To complete the table, we can either multiply both the top x-values and the bottom y-values by the same factor to create equivalent ratiosor we can add equivalent ratios which already exist in the table.
Example Answer:
Are the Ratios From Both Exercises Equivalent? No, see solution.
Practice makes perfect
We want to complete the given table using multiple operations. To do it, we can either multiply both the top x-values and the bottom y-values by the same factor to create equivalent ratiosor we can add equivalent ratios which already exist in the table. As an example, let's multiply both values by a factor of 3.
Now, to try something different, we can add 45 to the top x-value and add 12 to the bottom y-value, because it is an equivalent ratio which already exists in the table.
We can also divide by the same factor, because it is the same as multiplying by its reciprocal.
Notice that this is just an example way of filling in this table. Feel free to choose different factors for multiplying and different order of performing operations if you want to. We also want to know if this is an equivalent ratio to the one in the previous exercise. Two ratios are equivalent if they simplify to the same number. Let's first find the number which the given ratios simplify to.
4/5÷ 1/2
Recall that dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction.
4/5÷ 1/2 = 4/5* 2/1
When we multiply fractions, we need to remember that the product of two fractions is equal to the product of the numerators divided by the product of the denominators. Let's find the given product!
This ratio simplifies to 85. Now, let's recall the table we constructed in the previous exercise.
Let's find the number which the given ratios simplify to.
4÷ 10
Recall that dividing two numbers can be represented as a fraction.
4÷ 10 = 4/10
Let's simplify this fraction!
