Determine if one, both, or neither of the following is a proportion. 168=?2412, 84=?126(1 point)
Responses
Neither is a proportion.
Neither is a proportion.
168=2412, 84=126
Start Fraction 16 over 8 End Fraction equals Start Fraction 24 over 12 End Fraction , , , Start Fraction 8 over 4 End Fraction equals Start Fraction 12 over 6 End Fraction
84=126 only
Start Fraction 8 over 4 End Fraction equals Start Fraction 12 over 6 End Fraction , only
168=2412 only
Both are proportions.
To check if they are proportional, we need to see if the ratio of the first pair of numbers is equal to the ratio of the second pair of numbers.
For the first pair:
168/24 = 7
2412/12 = 201
7 is equal to 201, so the first pair is proportional.
For the second pair:
84/12 = 7
126/6 = 21
7 is equal to 21, so the second pair is proportional as well.
If you had a choice between eating 1 1/3 of a candy bar or 4/3 of a candy bar, which would you choose? Did you know that a mixed number (like 1 1/3) and an improper fraction (like 4/3) can represent the exact same amount? These two numbers are equal, so no matter which one you chose, you would have the same amount of candy bar! This lesson will show you why this is true and how to convert mixed numbers to improper fractions.
We use fractions when we are referring to a part of a whole instead of a whole number. Fractional notation simply means that a number is written in fraction form. It is written as a/b where neither a nor b is equal to 0.
A fraction has two parts, the numerator and denominator. The numerator is the number on top of the line and it represents how many pieces of the whole we are referring to. The denominator is the number below the line, and it represents how many pieces make up one whole. Look at these examples:
1
Visualizing Fractional Notation
It's said that a picture is worth a thousand words, so let's look at some images that will help us understand fractional notation. The following image shows a bar broken into 5 equal pieces. Therefore, 5 pieces make up a whole bar in this example, so the denominator is 5. Of the 5 pieces, 2 are shaded in. Because we are referring to 2 of the 5 pieces, the numerator in this example is 2. This image represents the fraction 2/5.2
Mixed Numbers in Fractional Notation
We can also write mixed numbers in fractional notation. A mixed number is one that consists of a whole number and a fraction. When we convert a mixed number to fractional notation, it makes an improper fraction. An improper fraction is a fraction that represents more than one whole.
Well, it seems we have a math problem on our hands. Let me put on my thinking cap... or rather, my clown wig!
Neither of the equations is a proportion. They cannot be simplified down to equal fractions.
But hey, I have a joke for you - why don't scientists trust atoms?
Because they make up everything!
Neither of the given equations is a proportion.
To determine if one, both, or neither of the given equations is a proportion, we need to compare the ratios on both sides.
For the first equation, 168 = ? 2412, we need to simplify both sides of the equation. However, we can immediately see that the values are not proportional since 168 is not equal to 2412. Therefore, we can conclude that neither is a proportion.
For the second equation, 84 = ? 126, we can simplify both sides by dividing them by their greatest common divisor (GCD), which is 42 in this case. Dividing both sides by 42 gives us 2 = ? 3. Here, the simplified equation shows that the ratio on both sides is equal, with 2/3 = 2/3, so we can conclude that this equation is a proportion.
To summarize:
- Neither 168 = ? 2412 nor 84 = ? 126 are proportions.
- The equation 84 = ? 126 is a proportion.