# Video: Deciding Whether Two Given Quantities Are in a Proportional Relationship

The table shows crop statistics for three different farms. Which two farms have the same wheat-to-barley ratio?

03:33

### Video Transcript

The table shows crop statistics for three different farms. Which two farms have the same wheat-to-barley ratio?

The ratio of wheat to barley in Farm A is 930 to 210; for Farm B, it is 1860 to 275; and for Farm C, it is 2635 to 595. In order to work out which two farms have the same ratio, we need to write all three ratios in their simplest form. In order to simplify ratio, we need to divide both sides by the same number. The simplified ratio must contain only integer values.

10 is a common factor of 930 and 210. 210 divided by 10 is 21 and 930 divided by 10 is 93. Therefore, the simplified ratio for Farm A is 93 to 21. Both of these numbers are also divisible by three. 93 divided by three is equal to 31 and 21 divided by three is equal to seven. The ratio of wheat to barley for farm A in its simplest form is 31 to seven. We can’t simplify this any further as there is no integer apart from one that is a factor of 31 and seven.

The ratio for Farm B was 1860 to 275. Both of these numbers are divisible by five as they end in five or zero. 1860 divided by five is 372 and 275 divided by five is equal to 55. The only factors of 55 are one, five, 11, and 55. None of these numbers apart from one divide exactly into 372. This means that the ratio of wheat to barley in Farm B in its simplest form is 372 to 55.

The ratio of wheat to barley in Farm C was 2635 to 595. Once again, both of these numbers are clearly divisible by five. 2635 divided by five is equal to 527 and 595 divided by five is equal to 119. Both of these numbers are divisible by 17. 527 divided by 17 is 31 and 119 divided by 17 is equal to seven. This means that the ratio of wheat to barley for Farm C in its simplest form is 31 to seven.

We can, therefore, say that Farm A and Farm C have the same wheat-to-barley ratio: 31 to seven in its simplest form.