Overview

Task: Study and work through the following math lesson and complete the Math Gathering Activity prior to Gathering.

Last week you started learning about fractions. This week you will learn how to compare, add, and subtract fractions with different denominators. In real life when working with fractions, they rarely have the same denominator. Understanding how to compare fractions of different sizes is critical to understanding fractions.

For example, in order to better analyze your budget, you need to know how much of your budget is spent in two areas. You have the fractions of the budget spent on each area, but how much do they add up to together? How could this information help you with your personal budget? How could this help you with a ward or business budget?

Music Connection

Did you know music uses fractions? The notes represent fractions of each measure. The time signature at the beginning of a song tells us how many total beats are in each measure and which notes receive 1 beat out of the total beats in the measure. Here is an example of two measures that each have 4 beats. There are several beat patterns that can be used to equal one whole measure.

Music bars. Tell us each measure is divided into 4 beats.

On the top row of the first measure, we see $LaTeX: \frac{1}{4} + \frac{1}{8}+ \frac{1}{8}+ \frac{1}{4}+ \frac{1}{4}= 1$ whole.

On the bottom row of the second measure, we see $LaTeX: \frac{1}{2} + \frac{1}{2}= 1$ whole measure.

If you would like to learn more about reading music you can find additional information here.

Math Instruction and Practice

This math lesson is broken into several mini-lessons, each containing a lot of material. Be sure to start early in the week in case you need extra time to study and practice. To save you time and quickly discover which concepts you need more help with, you may first take the math exercises quiz. If you choose a wrong answer on any quiz question, you will receive feedback linking to lessons you can study to improve your skills in that area. You may take these quizzes as many times as you like until the due date in order to improve your score.

All the mini-lessons to help you improve your skills in this week's Math concepts are linked below, located in the PathwayConnect Resource Center. If you still need help after going through the available materials, there are suggestions at the bottom of each lesson page to get more help.

Fractions

Week 8 Math Gathering Activity

This week’s math gathering activity reviews what you learned this week about adding fractions with different denominators. It also reviews simplifying fractions.

While putting together your budget you notice that your mortgage accounts for $\frac{1}{5}$ of your total income and your utilities typically account for $\frac{1}{20}$ of your total income. What fraction of your total income is your mortgage and utilities combined?

Check Answers

$\frac{1}{5} + \frac{1}{20} = \frac{4}{20} + \frac{1}{20} = \frac{5}{20}$

$\frac{5}{20}$ Can be simplified to $\frac{1}{4}$

( $\frac{5}{20} = \frac{5 \times 1}{5 \times 4} = \frac{5}{5} \times \frac{1}{4} = 1 \times \frac{1}{4} = \frac{1}{4}$ )

It may be helpful to draw a picture in order to see that $\frac{5}{20}$ = $\frac{1}{4}$ .

Conclusion: Mortgage and utilities account for $\frac{5}{20}$ = $\frac{1}{4}$ of the total income. It may be helpful to draw pictures of $LaTeX: \frac{1}{5}$ and $LaTeX: \frac{1}{20}$ for people to see.