Describe how to use area models to find the quotient two-thirds divided by one-fifth. Check your work by also finding the quotient two-thirds divided by one-fifth using numerical operations only.
(5 points)
To use area models to find the quotient of two-thirds divided by one-fifth, follow these steps:
1. Draw a rectangle to represent the whole quantity, which is two-thirds.
2. Divide the rectangle into three equal parts horizontally to represent the numerator, which is two.
3. Shade two out of the three parts to represent the fraction two-thirds.
4. Draw another rectangle to represent the divisor, which is one-fifth.
5. Divide the rectangle into five equal parts horizontally to represent the numerator, which is one.
6. Shade one out of the five parts to represent the fraction one-fifth.
7. Arrange the two shaded areas side by side and observe the overlapping part.
8. Count the number of shaded parts in the overlapping area.
9. The count of shaded parts in the overlapping area represents the quotient of two-thirds divided by one-fifth.
To check your work using numerical operations only, follow these steps:
1. Take the numerator of the dividend, which is two, and multiply it by the reciprocal of the divisor, which is five over one. (Reciprocating means swapping the numerator and denominator of the divisor).
2. Multiply two by five over one. The product is ten.
3. Divide the product, which is ten, by the denominator of the dividend, which is three.
4. Divide ten by three using long division or a calculator to get the quotient.
The quotient of two-thirds divided by one-fifth using numerical operations only should be approximately 3.33333 (repeating decimals).
To use area models to find the quotient of two-thirds divided by one-fifth, follow these steps:
Step 1: Draw a rectangle to represent the whole, which is two-thirds (2/3).
Step 2: Divide the rectangle into three equal parts horizontally since the denominator of two-thirds is 3.
Step 3: Shade two of the three parts to represent the numerator (2) in two-thirds.
Step 4: Draw another rectangle to represent the divisor, which is one-fifth (1/5).
Step 5: Divide the second rectangle into five equal parts horizontally since the denominator of one-fifth is 5.
Step 6: Shade one of the five parts to represent the numerator (1) in one-fifth.
Step 7: Count the number of shaded areas in the first rectangle (2 shaded parts) and the number of shaded areas in the second rectangle (1 shaded part).
Step 8: The quotient is the number of shaded areas in the first rectangle (2 shaded parts) divided by the number of shaded areas in the second rectangle (1 shaded part).
Step 9: Therefore, the quotient of two-thirds divided by one-fifth is 2 divided by 1, which is equal to 2.
To check our work, let's also find the quotient of two-thirds divided by one-fifth using numerical operations only.
To divide fractions, we invert the divisor and multiply. So, two-thirds divided by one-fifth can be written as (2/3) x (5/1).
Multiplying the numerators (2 x 5) gives us 10, and multiplying the denominators (3 x 1) gives us 3. Therefore, the quotient of two-thirds divided by one-fifth is 10/3.
We can simplify 10/3 by dividing both the numerator and denominator by their greatest common divisor, which is 1. This gives us 10/3 as the simplified quotient.
Therefore, using numerical operations only, we have found that the quotient of two-thirds divided by one-fifth is 10/3, which is approximately 3.33 (rounded to two decimal places).
In conclusion, both the area model method and the numerical operations method confirm that the quotient of two-thirds divided by one-fifth is 2 or approximately 3.33.