c)
Solving number puzzles (page 8)
Y6 Sum Week 2 Day 5
7. Work out the missing numbers in these addition grids.
a)
+ / 27 / 35 / 4820 / 47 / 55 / 68
41 / 68 / 76 / 89
19 / 46 / 54 / 67
b)
+ / 35 / 17 / 5168 / 103 / 85 / 119
33 / 68 / 50 / 84
47 / 82 / 64 / 98
Week 3
Multiplying and dividing decimals by whole numbers(page 1)
Y6 Sum Week 3 Day 1
1.
8 × 0.7 = 5.6
2.
0.6 × 9 = 5.4
3.
4 × 0.8 = 3.2
4.
0.6 × 5 = 3.0
5.
7 × 0.4 = 2.8
6.
0.8 × 3 = 2.4
7.
8 × 0.04 = 0.32
8.
0.03 × 3 = 0.09
9.
7 × 0.04 = 0.28
10.
0.08 × 4 = 0.32
11.
0.48 ÷ 6 = 0.08
12.
0.81 ÷ 9 = 0.09
13.
0.45 ÷ 5 = 0.09
14.
7 × 0.5 = 3.5
Multiplying and dividing decimals by whole numbers(page 1 continued)
Y6 Sum Week 3 Day 1
15.
7.2 ÷ 6 = 1.2
16.
3 × 1.5 = 4.5
17.
5.4 × 3 = 16.2
18.
7 × 12.4 = 86.8
19.
11.3 × 6 = 67.8
20.
4 × 2.35 = 9.4
Finding fractions and percentages (page 2)
Y6 Sum Week 3 Day 3 MH
1. Find 10% of:
£25 = £2.50
340m = 34.0m
46kg = 4.6kg
75cm = 7.5cm
2. Find 15% of:
300 = 45
240 = 36
160 = 24
248 = 37.2
3. Find 25% of:
580km = 145km
£26 = £6.50
2.8 litres = 0.7 litres
14kg = 3.5kg
4. Find the new prices in the summer sales.
10% off £120 = £108
50% off £248 = £124
20% off £100 = £80
30% off £140 = £98
5. What is £7.50 as percentage of £10?
75%
6. What is £4 as a percentage of £5?
80%
7. What is 250g as a percentage of 1kg?
25%
8.
A shop has offers on two sizes of packets of biscuits. Which is the best value?
Digestive biscuits are the best value
Rich tea biscuits: 20% off £1 = 80p for 500 g
Digestive biscuits 400g + 25% extra = 75p for 500g
Adding and subtracting fractions (page 4)
Y6 Sum Week 3 Day 4 MH
1.
3⁄5 + 3⁄10 = 9⁄10
2.
¾ + ⅛ = 7⁄8
3.
⅔ + ⅙ = 5⁄6
4.
⅓ + ⅚ = 11⁄6
5.
⅘ + 7⁄10= 3⁄2(11⁄2)
6.
⅔ + ¾ = 17⁄12(15⁄12)
7.
⅓ + ¼ = 7⁄12
8.
½ + ⅙ = ⅔
9.
½ + ⅚= 4⁄3 (11⁄3)
10.
1½ + 2⅜ =31⁄8 (37⁄8)
11.
⅞ - ¼ = 5⁄8
12.
⅘ -3⁄10= ½
13.
2 ¾ - 1⅛ = 13⁄8 (15⁄8)
Adding and subtracting fractions (page 4 continued)
Y6 Sum Week 3 Day 4 MH
14.
13⁄7 - 5⁄7 = 5⁄7
15.
⅔ - ¼ = 5⁄12
16.
⅚ - ½ = ⅓
17.
1⅔ - ⅚= ⅚
18.
Write as many pairs of fractions with a total of 1 as you can. The denominators in each pair must be different!
For example:
½ + 2⁄4 = 1
⅔ +2⁄6 = 1
6⁄12 + 3⁄6 = 1
Multiplying and dividing fractions (page 6)
Y6 Sum Week 3 Day 5
1.
½ × ¼ = ⅛
2.
⅓ × ½ = ⅙
3.
½ × ⅕= 1⁄10
4.
½ × ⅔ = ⅓
5.
⅓ × ¾ = ¼
6.
⅔ × ¾ = ½
7.
⅗ × ½ = 3⁄10
8. There is ⅔ of a cheesecake left. Four people share what is left. They have a ¼ each. What fraction of the whole cheesecake do they have each?
⅔×¼= ⅙
9. ¾ of a class of children like athletics. ½ of these like running best. What fraction of the class prefer running?
¾× ½ = 3⁄8
10.
⅓ ÷ 2 = ⅙
11.
½ ÷ 3 = ⅙
12.
⅘ ÷ 2 = 2⁄5
Multiplying and dividing fractions (page 6 continued)
Y6 Sum Week 3 Day 5
13.
⅘ ÷ 4 =⅕
14.
¼ ÷ 2 = ⅛
15.
¼ ÷ 3 = 1⁄12
16.
⅔ ÷ 3 = 2⁄9
17. ½ of a pizza is shared between 4 children. What fraction of the pizza does each child get?
½ ÷ 4= ⅛
18. ¾ of an allotment needs digging over. If the amount to be dug is shared fairly between six people, what fraction of the whole allotment would each person dig?
¾ ÷ 6= ⅛
Week 4
Solve these equations(page 1)
Y6 Sum Week 4 Day 1
1.
12 – a = 7
a = 5
2.
8 + b = 115
b = 107
3.
4c = 36
c = 9
4.
80 ÷ d = 40
d = 2
5.
10e + 2 = 32
e = 3
6.
3f = 15
f = 5
7.
10 + g = 16
g = 6
8.
2h + 6 = 12
h = 3
9.
20 – 4i = 12
i = 2
10.
45 ÷ j = 9
j = 5
11.
5k ÷ 2 = 10
k = 4
12.
10 + m = 56 ÷ 8
m = - 3
Missing angles (page 3)
Y6 Sum Week 4 Day 2 MH
Missing angles (page 4)
Y6 Sum Week 4 Day 2 E
Reflections and translations (page 6)
Y6 Sum Week 4 Day 3 MH
Q.
A.
Reflections and translations (page 6 continued 1)
Y6 Sum Week 4 Day 3 MH
Q.
A.
Reflections and translations (page 6 continued 2)
Y6 Sum Week 4 Day 3 MH
Q.
A.
Reflections and translations (page 7)
Y6 Sum Week 4 Day 3 MH
Q.
- Together with coordinates of the new vertices:
Reflections and translations (page 7 continued )
Y6 Sum Week 4 Day 3 MH
Q.
- Together with coordinates of the new vertices:
Reflections and translations (page 8)
Y6 Sum Week 4 Day 3 MH
a)Left 2 squares and down 2 squares
b)Left1 square and up 2 squares
Reflections and translations (page 8 continued)
Y6 Sum Week 4 Day 3 MH
Reflections and translations (page 9)
Y6 Sum Week 4 Day 3 MH
Reflect this shape in the x axis. Label the co-ordinates of the new vertices.
Reflections and translations (page 10)
Y6 Sum Week 4 Day 3 E
- Reflect this shape in the line of symmetry
- Draw the reflection of this shape
Reflections and translations (page 10 continued)
Y6 Sum Week 4 Day 3 E
Q.
A.
Reflections and translations (page 11)
Y6 Sum Week 4 Day 3 E
- Reflect this shape in the mirror line and label the co-ordinates of its vertices.
- Move this shape across 4 squares and down 2 squares. Write the new co-ordinates of its vertices.
Reflections and translations (page 12)
Y6 Sum Week 4 Day 3 E
- How have these shapes been translated?
a)Down 2 squares.
b)Left 2 squares.
- Move this shape right three squares and up two squares
Reflections and translations (page 13)
Y6 Sum Week 4 Day 3 E
Interpreting graphs (page 16)
Y6 Sum Week 4 Day 4 M
Interpreting graphs (page 16 continued)
Y6 Sum Week 4 Day 4 M
Interpreting graphs (page 17)
Y6 Sum Week 4 Day 4 M
Interpreting graphs (page 17 continued)
Y6 Sum Week 4 Day 4 M
Interpreting graphs (page 18)
Y6 Sum Week 4 Day 4 M
Interpreting graphs (page 18 continued)
Y6 Sum Week 4 Day 4 M
Interpreting graphs (page 20)
Y6 Sum Week 4 Day 4 E
Interpreting graphs (page 20 continued)
Y6 Sum Week 4 Day 4 E
Interpreting graphs (page 21)
Y6 Sum Week 4 Day 4 E
Interpreting graphs (page 21 continued)
Y6 Sum Week 4 Day 4 E
Interpreting graphs (page 22)
Y6 Sum Week 4 Day 4 E
Sequences (page 23)
Y6 Sum Week 4 Day 5
1. This is part of a number sequence. The numbers increase by the same amount each time. Write the next three numbers. 18, 26, 34, 42, 50,58, 66, 74
2. Circle ALL of the numbers which will appear in this number sequence: 25, 75, 125, 175, 225.
250, 275, 425, 550, 800, 1025
(sequence contains any number which ends in 25).
3. Write the missing numbers in this sequence. -9, -7, -5, , -1, , 3, 5, , 9
Write one other number which would appear in this number pattern.
4. Write the next three numbers in this sequence.
1.2, 2.4, 3.6, 4.8, 6, 7.2,8.4,9.6
5. Describe this sequence. 80, 73, 66, 59, 52, 45
Subtract 7 each time.
Write the numbers before 80 and after 45 in this pattern.
87 and 38.
6. Write the first two numbers less than zero in this sequence: 200, 175, 150, 125, 100, 75
-25, -50
Josh started writing this sequence of numbers. 6, 11, 16, 21, 26, 31, 36 Will the number 94 appear in this sequence? Circle yes / no.
Explain how you know.
Sequence is an increase of 5 each time, numbers will proceed:
41, 46, 51, 56, 61, 66, 71, 76, 81, 86, 91, 96
Sequences (page 24)
Y6 Sum Week 4 Day 5
8. The numbers in this sequence increase by the same amount each time. Write in the missing numbers. 2 26
© Hamilton Trust Year 6 Summer Maths Answers