# Ch. 2 Fraction Operationsmr. Mac's Page

SolveMyMath - Your math help website. Get math help fast and online with more than one hundred instant and even step-by-step math solvers and calculators designed to help you solve your math problems and understand the concepts behind them! In this case, both 2 and 3 go into 6 evenly, so we will have to change each fraction to have a denominator of 6. Let's start with 1/2 first. We have to determine what we need to multiply 2 by to. Chapter 2 Test (Form B).47. Perform math procedures and make problem-solving decisions that require an understanding of math concepts.

To ** add (or subtract) ** two fractions :

1) Find the least common denominator .

2) Write both original fractions as equivalent fractions with the least common denominator.

3) Add (or subtract) the numerators.

4) Write the result with the denominator.

** Example 1: **

Add $\frac{1}{3}+\frac{3}{7}$ .

The least common denominator is $21$ .

$\begin{array}{l}\frac{1}{3}+\frac{3}{7}=\frac{1\cdot 7}{3\cdot 7}+\frac{3\cdot 3}{7\cdot 3}\\ =\frac{7}{21}+\frac{9}{21}\\ =\frac{16}{21}\end{array}$

To ** multiply ** two fractions:

1) Multiply the numerator by the numerator.

2) Multiply the denominator by the denominator.

For all real numbers $a,b,c,d\left(b\ne 0,d\ne 0\right)$

$\frac{a}{b}\cdot \frac{c}{d}=\frac{ac}{bd}$

** Example 2: **

Multiply $\frac{1}{4}\cdot \frac{5}{6}$ .

$\begin{array}{l}\frac{1}{4}\cdot \frac{5}{6}=\frac{1\cdot 5}{4\cdot 6}\\ =\frac{5}{24}\end{array}$

To ** divide ** by a fraction, multiply by its reciprocal .

For all real numbers $a,b,c,d\left(b\ne 0,c\ne ,d\ne 0\right)$

$\frac{a}{b}\xf7\frac{c}{d}=\frac{a}{b}\cdot \frac{d}{c}=\frac{ad}{bc}$

** Example 3: **

Divide $\frac{3}{4}\xf7\frac{5}{7}$ .

$\begin{array}{l}\frac{3}{4}\xf7\frac{5}{7}=\frac{3}{4}\cdot \frac{7}{5}\\ =\frac{3\cdot 7}{4\cdot 5}\\ =\frac{21}{20}\end{array}$

Mixed numbers can be written as an improper fraction and an improper fraction can be written as a mixed number.

** Example 4: **

Write $7\frac{2}{5}$ as an improper fraction.

$\begin{array}{l}7\frac{2}{5}=\frac{7}{1}+\frac{2}{5}\\ =\frac{7\cdot 5}{1\cdot 5}+\frac{2}{5}\\ =\frac{35}{5}+\frac{2}{5}\\ =\frac{37}{5}\end{array}$

** Example 5: **

Write $\frac{11}{7}$ as a mixed number in simple form.

$\frac{11}{7}=11\xf77=1\text{R}4$

Therefore, $\frac{11}{7}=1\frac{4}{7}$ .

A fraction is in lowest terms when the numerator and denominator have no common factor other than $1$ . To write a fraction in lowest terms, divide the numerator and denominator by the greatest common factor .

** Example 6: **

Write $\frac{45}{75}$ in lowest terms.

$45$ and $75$ have a common factor of $15$ .

$\frac{45}{75}=\frac{45\xf715}{75\xf715}=\frac{3}{5}$

Fractions represent parts of a whole — that is, quantities that fall between the whole numbers. Probably the most commonly used fraction is 1/2, which is *one-half.* When you cut a cake into two pieces and take one for yourself, you get 1/2 of the cake —hope you’re hungry!

When you slice yourself a fraction of a cake, that fraction contains two numbers, and each number tells you something different:

The top number — called the

*numerator*— tells you the number of*shaded*slices.The bottom number — called the

*denominator*— tells you the*total*number of slices.

When the numerator of a fraction is less than the denominator, that fraction is a *proper fraction.* If the numerator is greater than the denominator, that fraction is an *improper fraction.* You can convert improper fractions into mixed numbers.

Some fractions can be easily written as whole numbers:

## Ch. 2 Fraction Operationsmr. Mac's Page Sheet

When a fraction’s denominator is 1, that fraction is equal to its numerator.

When a fraction’s numerator and denominator are the same, that fraction is equal to 1. (This idea is important when you want to change the terms of a fraction.)

When you reverse the order of the numerator and denominator in a fraction, the result is the *reciprocal* of that fraction. You use reciprocals to divide by fractions.

## Sample questions

For each cake pictured below, identify the fraction of the cake that’s shaded.

Put the number of shaded slices over the number of total slices in each cake:

**a.****b.****c.****d.**What’s the reciprocal of each of the following fractions?

**a.****b.****c.****d.**To find the reciprocal, switch around the numerator and the denominator:

**a.****The reciprocal is****b.****The reciprocal is****c.****The reciprocal is****d.****The reciprocal is**

## Practice questions

## Ch. 2 Fraction Operationsmr. Mac's Page Numbers

For each cake pictured, identify the fraction of the cake that’s shaded.

Which of the following fractions are proper? Which are improper?

**a.****b.****c.****d.**Rewrite each of the following fractions as a whole number:

**a.****b.****c.****d.**Find the reciprocal of the following fractions:

**a.****b.****c.****d.**

## Ch. 2 Fraction Operationsmr. Mac's Pages

Following are the answers to the practice questions:

Identify the fraction of the cake that’s shaded.

**a.****You have 1 shaded slice and 3 slices in total, so it’s****b.****You have 3 shaded slices and 4 slices in total, so it’s****c.****You have 5 shaded slices and 6 slices in total, so it’s****d.****You have 7 shaded slices and 12 slices in total, so it’s**Which of the following fractions are proper? Which are improper?

**a.****The numerator (3) is greater than the denominator (2), so****this fraction****is an****improper fraction.****b.****The numerator (8) is less than the denominator (9), so****this fraction****is a****proper fraction.****c.****The numerator (20) is less than the denominator (23), so****this fraction****is a****proper fraction.****d.****The numerator (75) is greater than the denominator (51), so****this fraction****is an****improper fraction.**Rewrite each of the following fractions as a whole number.

**a.****The numerator and denominator are the same, so****b.****The denominator is 1, so****c.****The numerator and denominator are the same, so****d.****The denominator is 1, so**Find the reciprocal of the following fractions by switching the numerator and denominator.

**a.****The reciprocal is****b.****The reciprocal is****c.****The reciprocal is****d.****The reciprocal is**