Fractions and Decimals

1. To find equivalent fractions, multiply (or divide) both the numerator and denominator by the same number.

Multiply by 2:

$\frac{3 \times 2}{5 \times 2} = \frac{6}{10}$

Multiply by 3:

$\frac{3 \times 3}{5 \times 3} = \frac{9}{15}$

So $\frac{6}{10}$ and $\frac{9}{15}$ are both equivalent to $\frac{3}{5}$.

2. Comparing $\frac{3}{8}$ and $\frac{5}{8}$:

Both fractions have the same denominator (8), so we compare numerators. Since $3 < 5$:

$\frac{3}{8} < \frac{5}{8}$

Comparing $\frac{2}{3}$ and $\frac{2}{5}$:

Both fractions have the same numerator (2), so we compare the sizes of the pieces. Thirds are larger pieces than fifths (fewer parts means bigger pieces). Since the pieces in $\frac{2}{3}$ are bigger:

$\frac{2}{3} > \frac{2}{5}$

3. Both fractions have the same denominator, so we add the numerators:

$\frac{2}{6} + \frac{3}{6} = \frac{2 + 3}{6} = \frac{5}{6}$

The students ate $\frac{5}{6}$ of the pizza.

The fraction left over:

$\frac{6}{6} - \frac{5}{6} = \frac{1}{6}$

There is $\frac{1}{6}$ of the pizza left.

4. $\frac{7}{10}$ means 7 tenths. In decimal form:

$\frac{7}{10} = 0.7$

$\frac{23}{100}$ means 23 hundredths. In decimal form:

$\frac{23}{100} = 0.23$

5. Both fractions have the same denominator (4), so we add the numerators:

$\frac{3}{4} + \frac{2}{4} = \frac{3 + 2}{4} = \frac{5}{4}$

We can write this as a mixed number: $\frac{5}{4} = 1\frac{1}{4}$.

This fraction is already in simplest form (5 and 4 share no common factor other than 1).

You need $1\frac{1}{4}$ cups of flour in total.