Maths Answers
Summer Year 5
Week 1:
Whole class practice
1. 456,237 + 1 = 456,238 456,237 - 1 = 456,236
2. 578,483 + 10 = 578,493 578,483 - 10 = 578,473
3. 347,329 + 100 = 347,429 347,329 - 100 = 347,229
4. 235,820 + 1000 = 236,820 235,820 - 1000 = 234,820
5. 658,231 + 10,000 = 668,231 658,231 - 10,000 = 648,231
6. 345,784 + 100,000 = 445,784 345,784 - 100,000 = 245,784
7. 456,378 + 20 = 456,398 456,378 - 20 = 456,358
8. 235,429 + 300 = 235,729 235,429 - 300 = 235,129
9. 428,375 + 20,000 = 448,375 428,375 - 20,000 = 408,375
10. 324,790 + 10 = 324,800 324,790 - 10 = 324,780
11. 473,699 + 1 = 473,700 473,699 + 10 = 473,709
12. 299,999 + 1 = 300,000 299,999 - 1 = 299,998
13. 500,000 - 1 = 499,999 500,000 - 10 = 499,990
14. 300,000 - 100 = 299,900 300,000 - 1000 = 299,000
Placing numbers (E)
Placing numbers (M)
Rounding
100,000 / 10,000 / 1000Tenerife / 906,854 / 900,000 / 910,000 / 907,000
Majorca / 862,397 / 900,000 / 860,000 / 862,000
Tasmania / 507,626 / 500,000 / 510,000 / 508,000
Newfoundland / 479,105 / 500,000 / 480,000 / 479,000
Malta / 373,955 / 400,000 / 370,000 / 374,000
Corsica / 316,578 / 300,000 / 320,000 / 317,000
Iceland / 311,396 / 300,000 / 310,000 / 311,000
Madeira / 245,806 / 200,000 / 250,000 / 246,000
Ibiza / 117,698 / 100,000 / 120,000 / 118,000
Corfu / 104,371 / 100,000 / 100,000 / 104,000
Week 2:
Roman numerals
I. XXII, XXIII, XXIV, XXV, XXVI
II. LI, LII, LIII, LIV, LV
III. XXVII, XXVIII, XXIX, XXX, XXXI
IV. XLVI, XLVII, XLVIII, XLIX, L
V. LXV, LXVI, LXVII, LXVIII, LXIX
VI. CI, CII, CIII, CIV, CV
VII. CXXV, CXXVI, CXXVII, CXXVIII, CXXIX
VIII. CCXVII, CCXVIII, CCXIX, CCXX, CCXXI
IX. CCLX, CCLXI, CCLXII, CCLXIII, CCLXIV
X. DXXII, DXXIII, DXXIV, DXXV, DXXVI
XI. CDXV, CDXVI, CDXVII, CDXVIII, CDXIX
XII. DCXI, DCXII, DCXIII, DCXIV, DCXV
Dates
Place value (H)
2.304 + 0.05 = 2.354
2.37 + 0.002 = 2.372
2.074 + 0.5 = 2.574
23.78 + 0.009 = 23.789
1.58 + 0.005 = 1.585
2.305 + 0.02 = 2.325
78.409 + 0.02 = 78.429
3.075 + 0.1 = 3.175
45.015 + 0.2 = 45.215
2.505 + 0.05 = 2.555
Place value (M)
2.304 + 0.05 = 2.354
2.37 + 0.002 = 2.372
2.074 + 0.5 = 2.574
23.78 + 0.009 = 23.789
1.58 + 0.005 = 1.585
2.305 + 0.02 = 2.325
78.409 + 0.02 = 78.429
3.075 + 0.1 = 3.175
45.015 + 0.2 = 45.215
2 + 0.555 = 2.555
Function machines
0.36 x 10 = 3.6
1.456 x 10 = 14.56
0.047 x 10 = 0.47
0.06 ÷ 10 = 0.006
3.45 ÷ 10 = 0.345
0.67 ÷ 10 = 0.067
0.345 x 100 = 34.5
0.007 x 100 = 0.7
6.354 x 100 = 635.4
0.8 ÷ 100 = 0.008
4.3 ÷ 100 = 0.043
6 ÷ 100 = 0.06
0.008 x 1000 = 8
0.45 x 1000 = 450
1.728 x 1000 = 1728
7 ÷ 1000 = 0.007
45 ÷ 1000 = 0.045
345 ÷ 1000 = 0.345
Week 3:
Using known facts to help with divisions
20 x 6 = 120 30 x 6 = 180 40 x 6 = 240
20 x 7 = 140 30 x 7 = 210 40 x 7 = 280
20 x 8 = 160 30 x 8 = 240 40 x 8 = 320
1. 129 ÷ 6 = 21 3/6 or 21 1/2
2. 147 ÷ 7 = 21
3. 164 ÷ 8 = 20 4/8 or 20 1/2
4. 122 ÷ 6 = 20 2/6 or 20 1/3
5. 162 ÷ 8 = 20 2/8 or 20 1/4
6. 166 ÷ 8 = 20 6/8 or 20 3/4
7. 183 ÷ 6 = 30 3/6 or 30 1/2
8. 224 ÷ 7 = 32
9. 244 ÷ 8 = 30 4/8 or 30 1/2
10. 255 ÷ 6 = 42 3/6 or 42 1/2
11. 287 ÷ 7 = 41
12. 332 ÷ 8 = 41 4/8 or 41 1/2
Using known facts to help with divisions (E)
10 x 6 = 60 20 x 6 = 120 30 x 6 = 180
10 x 7 = 70 20 x 7 = 140 30 x 7 = 210
10 x 8 = 80 20 x 8 = 160 30 x 8 = 240
1. 69 ÷ 6 = 11 3/6 or 11 1/2
2. 129 ÷ 6 = 21 3/6 or 21 1/2
3. 77 ÷ 7 = 11
4. 147 ÷ 7 = 21
5. 88 ÷ 8 = 11
6. 164 ÷ 8 = 20 4/8 or 20 1/2
7. 122 ÷ 6 = 20 2/6 or 20 1/3
8. 162 ÷ 8 = 20 2/8 or 20 1/4
9. 145 ÷ 6 = 24 1/6
10. 183 ÷ 6 = 30 3/6 or 30 1/2
Using known facts to help with divisions (H)
20 x 6 = 120 30 x 6 = 180 40 x 6 = 240
20 x 7 = 140 30 x 7 = 210 40 x 7 = 280
20 x 8 = 160 30 x 8 = 240 40 x 8 = 320
1. 135 ÷ 6 = 22 3/6 or 22 1/2
2. 154 ÷ 7 = 22
3. 172 ÷ 8 = 21 4/8 or 21 1/2
4. 128 ÷ 6 = 21 2/6 or 21 1/3
5. 170 ÷ 8 = 21 2/8 or 21 1/4
6. 174 ÷ 8 = 21 6/8 or 21 3/4
7. 195 ÷ 6 = 32 3/6 or 32 1/2
8. 238 ÷ 7 = 34
9. 270 ÷ 8 = 33 6/8 or 33 3/4
10. 261 ÷ 6 = 43 3/6 or 43 1/2
11. 294 ÷ 7 = 42
12. 332 ÷ 8 = 41 4/8 or 41 1/2
Multiplication and division word problems (M)
1. 49 x 20 = 980 The tea shop has 980 tea bags.
2. 92 ÷ 8 = 11 4/8 The tea shop has 11 ½ cakes left.
3. 32 x 20p = 640p or £6.40 The children have brought in £6.40 altogether.
4. 154 ÷ 7 = 22 There are 22 weeks in 154 days.
5. £75 ÷ 6 = £12.50 The meal cost £12.50 per person.
6. 38 x 15 = 570 The driver drives 570 miles in a day.
7. 217 ÷ 7 = 31 There are 31 children in each class.
8. 26 x 5min = 130min It will take the runner 2 hours and 10 minutes.
Multiplication and division word problems (E)
1. 23 x 20 = 460 The tea shop has 460 tea bags.
2. 84 ÷ 8 = 10 4/8 The tea shop has 10 ½ cakes left.
3. 16 x 20p = 320p or £3.20 The children have brought in £3.20 altogether.
4. 91 ÷ 7 = 13 There are 13 weeks in 91 days.
5. £63 ÷ 6 = £10.50 The meal cost £10.50 per person.
6. 17 x 20 = 340 The driver drives 340 miles in a day.
7. 147 ÷ 7 = 21 There are 21 children in each class.
8. 14 x 5min = 70min It will take the runner 1 hour and 10 minutes.
Multiplication and division word problems (H)
1. 59 x 20 = 1180 The tea shop has 1180 tea bags.
2. 90 ÷ 8 = 11 2/8 The tea shop has 11 1/4 cakes left.
3. 37 x 20p = 740p or £7.40 The children have brought in £7.40 altogether.
4. 224 ÷ 7 = 32 There are 32 weeks in 224 days.
5. £81 ÷ 6 = £13.50 The meal cost £13.50 per person.
6. 32 x 19 = 608 The driver drives 608 miles in a day.
7. 203 ÷ 7 = 29 There are 29 children in each class.
8. 27 x 5min = 135min It will take the runner 2 hours and 15 minutes.
Percentages
20% = 0.2 = 1/5
3% = 0.03 = 3/100
10% = 0.1 = 1/10
50% = 0.5 = ½
25% = 0.25 = ¼
75% = 0.75 = ¾
99% = 0.99 = 99/100
15% = 0.15 = 3/20
46% = 0.46 = 23/50
80% = 0.8 = 4/5
Equivalent percentages (E)
Children were asked to vote for cycling, swimming or football as their favourite weekend activityFraction / Percentage
½ children prefer swimming / 50%
¼ of children prefer cycling / 25%
The rest prefer football / 25%
Children were asked to vote for oranges, bananas or apples as their favourite fruit
Fraction / Percentage
4/10 children prefer bananas / 40%
3/10 of children prefer apples / 30%
The rest prefer oranges / 30%
Children were asked to vote for dogs, cats or rabbits as their ideal pet
Fraction / Percentage
½ prefer dogs / 50%
3/10 prefer cats / 30%
The rest prefer rabbits / 20%
Equivalent percentages (M)
Children were asked to vote for cycling, swimming or football as their favourite weekend activityFraction / Percentage
½ children prefer swimming / 50%
3/10 of children prefer cycling / 30%
The rest prefer football / 20%
Children were asked to vote for oranges, bananas or apples as their favourite fruit
Fraction / Percentage
2/5 children prefer bananas / 40%
3/10 of children prefer apples / 30%
The rest prefer oranges / 30%
Children were asked to vote for dogs, cats or rabbits as their ideal pet
Fraction / Percentage
½ prefer dogs / 50%
1/5 prefer cats / 20%
The rest prefer rabbits / 30%
Comparing percentages (E)
Burley Common has:
50 oak, 20 ash, 15 beech and 15 willow.
Merttens Meadow has:
60 oak, 60 hazel, 120 willow and 60 beech.
Chidgey Common has:
80 oak, 60 beech, 20 ash and 40 sweet chestnut.
Holes Hollow has:
50 oak, 20 hazel, 40 willow, 30 beech and 60 ash.
Comparing percentages (M)
Burley Common has:
50 oak, 20 ash, 15 beech and 15 willow.
Merttens Meadow has:
30 oak, 30 hazel, 60 willow and 30 beech.
Chidgey Common has:
80 oak, 60 beech, 20 ash and 40 sweet chestnut.
Holes Hollow has:
30 oak, 12 hazel, 18 willow, 36 beech and 24 ash.
Week 4:
Missing angles
120° + 110° + 130° = 360°
135° + 115° + 110° = 360°
62° + 185° + 113° = 360°
112° + 56° + 192° = 360°
78° + 143° + 139° = 360°
80° + 130° + 70° + 80° = 360°
125° + 75° + 45° + 115° = 360°
116° + 65° + 42° + 137° = 360°
Missing angles (E)
140° + 70° + 150° = 360°
150° + 140° + 70° = 360°
65° + 175° + 120° = 360°
185° + 45° + 130° = 360°
76° + 123° + 161° = 360°
68° + 153° + 139° = 360°
130° + 70° + 60° + 100° = 360°
105° + 65° + 45° + 145° = 360°
Multiplication table
x / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 121 / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 12
2 / 2 / 4 / 6 / 8 / 10 / 12 / 14 / 16 / 18 / 20 / 22 / 24
3 / 3 / 6 / 9 / 12 / 15 / 18 / 21 / 24 / 27 / 30 / 33 / 36
4 / 4 / 8 / 12 / 16 / 20 / 24 / 28 / 32 / 36 / 40 / 44 / 48
5 / 5 / 10 / 15 / 20 / 25 / 30 / 35 / 40 / 45 / 50 / 55 / 60
6 / 6 / 12 / 18 / 24 / 30 / 36 / 42 / 48 / 54 / 60 / 66 / 72
7 / 7 / 14 / 21 / 28 / 35 / 42 / 49 / 56 / 63 / 70 / 77 / 84
8 / 8 / 16 / 24 / 32 / 40 / 48 / 56 / 64 / 72 / 80 / 88 / 96
9 / 9 / 18 / 27 / 36 / 45 / 54 / 63 / 72 / 81 / 90 / 99 / 108
10 / 10 / 20 / 30 / 40 / 50 / 60 / 70 / 80 / 90 / 100 / 110 / 120
11 / 11 / 22 / 33 / 44 / 55 / 66 / 77 / 88 / 99 / 110 / 121 / 132
12 / 12 / 24 / 36 / 48 / 60 / 72 / 84 / 96 / 108 / 120 / 132 / 144
Week 5:
Whole class practice
1. 1/4 3/8
2. 3/10 2/5
3. 1/2 5/8
4. 2/3 5/6
5. 5/9 2/3
6. 1/4 1/2 5/8
7. 1/3 1/2 5/6
8. 1/2 7/10 4/5
9. 4/9 2/3 7/9
10. 7/12 2/3 ¾
11. 2 1/2 9/2
12. 1 1/4 3 ¼
13. 1 7/3 5 1/3
14. 1 9/6 4 5/6
15. 1 6/5 3 2/5
16. 2 1/10 2 3/10
17. 1 3/4 2 1/2 7/2
18. 1 7/8 9/4 2 1/2
Adding and subtracting fractions
1/2 + 1/4 = 3/4 1/2 + 3/4 = 5/4
1/2 + 1/8 = 5/8 1/2 + 3/8 = 7/8 1/2 + 5/8 = 9/8 1/2 + 7/8 = 11/8
1/2 + 1/10 = 6/10 1/2 + 3/10 = 8/10 1/2 + 5/10 = 10/10
1/2 + 7/10 = 12/10 1/2 + 9/10 = 14/10
1/4 + 1/8 = 3/8 1/4 + 3/8 = 5/8 1/4 + 5/8 = 7/8 1/4 + 7/8 = 9/8
3/4 + 1/8 = 7/8 3/4 + 3/8 = 9/8 3/4 + 5/8 = 11/8 3/4 + 7/8 = 13/8
1/3 + 1/6 = 3/6 1/3 + 5/6 = 7/6
2/3 + 1/6 = 5/6 2/3 + 5/6 = 9/6
1/3 + 1/9 = 4/9 1/3 + 2/9 = 5/9 1/3 + 4/9 = 7/9
1/3 + 5/9 = 8/9 1/3 + 7/9 = 10/9 1/3 + 8/9 = 11/9
2/3 + 1/9 = 7/9 2/3 + 2/9 = 8/9 2/3 + 4/9 = 10/9
2/3 + 5/9 = 11/9 2/3 + 7/9 = 13/9 2/3 + 8/9 = 14/9
1/5 + 1/10 = 3/10 1/5 + 3/10 = 5/10 1/5 + 5/10 = 7/10
1/5 + 7/10 = 9/10 1/5 + 9/10 = 11/10
2/5 + 1/10 = 5/10 2/5 + 3/10 = 7/10 2/5 + 5/10 = 9/10
2/5 + 7/10 = 11/10 2/5 + 9/10 = 13/10
3/5 + 1/10 = 7/10 3/5 + 3/10 = 9/10 3/5 + 5/10 = 11/10
3/5 + 7/10 = 13/10 3/5 + 9/10 = 15/10
4/5 + 1/10 = 9/10 4/5 + 3/10 = 11/10 4/5 + 5/10 = 13/10
4/5 + 7/10 = 15/10 4/5 + 9/10 = 17/10
1/2 - 1/4 = 1/4 3/4 - 1/2 = 1/4
1/2 - 1/8 = 3/8 1/2 - 3/8 = 1/8 5/8 - 1/2 = 1/8 7/8 - 1/2 = 3/8
1/2 - 1/10 = 4/10 1/2 - 3/10 = 2/10 1/2 - 5/10 = 0/10
7/10 - 1/2 = 2/10 9/10 - 1/2 = 4/10
1/4 - 1/8 = 1/8 3/8 - 1/4 = 1/8 5/8 - 1/4 = 3/8 7/8 - 1/4 = 5/8
3/4 - 1/8 = 5/8 3/4 - 3/8 = 3/8 3/4 - 5/8 = 1/8 7/8 - 3/4 = 1/8
1/3 - 1/6 = 1/6 5/6 - 1/3 = 3/6
2/3 - 1/6 = 3/6 5/6 - 2/3 = 1/6
1/3 - 1/9 = 2/9 1/3 - 2/9 = 1/9 4/9 - 1/3 = 1/9
5/9 - 1/3 = 2/9 7/9 - 1/3 = 4/9 8/9 - 1/3 = 5/9
2/3 - 1/9 = 5/9 2/3 - 2/9 = 4/9 2/3 - 4/9 = 2/9
2/3 - 5/9 = 1/9 7/9 - 2/3 = 1/9 8/9 - 2/3 = 2/9
1/5 - 1/10 = 1/10 3/10 - 1/5 = 1/10 5/10 - 1/5 = 3/10
7/10 - 1/5 = 5/10 9/10 - 1/5 = 7/10
2/5 - 1/10 = 3/10 2/5 - 3/10 = 1/10 5/10 - 2/5 = 1/10
7/10 - 2/5 = 3/10 9/10 - 2/5 = 5/10
3/5 - 1/10 = 5/10 3/5 - 3/10 = 3/10 3/5 - 5/10 = 1/10
7/10 - 3/5 = 1/10 9/10 - 3/5 = 3/10
4/5 - 1/10 = 7/10 4/5 - 3/10 = 5/10 4/5 - 5/10 = 3/10
4/5 - 7/10 = 1/10 9/10 - 4/5 = 1/10
Adding and subtracting fractions
1. 1/4 + 3/8 = 5/8
2. 5/8 + 1/4 = 7/8
3. 3/4 + 1/8 = 7/8
4. 7/8 + 1/4 = 1 1/8
5. 7/8 - 1/4 = 5/8
6. 5/8 - 1/4 = 3/8
7. 1/3 + 1/6 = 3/6 = 1/2
8. 2/3 + 1/6 = 5/6
9. 5/6 + 1/3 = 1 1/6
10. 5/6 - 1/3 = 3/6 = 1/2
Adding and subtracting mixed numbers
1. 2 3/5 + 1 3/10 = 3 9/10
2. 1 1/6 + 1 2/3 = 2 5/6
3. 2 1/2 + 1 5/8 = 4 1/8
4. 3 1/3 + 2 1/6 = 5 1/2
5. 2 3/4 + 2 3/8 = 5 1/8
6. 4 7/10 - 2 1/2 = 2 1/5
7. 3 5/6 - 2 1/3 = 1 1/2
8. 2 7/8 - 1 3/4 = 1 1/8
9. 5 3/4 - 2 3/8 = 3 3/8
10. 4 5/6 - 2 1/3 = 2 1/2