# 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?

He charges $125 per job. His monthly expenses are$1,600. How many jobs must he work in order to make a profit of at least $2,400? Alicia Reply at least 20 Ayla what are the steps? Alicia 6.4 jobs Grahame 32 Grahame what is algebra Azhar Reply repeated addition and subtraction of the order of operations. i love algebra I'm obsessed. Shemiah hi Krekar One-fourth of the candies in a bag of M&M’s are red. If there are 23 red candies, how many candies are in the bag? Leanna Reply rectangular field solutions Navin Reply What is this? Donna the proudact of 3x^3-5×^2+3 and 2x^2+5x-4 in z7[x]/ is anas Reply ? Choli a rock is thrown directly upward with an initial velocity of 96feet per second from a cliff 190 feet above a beach. The hight of tha rock above the beach after t second is given by the equation h=_16t^2+96t+190 Usman Stella bought a dinette set on sale for$725. The original price was $1,299. To the nearest tenth of a percent, what was the rate of discount? Manhwa Reply 44.19% Scott 40.22% Terence 44.2% Orlando I don't know Donna if you want the discounted price subtract$725 from $1299. then divide the answer by$1299. you get 0.4419... but as percent you get 44.19... but to the nearest tenth... round .19 to .2 and you get 44.2%
Orlando
you could also just divide $725/$1299 and then subtract it from 1. then you get the same answer.
Orlando
p mulripied-5 and add 30 to it
Tausif
Tausif
Can you explain further
p mulripied-5 and add to 30
Tausif
-5p+30?
Corey
p=-5+30
Jacob
How do you find divisible numbers without a calculator?
TAKE OFF THE LAST DIGIT AND MULTIPLY IT 9. SUBTRACT IT THE DIGITS YOU HAVE LEFT. IF THE ANSWER DIVIDES BY 13(OR IS ZERO), THEN YOUR ORIGINAL NUMBER WILL ALSO DIVIDE BY 13!IS DIVISIBLE BY 13
BAINAMA
When she graduates college, Linda will owe $43,000 in student loans. The interest rate on the federal loans is 4.5% and the rate on the private bank loans is 2%. The total interest she owes for one year was$1,585. What is the amount of each loan?
Sean took the bus from Seattle to Boise, a distance of 506 miles. If the trip took 7 2/3 hours, what was the speed of the bus?
66miles/hour
snigdha
How did you work it out?
Esther
s=mi/hr 2/3~0.67 s=506mi/7.67hr = ~66 mi/hr
Orlando
hello, I have algebra phobia. Subtracting negative numbers always seem to get me confused.
what do you need help in?
Felix
Heather
look at the numbers if they have different signs, it's like subtracting....but you keep the sign of the largest number...
Felix
for example.... -19 + 7.... different signs...subtract.... 12 keep the sign of the "largest" number 19 is bigger than 7.... 19 has the negative sign... Therefore, -12 is your answer...
Felix
—12
Thanks Felix.l also get confused with signs.
Esther
Thank you for this
Shatey
ty
Graham
think about it like you lost $19 (-19), then found$7(+7). Totally you lost just $12 (-12) Annushka I used to struggle a lot with negative numbers and math in general what I typically do is look at it in terms of money I have -$5 in my account I then take out 5 more dollars how much do I have in my account well-\$10 ... I also for a long time would draw it out on a number line to visualize it
Meg
practicing with smaller numbers to understand then working with larger numbers helps too and the song/rhyme same sign add and keep opposite signs subtract keep the sign of the bigger # then you'll be exact
Meg
Bruce drives his car for his job. The equation R=0.575m+42 models the relation between the amount in dollars, R, that he is reimbursed and the number of miles, m, he drives in one day. Find the amount Bruce is reimbursed on a day when he drives 220 miles
168.50=R
Heather
john is 5years older than wanjiru.the sum of their years is27years.what is the age of each
46
mustee
j 17 w 11
Joseph
john is 16. wanjiru is 11.
Felix
27-5=22 22÷2=11 11+5=16
Joyce
I don't see where the answers are.
Ed