# 1.1 Fractions

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

## 1 Equivalent Fractions

<iframe width="300" height="auto" src="https://www.youtube.com/embed/U2ovEuEUxXQ" title="Equivalent fractions | Fractions | Pre-Algebra | Khan Academy" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe>

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.

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

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

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

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d) If $x > 0$, what is larger: $\frac{x}{2}$ or $\frac{3x}{6}$?

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e) If $x > 0$, what is larger: $\frac{x}{2}$ or $\frac{4x}{6}$?

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f) Solve for $y$: $\frac{3}{4} = \frac{y}{8}$.

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## 2 Adding Fractions

<iframe width="300" height="auto" src="https://www.youtube.com/embed/bcCLKACsYJ0" title="Adding fractions with unlike denominators" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe>

a) What is the least common multiple of 6 and 18?

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

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

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

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## 3 Fraction Multiplication as Scaling

<iframe width="300" height="auto" src="https://www.youtube.com/embed/yUYDhmQsiXY" title="Seeing multiplication as scaling with fractions | Fractions | Pre-Algebra | Khan Academy" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe>

a) 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 $\frac{8 \times 2}{3 \times 8}$

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## 4 Dividing a fraction by a whole number

<iframe width="300" height="auto" src="https://www.youtube.com/embed/RygpFkLCSaM" title="Visually dividing unit fraction by a whole number" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe>

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

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

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## 5 Reciprocals

<iframe width="300" height="auto" src="https://www.youtube.com/embed/yM9Yrz69Tys" title="Meaning of the reciprocal" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe>

a) How many times does $\frac{1}{2}$ go into 1?

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b) How many times does $\frac{3}{2}$ go into 1?

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c) Simplify $\frac{1}{1/2}$.

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d) Simplify $\frac{1}{3/2}$.

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## 6 Fraction Division

<iframe width="300" height="auto" src="https://www.youtube.com/embed/m-pRnFIeoNA" title="Dividing fractions example | Fractions | Pre-Algebra | Khan Academy" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe>

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

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b) Simplify $\frac{1}{3} \div \frac{2}{3}$.

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

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