# 1.6 Add and subtract fractions  (Page 3/4)

 Page 3 / 4

Simplify: $\frac{3a}{4}-\phantom{\rule{0.2em}{0ex}}\frac{8}{9}$ $\frac{3a}{4}·\frac{8}{9}.$

$\frac{27a-32}{36}$ $\frac{2a}{3}$

Simplify: $\frac{4k}{5}-\phantom{\rule{0.2em}{0ex}}\frac{1}{6}$ $\frac{4k}{5}·\frac{1}{6}.$

$\frac{24k-5}{30}$ $\frac{2k}{15}$

## Use the order of operations to simplify complex fractions

We have seen that a complex fraction is a fraction in which the numerator or denominator contains a fraction. The fraction bar indicates division . We simplified the complex fraction $\frac{\frac{3}{4}}{\frac{5}{8}}$ by dividing $\frac{3}{4}$ by $\frac{5}{8}.$

Now we’ll look at complex fractions where the numerator or denominator contains an expression that can be simplified. So we first must completely simplify the numerator and denominator separately using the order of operations. Then we divide the numerator by the denominator.

## How to simplify complex fractions

Simplify: $\frac{{\left(\frac{1}{2}\right)}^{2}}{4+{3}^{2}}.$

## Solution

Simplify: $\frac{{\left(\frac{1}{3}\right)}^{2}}{{2}^{3}+2}.$

$\frac{1}{90}$

Simplify: $\frac{1+{4}^{2}}{{\left(\frac{1}{4}\right)}^{2}}.$

$272$

## Simplify complex fractions.

1. Simplify the numerator.
2. Simplify the denominator.
3. Divide the numerator by the denominator. Simplify if possible.

Simplify: $\frac{\frac{1}{2}+\frac{2}{3}}{\frac{3}{4}-\phantom{\rule{0.2em}{0ex}}\frac{1}{6}}.$

## Solution

It may help to put parentheses around the numerator and the denominator.

$\begin{array}{cccccc}& & & & & \frac{\left(\frac{1}{2}+\frac{2}{3}\right)}{\left(\frac{3}{4}-\phantom{\rule{0.2em}{0ex}}\frac{1}{6}\right)}\hfill \\ \\ \\ \begin{array}{c}\text{Simplify the numerator (LCD = 6)}\hfill \\ \text{and simplify the denominator (LCD = 12).}\hfill \end{array}\hfill & & & & & \hfill \frac{\left(\frac{3}{6}+\frac{4}{6}\right)}{\left(\frac{9}{12}-\phantom{\rule{0.2em}{0ex}}\frac{2}{12}\right)}\hfill \\ \\ \\ \text{Simplify.}\hfill & & & & & \hfill \frac{\left(\frac{7}{6}\right)}{\left(\frac{7}{12}\right)}\hfill \\ \\ \\ \text{Divide the numerator by the denominator.}\hfill & & & & & \hfill \frac{7}{6}÷\frac{7}{12}\hfill \\ \\ \\ \text{Simplify.}\hfill & & & & & \hfill \frac{7}{6}·\frac{12}{7}\hfill \\ \\ \\ \text{Divide out common factors.}\hfill & & & & & \hfill \frac{7·6·2}{6·7}\hfill \\ \\ \\ \text{Simplify.}\hfill & & & & & \hfill 2\hfill \end{array}$

Simplify: $\frac{\frac{1}{3}+\frac{1}{2}}{\frac{3}{4}-\phantom{\rule{0.2em}{0ex}}\frac{1}{3}}.$

2

Simplify: $\frac{\frac{2}{3}-\phantom{\rule{0.2em}{0ex}}\frac{1}{2}}{\frac{1}{4}+\frac{1}{3}}.$

$\frac{2}{7}$

## Evaluate variable expressions with fractions

We have evaluated expressions before, but now we can evaluate expressions with fractions. Remember, to evaluate an expression, we substitute the value of the variable into the expression and then simplify.

Evaluate $x+\frac{1}{3}$ when $x=-\phantom{\rule{0.2em}{0ex}}\frac{1}{3}$ $x=-\phantom{\rule{0.2em}{0ex}}\frac{3}{4}.$

1. To evaluate $x+\frac{1}{3}$ when $x=-\phantom{\rule{0.2em}{0ex}}\frac{1}{3},$ substitute $-\phantom{\rule{0.2em}{0ex}}\frac{1}{3}$ for $x$ in the expression.
 Simplify. $\phantom{\rule{18em}{0ex}}$ 0

2. To evaluate $x+\frac{1}{3}$ when $x=-\phantom{\rule{0.2em}{0ex}}\frac{3}{4},$ we substitute $-\phantom{\rule{0.2em}{0ex}}\frac{3}{4}$ for x in the expression.
 Rewrite as equivalent fractions with the LCD, 12. Simplify. Add. $-\phantom{\rule{0.2em}{0ex}}\frac{5}{12}$

Evaluate $x+\frac{3}{4}$ when $x=-\phantom{\rule{0.2em}{0ex}}\frac{7}{4}$ $x=-\phantom{\rule{0.2em}{0ex}}\frac{5}{4}.$

$-1$ $-\phantom{\rule{0.2em}{0ex}}\frac{1}{2}$

Evaluate $y+\frac{1}{2}$ when $y=\frac{2}{3}$ $y=-\phantom{\rule{0.2em}{0ex}}\frac{3}{4}.$

$\frac{7}{6}$ $-\phantom{\rule{0.2em}{0ex}}\frac{1}{12}$

Evaluate $-\phantom{\rule{0.2em}{0ex}}\frac{5}{6}-y$ when $y=-\phantom{\rule{0.2em}{0ex}}\frac{2}{3}.$

## Solution

 Rewrite as equivalent fractions with the LCD, 6. Subtract. Simplify. $-\phantom{\rule{0.2em}{0ex}}\frac{1}{6}$

Evaluate $-\phantom{\rule{0.2em}{0ex}}\frac{1}{2}-y$ when $y=-\phantom{\rule{0.2em}{0ex}}\frac{1}{4}.$

$-\phantom{\rule{0.2em}{0ex}}\frac{1}{4}$

Evaluate $-\phantom{\rule{0.2em}{0ex}}\frac{3}{8}-y$ when $x=-\phantom{\rule{0.2em}{0ex}}\frac{5}{2}.$

$-\phantom{\rule{0.2em}{0ex}}\frac{17}{8}$

Evaluate $2{x}^{2}y$ when $x=\frac{1}{4}$ and $y=-\phantom{\rule{0.2em}{0ex}}\frac{2}{3}.$

## Solution

Substitute the values into the expression.

 $2{x}^{2}y$ Simplify exponents first. $2\left(\frac{1}{16}\right)\left(-\phantom{\rule{0.2em}{0ex}}\frac{2}{3}\right)$ Multiply. Divide out the common factors. Notice we write 16 as $2\cdot 2\cdot 4$ to make it easy to remove common factors. $-\phantom{\rule{0.2em}{0ex}}\frac{\overline{)2}\cdot 1\cdot \overline{)2}}{\overline{)2}\cdot \overline{)2}\cdot 4\cdot 3}$ Simplify. $-\phantom{\rule{0.2em}{0ex}}\frac{1}{12}$

Evaluate $3a{b}^{2}$ when $a=-\phantom{\rule{0.2em}{0ex}}\frac{2}{3}$ and $b=-\phantom{\rule{0.2em}{0ex}}\frac{1}{2}.$

$-\phantom{\rule{0.2em}{0ex}}\frac{1}{2}$

Evaluate $4{c}^{3}d$ when $c=-\phantom{\rule{0.2em}{0ex}}\frac{1}{2}$ and $d=-\phantom{\rule{0.2em}{0ex}}\frac{4}{3}.$

$\frac{2}{3}$

The next example will have only variables, no constants.

Evaluate $\frac{p+q}{r}$ when $p=-4,q=-2,\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}r=8.$

## Solution

To evaluate $\frac{p+q}{r}$ when $p=-4,q=-2,\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}r=8,$ we substitute the values into the expression.

 $\frac{p+q}{r}$ Add in the numerator first. $\frac{-6}{8}$ Simplify. $-\phantom{\rule{0.2em}{0ex}}\frac{3}{4}$

Evaluate $\frac{a+b}{c}$ when $a=-8,b=-7,\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}c=6.$

$-\phantom{\rule{0.2em}{0ex}}\frac{5}{2}$

Evaluate $\frac{x+y}{z}$ when $x=9,y=-18,\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}z=-6.$

$\frac{3}{2}$

## Key concepts

• Fraction Addition and Subtraction: If $a,b,\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}c$ are numbers where $c\ne 0,$ then
$\frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}$ and $\frac{a}{c}-\phantom{\rule{0.2em}{0ex}}\frac{b}{c}=\frac{a-b}{c}.$
To add or subtract fractions, add or subtract the numerators and place the result over the common denominator.
• Strategy for Adding or Subtracting Fractions
1. Do they have a common denominator?
Yes—go to step 2.
No—Rewrite each fraction with the LCD (Least Common Denominator). Find the LCD. Change each fraction into an equivalent fraction with the LCD as its denominator.
2. Add or subtract the fractions.
3. Simplify, if possible. To multiply or divide fractions, an LCD IS NOT needed. To add or subtract fractions, an LCD IS needed.
• Simplify Complex Fractions
1. Simplify the numerator.
2. Simplify the denominator.
3. Divide the numerator by the denominator. Simplify if possible.

## Practice makes perfect

Add and Subtract Fractions with a Common Denominator

$\frac{6}{13}+\frac{5}{13}$

$\frac{11}{13}$

$\frac{4}{15}+\frac{7}{15}$

$\frac{x}{4}+\frac{3}{4}$

$\frac{x+3}{4}$

$\frac{8}{q}+\frac{6}{q}$

$-\phantom{\rule{0.2em}{0ex}}\frac{3}{16}+\left(-\phantom{\rule{0.2em}{0ex}}\frac{7}{16}\right)$

$-\phantom{\rule{0.2em}{0ex}}\frac{5}{8}$

$-\phantom{\rule{0.2em}{0ex}}\frac{5}{16}+\left(-\phantom{\rule{0.2em}{0ex}}\frac{9}{16}\right)$

$-\phantom{\rule{0.2em}{0ex}}\frac{8}{17}+\frac{15}{17}$

$\frac{7}{17}$

$-\phantom{\rule{0.2em}{0ex}}\frac{9}{19}+\frac{17}{19}$

$\frac{6}{13}+\left(-\phantom{\rule{0.2em}{0ex}}\frac{10}{13}\right)+\left(-\phantom{\rule{0.2em}{0ex}}\frac{12}{13}\right)$

$-\phantom{\rule{0.2em}{0ex}}\frac{16}{13}$

$\frac{5}{12}+\left(-\phantom{\rule{0.2em}{0ex}}\frac{7}{12}\right)+\left(-\phantom{\rule{0.2em}{0ex}}\frac{11}{12}\right)$

In the following exercises, subtract.

$\frac{11}{15}-\phantom{\rule{0.2em}{0ex}}\frac{7}{15}$

$\frac{4}{15}$

$\frac{9}{13}-\phantom{\rule{0.2em}{0ex}}\frac{4}{13}$

$\frac{11}{12}-\phantom{\rule{0.2em}{0ex}}\frac{5}{12}$

$\frac{1}{2}$

$\frac{7}{12}-\phantom{\rule{0.2em}{0ex}}\frac{5}{12}$

$\frac{19}{21}-\phantom{\rule{0.2em}{0ex}}\frac{4}{21}$

$\frac{5}{7}$

$\frac{17}{21}-\phantom{\rule{0.2em}{0ex}}\frac{8}{21}$

$\frac{5y}{8}-\phantom{\rule{0.2em}{0ex}}\frac{7}{8}$

$\frac{5y-7}{8}$

$\frac{11z}{13}-\phantom{\rule{0.2em}{0ex}}\frac{8}{13}$

$-\phantom{\rule{0.2em}{0ex}}\frac{23}{u}-\phantom{\rule{0.2em}{0ex}}\frac{15}{u}$

$-\phantom{\rule{0.2em}{0ex}}\frac{38}{u}$

$-\phantom{\rule{0.2em}{0ex}}\frac{29}{v}-\phantom{\rule{0.2em}{0ex}}\frac{26}{v}$

$-\phantom{\rule{0.2em}{0ex}}\frac{3}{5}-\left(-\phantom{\rule{0.2em}{0ex}}\frac{4}{5}\right)$

$\frac{1}{5}$

$-\phantom{\rule{0.2em}{0ex}}\frac{3}{7}-\left(-\phantom{\rule{0.2em}{0ex}}\frac{5}{7}\right)$

$-\phantom{\rule{0.2em}{0ex}}\frac{7}{9}-\left(-\phantom{\rule{0.2em}{0ex}}\frac{5}{9}\right)$

$-\phantom{\rule{0.2em}{0ex}}\frac{2}{9}$

$-\phantom{\rule{0.2em}{0ex}}\frac{8}{11}-\left(-\phantom{\rule{0.2em}{0ex}}\frac{5}{11}\right)$

Mixed Practice

In the following exercises, simplify.

$-\phantom{\rule{0.2em}{0ex}}\frac{5}{18}·\frac{9}{10}$

$-\phantom{\rule{0.2em}{0ex}}\frac{1}{4}$

$-\phantom{\rule{0.2em}{0ex}}\frac{3}{14}·\frac{7}{12}$

$\frac{n}{5}-\phantom{\rule{0.2em}{0ex}}\frac{4}{5}$

$\frac{n-4}{5}$

$\frac{6}{11}-\phantom{\rule{0.2em}{0ex}}\frac{s}{11}$

$-\phantom{\rule{0.2em}{0ex}}\frac{7}{24}+\frac{2}{24}$

$-\phantom{\rule{0.2em}{0ex}}\frac{5}{24}$

$-\phantom{\rule{0.2em}{0ex}}\frac{5}{18}+\frac{1}{18}$

$\frac{8}{15}÷\frac{12}{5}$

$\frac{2}{9}$

$\frac{7}{12}÷\frac{9}{28}$

Add or Subtract Fractions with Different Denominators

In the following exercises, add or subtract.

$\frac{1}{2}+\frac{1}{7}$

$\frac{9}{14}$

$\frac{1}{3}+\frac{1}{8}$

$\frac{1}{3}-\left(-\phantom{\rule{0.2em}{0ex}}\frac{1}{9}\right)$

$\frac{4}{9}$

$\frac{1}{4}-\left(-\phantom{\rule{0.2em}{0ex}}\frac{1}{8}\right)$

$\frac{7}{12}+\frac{5}{8}$

$\frac{29}{24}$

$\frac{5}{12}+\frac{3}{8}$

$\frac{7}{12}-\phantom{\rule{0.2em}{0ex}}\frac{9}{16}$

$\frac{1}{48}$

$\frac{7}{16}-\phantom{\rule{0.2em}{0ex}}\frac{5}{12}$

$\frac{2}{3}-\phantom{\rule{0.2em}{0ex}}\frac{3}{8}$

$\frac{7}{24}$

$\frac{5}{6}-\phantom{\rule{0.2em}{0ex}}\frac{3}{4}$

$-\phantom{\rule{0.2em}{0ex}}\frac{11}{30}+\frac{27}{40}$

$\frac{37}{120}$

$-\phantom{\rule{0.2em}{0ex}}\frac{9}{20}+\frac{17}{30}$

$-\phantom{\rule{0.2em}{0ex}}\frac{13}{30}+\frac{25}{42}$

$\frac{17}{105}$

$-\phantom{\rule{0.2em}{0ex}}\frac{23}{30}+\frac{5}{48}$

$-\phantom{\rule{0.2em}{0ex}}\frac{39}{56}-\phantom{\rule{0.2em}{0ex}}\frac{22}{35}$

$-\phantom{\rule{0.2em}{0ex}}\frac{53}{40}$

$-\phantom{\rule{0.2em}{0ex}}\frac{33}{49}-\phantom{\rule{0.2em}{0ex}}\frac{18}{35}$

$-\phantom{\rule{0.2em}{0ex}}\frac{2}{3}-\left(-\phantom{\rule{0.2em}{0ex}}\frac{3}{4}\right)$

$\frac{1}{12}$

$-\phantom{\rule{0.2em}{0ex}}\frac{3}{4}-\left(-\phantom{\rule{0.2em}{0ex}}\frac{4}{5}\right)$

$1+\frac{7}{8}$

$\frac{15}{8}$

$1-\phantom{\rule{0.2em}{0ex}}\frac{3}{10}$

$\frac{x}{3}+\frac{1}{4}$

$\frac{4x+3}{12}$

$\frac{y}{2}+\frac{2}{3}$

$\frac{y}{4}-\phantom{\rule{0.2em}{0ex}}\frac{3}{5}$

$\frac{4y-12}{20}$

$\frac{x}{5}-\phantom{\rule{0.2em}{0ex}}\frac{1}{4}$

Mixed Practice

In the following exercises, simplify.

$\frac{2}{3}+\frac{1}{6}$ $\frac{2}{3}÷\frac{1}{6}$

$\frac{5}{6}$ 4

$-\phantom{\rule{0.2em}{0ex}}\frac{2}{5}-\phantom{\rule{0.2em}{0ex}}\frac{1}{8}$ $-\phantom{\rule{0.2em}{0ex}}\frac{2}{5}·\frac{1}{8}$

$\frac{5n}{6}÷\frac{8}{15}$ $\frac{5n}{6}-\phantom{\rule{0.2em}{0ex}}\frac{8}{15}$

$\frac{25n}{16}$ $\frac{25n-16}{30}$

$\frac{3a}{8}÷\frac{7}{12}$ $\frac{3a}{8}-\phantom{\rule{0.2em}{0ex}}\frac{7}{12}$

$-\phantom{\rule{0.2em}{0ex}}\frac{3}{8}÷\left(-\phantom{\rule{0.2em}{0ex}}\frac{3}{10}\right)$

$\frac{5}{4}$

$-\phantom{\rule{0.2em}{0ex}}\frac{5}{12}÷\left(-\phantom{\rule{0.2em}{0ex}}\frac{5}{9}\right)$

$-\phantom{\rule{0.2em}{0ex}}\frac{3}{8}+\frac{5}{12}$

$\frac{1}{24}$

$-\phantom{\rule{0.2em}{0ex}}\frac{1}{8}+\frac{7}{12}$

$\frac{5}{6}-\phantom{\rule{0.2em}{0ex}}\frac{1}{9}$

$\frac{13}{18}$

$\frac{5}{9}-\phantom{\rule{0.2em}{0ex}}\frac{1}{6}$

$-\phantom{\rule{0.2em}{0ex}}\frac{7}{15}-\phantom{\rule{0.2em}{0ex}}\frac{y}{4}$

$\frac{-28-15y}{60}$

$-\phantom{\rule{0.2em}{0ex}}\frac{3}{8}-\phantom{\rule{0.2em}{0ex}}\frac{x}{11}$

$\frac{11}{12a}·\frac{9a}{16}$

$\frac{33}{64}$

$\frac{10y}{13}·\frac{8}{15y}$

Use the Order of Operations to Simplify Complex Fractions

In the following exercises, simplify.

$\frac{{2}^{3}+{4}^{2}}{{\left(\frac{2}{3}\right)}^{2}}$

54

$\frac{{3}^{3}-{3}^{2}}{{\left(\frac{3}{4}\right)}^{2}}$

$\frac{{\left(\frac{3}{5}\right)}^{2}}{{\left(\frac{3}{7}\right)}^{2}}$

$\frac{49}{25}$

$\frac{{\left(\frac{3}{4}\right)}^{2}}{{\left(\frac{5}{8}\right)}^{2}}$

$\frac{2}{\frac{1}{3}+\frac{1}{5}}$

$\frac{15}{4}$

$\frac{5}{\frac{1}{4}+\frac{1}{3}}$

$\frac{\frac{7}{8}-\phantom{\rule{0.2em}{0ex}}\frac{2}{3}}{\frac{1}{2}+\frac{3}{8}}$

$\frac{5}{21}$

$\frac{\frac{3}{4}-\phantom{\rule{0.2em}{0ex}}\frac{3}{5}}{\frac{1}{4}+\frac{2}{5}}$

$\frac{1}{2}+\frac{2}{3}·\frac{5}{12}$

$\frac{7}{9}$

$\frac{1}{3}+\frac{2}{5}·\frac{3}{4}$

$1-\phantom{\rule{0.2em}{0ex}}\frac{3}{5}÷\frac{1}{10}$

$-5$

$1-\phantom{\rule{0.2em}{0ex}}\frac{5}{6}÷\frac{1}{12}$

$\frac{2}{3}+\frac{1}{6}+\frac{3}{4}$

$\frac{19}{12}$

$\frac{2}{3}+\frac{1}{4}+\frac{3}{5}$

$\frac{3}{8}-\phantom{\rule{0.2em}{0ex}}\frac{1}{6}+\frac{3}{4}$

$\frac{23}{24}$

$\frac{2}{5}+\frac{5}{8}-\phantom{\rule{0.2em}{0ex}}\frac{3}{4}$

$12\left(\frac{9}{20}-\phantom{\rule{0.2em}{0ex}}\frac{4}{15}\right)$

$\frac{11}{5}$

$8\left(\frac{15}{16}-\phantom{\rule{0.2em}{0ex}}\frac{5}{6}\right)$

$\frac{\frac{5}{8}+\frac{1}{6}}{\frac{19}{24}}$

1

$\frac{\frac{1}{6}+\frac{3}{10}}{\frac{14}{30}}$

$\left(\frac{5}{9}+\frac{1}{6}\right)÷\left(\frac{2}{3}-\phantom{\rule{0.2em}{0ex}}\frac{1}{2}\right)$

$\frac{13}{3}$

$\left(\frac{3}{4}+\frac{1}{6}\right)÷\left(\frac{5}{8}-\phantom{\rule{0.2em}{0ex}}\frac{1}{3}\right)$

Evaluate Variable Expressions with Fractions

In the following exercises, evaluate.

$x+\left(-\phantom{\rule{0.2em}{0ex}}\frac{5}{6}\right)$ when
$x=\frac{1}{3}$
$x=-\phantom{\rule{0.2em}{0ex}}\frac{1}{6}$

$-\phantom{\rule{0.2em}{0ex}}\frac{1}{2}$ $-1$

$x+\left(-\phantom{\rule{0.2em}{0ex}}\frac{11}{12}\right)$ when
$x=\frac{11}{12}$
$x=\frac{3}{4}$

$x-\phantom{\rule{0.2em}{0ex}}\frac{2}{5}$ when
$x=\frac{3}{5}$
$x=-\phantom{\rule{0.2em}{0ex}}\frac{3}{5}$

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

$x-\phantom{\rule{0.2em}{0ex}}\frac{1}{3}$ when
$x=\frac{2}{3}$
$x=-\phantom{\rule{0.2em}{0ex}}\frac{2}{3}$

$\frac{7}{10}-w$ when
$w=\frac{1}{2}$
$w=-\phantom{\rule{0.2em}{0ex}}\frac{1}{2}$

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

$\frac{5}{12}-w$ when
$w=\frac{1}{4}$
$w=-\phantom{\rule{0.2em}{0ex}}\frac{1}{4}$

$2{x}^{2}{y}^{3}$ when $x=-\phantom{\rule{0.2em}{0ex}}\frac{2}{3}$ and $y=-\phantom{\rule{0.2em}{0ex}}\frac{1}{2}$

$-\phantom{\rule{0.2em}{0ex}}\frac{1}{9}$

$8{u}^{2}{v}^{3}$ when $u=-\phantom{\rule{0.2em}{0ex}}\frac{3}{4}$ and $v=-\phantom{\rule{0.2em}{0ex}}\frac{1}{2}$

$\frac{a+b}{a-b}$ when $a=-3,b=8$

$-\phantom{\rule{0.2em}{0ex}}\frac{5}{11}$

$\frac{r-s}{r+s}$ when $r=10,s=-5$

## Everyday math

Decorating Laronda is making covers for the throw pillows on her sofa. For each pillow cover, she needs $\frac{1}{2}$ yard of print fabric and $\frac{3}{8}$ yard of solid fabric. What is the total amount of fabric Laronda needs for each pillow cover?

$\frac{7}{8}$ yard

Baking Vanessa is baking chocolate chip cookies and oatmeal cookies. She needs $\frac{1}{2}$ cup of sugar for the chocolate chip cookies and $\frac{1}{4}$ of sugar for the oatmeal cookies. How much sugar does she need altogether?

## Writing exercises

Why do you need a common denominator to add or subtract fractions? Explain.

How do you find the LCD of 2 fractions?

## Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

After looking at the checklist, do you think you are well-prepared for the next chapter? Why or why not?

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Mckenzie
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90 minutes
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13.5
Pervaiz
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bruce
greater than \$110,000
Michael