Lynn Byrd, Greg Byrd and, Chris Pearce Solutions for Chapter: Fractions, Exercise 4: Exercise 7.3

Benji is making a sauce. This is the recipe he uses.

Sauce serve for $4$ people:

$\frac{2}{3}$ cup of cashew nuts   $2$ tablespoons of honey

$\frac{1}{3}$ cup of water             $\frac{1}{2}$ teaspoon of salt

$\frac{1}{4}$ cup of vinegar

Benji makes sauce for two people, so he multiplies all the amounts by $\frac{1}{2}$. Copy and complete the table, which shows the amount of each ingredient that Benji needs.

Area of a square can be calculated by using the formula ${\mathrm{side}}^2$. What methods can you use to square a fraction? For example, what is ${\left(\frac{3}{4}\right)}^2$?

Arun says, "when you multiply two proper fractions together, you will never get an answer bigger than $1$". Is Arun correct? Explain your answer.

Samara uses the following method to estimate the answer to a multiplication.

Question: Work out $\frac{3}{4}\times \frac{1}{6}$

Estimate: $\frac{3}{4}$ is greater than $\frac{1}{2}$, but less than $1$.

                $\frac{1}{2}$ of $\frac{1}{6}$ is $\frac{1}{12}$, and $1\times \frac{1}{6}=\frac{1}{6}$

So, the answer must be greater than $\frac{1}{12}$ but is smaller than $\frac{1}{6}$.

Accurate $\frac{3}{4}\times \frac{1}{6}=\frac{3}{24}=\frac{1}{8}$

$\frac{1}{8}$ is greater than $\frac{1}{12}$ but smaller than $\frac{1}{6}$.

Now, use the Samara's method to first work out the given multiplication an estimate and then to find the accurate answer.

$\frac{2}{3}\times \frac{1}{8}$

Samara uses the following method to estimate the answer to a multiplication.

Question: Work out $\frac{3}{4}\times \frac{1}{6}$

Estimate: $\frac{3}{4}$ is greater than $\frac{1}{2}$, but less than $1$.

                $\frac{1}{2}$ of $\frac{1}{6}$ is $\frac{1}{12}$, and $1\times \frac{1}{6}=\frac{1}{6}$

So, the answer must be greater than $\frac{1}{12}$ but is smaller than $\frac{1}{6}$.

Accurate $\frac{3}{4}\times \frac{1}{6}=\frac{3}{24}=\frac{1}{8}$

$\frac{1}{8}$ is greater than $\frac{1}{12}$ but smaller than $\frac{1}{6}$.

Now, use the Samara's method to first work out the given multiplication an estimate and then to find the accurate answer.

$\frac{2}{9}\times \frac{1}{4}$

Samara uses the following method to estimate the answer to a multiplication.

Question: Work out $\frac{3}{4}\times \frac{1}{6}$

Estimate: $\frac{3}{4}$ is greater than $\frac{1}{2}$, but less than $1$.

                $\frac{1}{2}$ of $\frac{1}{6}$ is $\frac{1}{12}$, and $1\times \frac{1}{6}=\frac{1}{6}$

So, the answer must be greater than $\frac{1}{12}$ but is smaller than $\frac{1}{6}$.

Accurate $\frac{3}{4}\times \frac{1}{6}=\frac{3}{24}=\frac{1}{8}$

$\frac{1}{8}$ is greater than $\frac{1}{12}$ but smaller than $\frac{1}{6}$.

Now, use the Samara's method to first work out the given multiplication an estimate and then to find the accurate answer.

$\frac{5}{8}\times \frac{4}{9}$

Copy the secret code box.

Work out the answer to each of the multiplications in the box given below.

Find the answer in the secret code box, then write the letter from the multiplications box above the answer. For example, the first multiplication is $\frac{1}{4}\times \frac{2}{3}$.

$\frac{1}{4}\times \frac{2}{3}=\frac{2}{12}=\frac{1}{6}$, so write $E$ above $\frac{1}{6}$ in the secret code box. What is the secret message?

The diagram shows a square joined to a rectangle.

What is the total area of the shape?