# 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 $a,b,c,d\left(b\ne 0,c\ne ,d\ne 0\right)$

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

Example 3:

Divide $\frac{3}{4}÷\frac{5}{7}$ .

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

$\frac{11}{7}=11÷7=1\text{R}4$

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 $15$ .

$\frac{45}{75}=\frac{45÷15}{75÷15}=\frac{3}{5}$

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

1. 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.

2. 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

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

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

a.

b.

c.

d.

3. Rewrite each of the following fractions as a whole number:

a.

b.

c.

d.

4. 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:

1. 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

2. 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.

3. 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

4. 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