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Friday, 3 November 2017

Lowest Common Multiple And Greatest Common Factor

LI: to practise finding the highest common factor and the lowest common multiple.
LI: to simplify fractions.
This week for maths we were learning about the lowest common multiple and the greatest common factor. We learnt that the lowest common multiple is the lowest number that both numbers of the equation have in their times table. The greatest common factor has to be the highest matching amount that you can get from multiplying two numbers and it's the opposite for the lowest common multiple.


Number
Problem: show working
Answer in simplified fractions
Answer in mixed numerals
1
⅗ + 8/12. ⅗ + 8/12 = 36/60 + 40/60, 36/60 + 40/60 = 76/60, 76/60 ÷ 3 = 19/15.
19/15
1 & 4/15
2
5/7 + 6/8 = 40/56 + 42/56, 40/56 + 42/56 = 82/56, 82/56 ÷ 2 = 41/28.
41/28
1 & 13/28
3
2/4 + 7/10 = 20/40 + 28/40. 20/40 + 28/40 = 48/40, 48/40 ÷ 3 = 6/5.
6/5
1 & 1/6
4
⅓ + 6/9 = 9/27 + 18/27, 9/27 + 18/27 = 27/27. 27/27 ÷ 3 = 9/9.
1/1
1 whole
5
⅘ + ⅙ = 24/30 + 5/30, 24/30 + 5/30 = 29/30
29/30 (prime number)

6
5/8 + 5/16 = 80/128 + 40/128, 80/128 + 40/128 = 120/128. 120/128 ÷ 3 = 15/16.
15/16

7
5/9 + ⅓ = 15/27 + 9/27, 15/27 + 9/27 = 24/27. 24/27 ÷ 3 = 8/9.
8/9

8
4/12 + 6/18 = 72/216 + 72/216, 72/216 + 72/216 = 144/216. 144/216 ÷ 3 = 48/72
2/3

9
7/21 + 5/15 = 105/315 + 105/315, 105/315 + 105/315 = 210/315. 210/315 ÷ 3 = 70/105
2/3

10
6/18 + 24/32 = 192/576 + 432/576, 192/576 + 432/576 = 624/576. 624/576 ÷ 2 = 312/288
312/288
1 & 24/288
11
4/35 + 7/63 = 252/2205 + 245/2205, 252/2205 + 245/2205 = 497/2205. 497/2205 ÷ 7 = 71/315
71/315

12
9/18 + 3/12 = 108/216 + 54/216, 108/216 + 54/216 = 162/216. 162/216 ÷ 3 = 54/72.
3/4

13
43/100 + 28/50 = 2150/5000 + 2800/5000, 2150/5000 + 2800/5000 = 4950/5000. 4950/5000 ÷ 2 = 2475/2500
99/100

14
8/56 + 7/63 = 504/3528 + 392/3528, 504/3528 + 392/3528 = 896/3528. 896/3528 ÷ 4 = 224/882.
112/441

15
2/90 + 60/70 = 140/6300 + 5400/6300, 140/6300 + 5400/6300 = 5540/6300. 5540/6300 ÷ 4 = 1385/1575.
277/315

Number
Problem
Answer in simplified fractions
Answer in mixed numerals
1
8/16 - 3/12 = 96/192 + 48/192, 96/192 + 48/192 = 144/192. 144/192 ÷ 2 = 72/96.
72/96

2
¾ - 4/7 = 21/28 - 16/28, 21/28 - 16/28 = 5/28.


3
6/9 - ⅓ = 18/27 - 9/27, 18/27 - 9/27 = 9/27. 9/27 ÷ 3  = 3/9.
3/9

4
21/30 - 6/15 = 315/450 - 180/450, 315 - 180 = 135/450. 135/450 ÷ 3 = 45/150.
45/150

5
14/49 - 4/28 = 392/1372 - 196/1372, 392/1372 - 196/1372 = 196/1372. 196/1372 ÷ 2 = 98/686.
98/686

6
32/64 - 2/8 = 256/512 - 128/512, 256/512 - 128/512 = 128/512. 128/512 ÷ 2 = 64/256.
64/256

7
6/10 - ⅖ = 30/50 - 20/50, 30/50 - 20/50 = 10/50. 10/50 ÷ 2 = 5/25.
5/25

8
18/20 - ⅗ = 90/100 - 60/100, 90/100 - 60/100 = 30/100. 30/100 ÷ 2 = 15/50.
15/50

9
16/40 - 2/20 = 320/800 - 80/800, 320/800 - 80/800 = 240/800. 240/800 ÷ 4 = 60/200.
60/200

10
80/100 - 30/60 = 4800/6000 - 3000/6000, 4800/6000 - 3000/6000 = 1800/6000. 1800/6000 ÷ 3 = 600/2000
600/2000

11
21/30 - 4/15 = 315/450 - 120/450, 315/450 - 120/450 = 195/450. 195/450 ÷ 5 = 39/90
39/90

12
50/100 - 25/50 = 2500/5000 - 2500/5000, 2500/5000 - 2500/5000 = 0/5000.


13
7/10 - 600/1000 = 7000/10000 - 6000/10000, 7000/10000 - 6000/10000 = 1000/10000. 1000/10000 ÷ 5 = 200/2000.
200/2000

14
49/63 - 3/21 = 1029/1323 - 189/1323, 1029/1323 - 189/1323 = 840/1323. 840/1323 ÷ 3 = 280/441.
280/441

15
4240/6000 - 2000/10000 = 42400000/60000000 - 12000000/60000000, 42400000/60000000 - 12000000/60000000 = 30400000/60000000. 30400000/60000000 ÷ 100 = 304/600.
304/600

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