My son is struggling with ratios and Ploygons. The word problem is:
Lydia wants to use a photocopier to increase the size of a small chart. The chart is 4 in. by 5 in. If she uses a scale factor of 5:11 will the chart fit on a 8 1/2 x 11 sheet of paper? Can some explain to me how to factor this so I can help him with his other problems?
Thank you in advance
With a ratio of 5/11, that 5" will be adequate.
5/11 = 5/x
However, for the 4":
5/11 = 4/x
Multiply both sides by 11x and divide by5.
x = 4(11/5) = 8.8
To determine if the chart will fit on an 8 1/2 x 11 sheet of paper, we need to compare the dimensions of the chart after being scaled up using the given scale factor.
First, let's determine the dimensions of the scaled chart. The scale factor of 5:11 means that every dimension of the original chart will be multiplied by the same factor.
The length of the chart (4 inches) multiplied by the scale factor (5/11) gives us:
4 * (5/11) = 20/11 inches
The width of the chart (5 inches) multiplied by the scale factor (5/11) gives us:
5 * (5/11) = 25/11 inches
Now, let's compare these dimensions with the dimensions of the 8 1/2 x 11 sheet of paper.
The length of the sheet is 8 1/2 inches, which can be written as 17/2 inches.
The width of the sheet is 11 inches.
Comparing the dimensions:
Length of the scaled chart: 20/11 inches
Width of the scaled chart: 25/11 inches
Length of the sheet: 17/2 inches
Width of the sheet: 11 inches
To determine if the chart will fit on the sheet of paper, we need to check if both the length and width of the chart are smaller or equal to the length and width of the sheet, respectively.
Comparing the length:
20/11 inches ≤ 17/2 inches
To compare fractions, we convert them to the same denominator. The least common multiple (LCM) of 11 and 2 is 22.
(20/11) * (2/2) ≤ (17/2) * (11/11)
(40/22) ≤ (187/22)
Since 40 is less than 187, the length of the chart is smaller than the length of the sheet.
Now, let's compare the width:
25/11 inches ≤ 11 inches
We don't need to convert fractions here since the denominators are already the same.
Since 25/11 is less than 11, the width of the chart is smaller than the width of the sheet.
Therefore, the scaled chart will fit on the 8 1/2 x 11 sheet of paper.