1.1 Fractions

The use of calculators or other technologies are strictly prohibited for this assignment.

1 Equivalent Fractions

If you cut a pizza in half and ate one of the two slices, you ate \(\frac{1}{2}\) the pizza. That would be the same as cutting the pizza into four equal slices and eating 2 of the four slices: \(\frac{2}{4}\) of the pizza. That’s because \(\frac{1}{2} = \frac{2}{4}\): these are equivalent fractions.

If you take a fraction like \(\frac{1}{2}\) and multiply the numerator and the denominator by the same thing, you get an equivalent fraction. See that \(\frac{1}{2} = \frac{2}{4}\) by taking \(\frac{1}{2}\) and multiplying the numerator and denominator both by 2.

  1. Are these equivalent fractions? \(\frac{3}{4}\) and \(\frac{9}{12}\). Explain how you know.

  2. If you start with \(\frac{2}{3}\), what number did you multiply both the top and bottom by to get \(\frac{10}{15}\)?

  3. If you multiply both the numerator and the denominator of the fraction \(\frac{x}{3}\) by 4, what fraction do you get?

  4. If \(x > 0\), what is larger: \(\frac{x}{2}\) or \(\frac{3x}{6}\)?

  5. If \(x > 0\), what is larger: \(\frac{x}{2}\) or \(\frac{4x}{6}\)?

  6. Solve for \(y\): \(\frac{3}{4} = \frac{y}{8}\).

2 Adding Fractions

  1. What is the least common multiple of 6 and 18?

  2. Combine into one term and then simplify: \(\frac{1}{6} + \frac{5}{18}\).

  3. Combine into one term: \(\frac{x + 10}{12} + \frac{2y}{5}\).

  4. Combine into one term: \(\frac{a}{b} - \frac{c}{d}\).

3 Fraction Multiplication as Scaling

  1. Identify the largest of the three terms just by looking at them: \(\frac{2}{3} \times \frac{5}{4}\), or \(\frac{4}{5} \times \frac{2}{3}\), or \(\frac{8 \times 2}{3 \times 8}\)

4 Dividing a fraction by a whole number

  1. Draw a picture to visualize (no need to include the picture) and then answer: what is \(\frac{1}{2} \div 3\)?

  2. Draw a picture to visualize (no need to include the picture) and then answer: what is \(\frac{1}{3} \div 2\)?

5 Reciprocals

  1. How many times does \(\frac{1}{2}\) go into 1?

  2. How many times does \(\frac{3}{2}\) go into 1?

  3. Simplify \(\frac{1}{1/2}\).

  4. Simplify \(\frac{1}{3/2}\).

6 Fraction Division

  1. Simplify \(\frac{1}{3} \div \frac{1}{3}\). That is, how many times does 1/3 go into 1/3?

  2. Simplify \(\frac{1}{3} \div \frac{2}{3}\).

  3. Simplify \(\frac{1}{3} \div \frac{16}{24}\).