Equivalent Ratios Recall that ratios are comparisons.
Relating Decimals, Fractions and Percent Please go to the link below and complete the activities suggested below. Math Is Fun Virtual Manipulative Activities to demonstrate the relationship between fractions, decimals and percents, and reinforce and extend your understandings of percents being another way to represent fractions: By rotating the curser in an anti-clockwise direction around the pizza, shading the grid or moving along the number line, you can select a portion of the pizza.
Shade one of the squares on the grid. Notice that one hundredth of the pizza appears, and the pointer is a very small distance past zero on the number line. Imagine the number line from zero to 1 divided into one hundred equal parts.
One of these parts is one hundredth, or 0. This part is also one tenth of a tenth, or one tenth of 0. Highlight the top row of the grid, that is, ten of the one hundred squares. You have highlighted one tenth of the square, and will notice that one out of ten equal parts of the pizza has appeared.
The pointer shows one tenth, or 0. This can also be written as 0. Move your curser to show: The entire grid represents one 1or one whole. The grid can be divided into 10 equal parts, or tenths. One of these ten equal parts, or one tenth of the gridis shaded in red. One tenth, the red portion, can be divided into ten equal parts the yellow section shows this.
The yellow portion is a one hundredth as of these make the whole. A one hundredththe yellow portion, can also be divided into ten equal parts the blue section shows this. The blue portion is represents one thousandths of the whole, as of these thousands makes the whole.
The following statements can be made: The red area is one tenth or zero point one 0. A visual model for decimal fractions The following video uses a thousandths grid in a similar way, to demonstrate writing decimal fractions: It is written as or 0.
It is easy to see that this shaded area is one half of the whole grid. This shaded area can also be broken up into 50 hundredths. The fraction 50 hundredths is equivalent to thousandths. Furthermore, the shaded area in the video can be broken up into five tenths.
The fraction five tenths is equivalent to the fraction 50 hundredths and thousandths All of these fractions have the same value of one halfand so they are equivalent fractions.
Unlike whole numbers, a zero on the end right hand side does not change the value of the decimal. However, the zeros can sometimes assist when adding and subtracting decimals.In the statement "A _____ is a pair of equal ratios.", the word that completes is A, proportion.
A proportion is a numerical correlation between two numbers/5(5). Proportion says that two ratios (or fractions) are equal. Show Ads. Hide Ads About Ads. Let us write the proportion with the help of the 10/20 ratio from above: = / 20 = So you should draw the head 21 long.
Using Proportions to Solve Percents. A percent is actually a ratio! Saying "25%" is actually saying "25 per ": 25%. Ratio problems are often solved by using proportions. A proportion is an equation formed with two ratios that are equal.
One method for solving a proportion problem is to find the appropriate equivalent ratio. Sometimes it is useful to write a ratio in the form 1:x or x:1, where x is not necessarily an integer, to enable comparisons of different ratios.
For example, the ratio can be written as (dividing both sides by 4) Alternatively, it can be written as (dividing both sides by 5). Let us write the proportion with the help of the 10/20 ratio from above:? 42 = 10 Now we solve it using a special method: Multiply across the known corners, then divide by the third number.
And we get this:?
= (42 × 10) / 20 = / 20 = So you should draw the head 21 long. CHAPTER 6: Ratio and Percent Recognizing Ratios Write ratios to compare different numbers using a colon (:), the word to, or a fraction. Example: Use the strategy of your choice to calculate the percent equal to each decimal.
a. b. c. d. Describe and compare the strategies you used to write fractions as percents in.