How do you know that 6 to 14 is equivalent to 15 to 35 using a multiplication table?

Question

Here is a multiplication table:

1	2	3	4	5	6	7	8	9
2	4	6	8	10	12	14	16	18
3	6	9	12	15	18	21	24	27
4	8	12	16	20	24	28	32	36
5	10	15	20	25	30	35	40	45
6	12	18	24	30	36	42	48	54
7	14	21	28	35	42	49	56	63
8	16	24	32	40	48	56	64	72
9	18	27	36	45	54	63	72	81

 

Answer 1

Rows 3 and 7 and columns 2 and 5 are significant.

Row 3 and column 2 represent 3*2=2*3=6; row 7 and column 2 represent 2*7=7*2=14, making up the fraction 6/14=2*3/(2*7)=3/7, because the common factor 2 cancels out. The ratio 6:14 is the same as 6/14 so 3:7 is the same as 3/7.

Similarly, row 3 and column 5 represent 3*5=5*3=15; row 7 and column 5 represent 7*5=5*7=35, making up 15/35 or ratio 15:35=3*5/(7*5)=3/7, because the common factor 5 cancels out. 

So the table shows by the common rows 3/7 that both fractions reduce to the same fraction or ratio 3/7 or 3:7. Take column 9, for example. Here we have 27 and 63 so 27/63 is also 3/7. This is how the multiplication table can be used to show which fractions or ratios are equivalent.
 

In the table, you can also replace the word column for row and row for column, and the same rule applies.

Comments

Your one of the smart ones on here. Thank you for that answer. :)

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