9.1: Number Talk: Greater Than 1 or Less Than 1?
Decide whether each of the following is greater than 1 or less than 1.
- $\frac12\div\frac14$
- $1\div\frac34$
- $\frac23\div\frac78$
- $2\frac78\div2\frac35$
Let’s practice dividing fractions in different situations.
Decide whether each of the following is greater than 1 or less than 1.
How many liters of water fit in the water dispenser?
Write a multiplication equation and a division equation for the question, then find the answer. Draw a diagram, if needed. Check your answer using the multiplication equation.
Write a multiplication equation and a division equation and draw a diagram to represent each situation and question. Then find the answer. Explain your reasoning.
Trade descriptions with a member of your group.
Sometimes we have to think carefully about how to solve a problem that involves multiplication and division. Diagrams and equations can help us.
Let’s take this example: $\frac34$ of a pound of rice fills $\frac25$ of a container.
There are two whole amounts to keep track of: 1 whole pound, and 1 whole container. The equations we write and the diagram we draw depend on what question we are trying to answer. Here are two questions that could be asked:
We can represent and answer the first question (how many pounds fill a whole container) with:
$$\frac 25 \boldcdot {?} = \frac 34$$
$$\frac 34 \div \frac 25 = {?}$$
If $\frac25$ of a container is filled with $\frac 34$ pound, then $\frac 15$ of a container is filled with half of $\frac34$, or $\frac38$, pound. One whole container then has $5 \boldcdot \frac38$ (or $\frac {15}{8}$) pounds.
We can represent and answer the second question (what fraction of the container 1 pound fills) with:
$$\frac34 \boldcdot {?} = \frac25$$
$$\frac25 \div \frac34 ={?}$$
If $\frac 34$ pound fills $\frac25$ of a container, then $\frac14$ pound fills a third of $\frac25$, or $\frac {2}{15}$, of a container. One whole pound then fills $4 \boldcdot \frac{2}{15}$ (or $\frac {8}{15}$) of a container.