The Number System

1. To divide fractions, multiply by the reciprocal:

$\frac{3}{4} \div \frac{1}{2} = \frac{3}{4} \times \frac{2}{1} = \frac{3 \times 2}{4 \times 1} = \frac{6}{4} = \frac{3}{2}$

The answer is $\frac{3}{2}$, or equivalently $1\frac{1}{2}$.

2. We need $4 \div \frac{2}{3}$. Rewrite $4$ as $\frac{4}{1}$ and multiply by the reciprocal:

$\frac{4}{1} \div \frac{2}{3} = \frac{4}{1} \times \frac{3}{2} = \frac{12}{2} = 6$

You can make $6$ batches.

3. Align the decimal points and add:

$\begin{aligned} &\phantom{+}12.85 \\ &+\phantom{1}7.60 \\ &\overline{\phantom{+}20.45} \end{aligned}$

The sum is $20.45$.

4. Subtract, aligning decimal points:

$\begin{aligned} &\phantom{-}9.40 \\ &-3.75 \\ &\overline{\phantom{-}5.65} \end{aligned}$

There are $5.65$ meters of ribbon remaining.

5. Multiply ignoring the decimals first: $46 \times 35 = 1610$. The two original numbers have a combined $2$ decimal places, so place the decimal to get:

$4.6 \times 3.5 = 16.10 = 16.1$

The product is $16.1$.