Fraction Multiplication

1. (a) $3 \times \frac{3}{4}$

(b)

$3 \times \frac{3}{4} = \frac{3 \times 3}{4} = \frac{9}{4}$

As a mixed number: $\frac{9}{4} = 2\frac{1}{4}$

Elena needs $\frac{9}{4}$ cups, or $2\frac{1}{4}$ cups of sugar.

2. (a) $4 \times \frac{2}{5}$

(b)

$4 \times \frac{2}{5} = \frac{4 \times 2}{5} = \frac{8}{5}$

As a mixed number: $\frac{8}{5} = 1\frac{3}{5}$

He jogged $\frac{8}{5}$ miles, or $1\frac{3}{5}$ miles.

(c) No, he did not meet his goal. $1\frac{3}{5} = 1.6$ miles, which is less than $2$ miles. He is $2 - 1\frac{3}{5} = \frac{2}{5}$ of a mile short.

3. (a) $0.45 < 0.54$

In the tenths place: $4 < 5$, so $0.45$ is less.

(b) $0.8 = 0.80$

$0.8$ is the same as $0.80$ because adding a zero to the right of the last decimal digit does not change the value. Both equal $\frac{80}{100}$.

(c) $0.29 < 0.3$

Convert $0.3$ to hundredths: $0.3 = 0.30$. Now compare: $0.29 < 0.30$.

(d) $0.06 < 0.60$

In the tenths place: $0 < 6$, so $0.06$ is much less than $0.60$.

4. (a)

$5 \times \frac{3}{8} = \frac{5 \times 3}{8} = \frac{15}{8}$

(b) Convert to a mixed number:

$\frac{15}{8} = 1\frac{7}{8}$

since $15 \div 8 = 1$ remainder $7$.

The total length is $1\frac{7}{8}$ meters.

5. (a) First, write all measurements with the same number of decimal places (hundredths):

$0.35, \quad 0.40, \quad 0.09, \quad 0.41$

Now order from least to greatest:

$0.09 < 0.35 < 0.40 < 0.41$

Or using the original forms: $0.09, \; 0.35, \; 0.4, \; 0.41$.

(b) The two closest measurements are $0.4$ and $0.41$. Their difference is:

$0.41 - 0.40 = 0.01$

This is the smallest gap between any two adjacent values in the sorted list. (For comparison, $0.40 - 0.35 = 0.05$ and $0.35 - 0.09 = 0.26$.)