Lesson OVERVIEW of my lessons on fractions

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<H2>OVERVIEW of my lessons on fractions</H2>

Below is the list of my lessons on fractions in this site:

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Using-fractions-to-solve-word-problems.lesson>Using fractions to solve word problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Using-fractions-to-solve-Travel-problems.lesson>Using fractions to solve Travel problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Calculations-with-fractions.lesson>Calculations with fractions</A>

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Advanced-problems-on-ratios.lesson>Advanced problems on ratios</A>

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Entertainment-problem-on-fractions.lesson>Entertainment problems on fractions</A>

<H3>List of lessons with short annotations</H3><A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Using-fractions-to-solve-word-problems.lesson>Using fractions to solve word problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 1. &nbsp;Andrew can cover the roof of a house in &nbsp;3&nbsp; days. &nbsp;&nbsp;Bill can make this job in &nbsp;6&nbsp; days.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;How long will it take to Andrew and Bill to complete the job working together?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 2. &nbsp;One team of workers can install solar panels on the roof of a house in &nbsp;15&nbsp; days by covering the entire roof area.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The second team of workers can complete this job in &nbsp;10&nbsp; days.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;How long will it take for two teams to complete the job working together?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 3. &nbsp;One tube can fill the reservoir with the water in &nbsp;12&nbsp; hours.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The second tube can fill the reservoir with the water in &nbsp;36&nbsp; hours, &nbsp;if works separately.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;How long will it take to fill the reservoir, &nbsp;if two tubes work simultaneously?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 4. &nbsp;An elephant can drink all the water from a reservoir in &nbsp;4&nbsp; days.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The rhinoceros can drink all the water from the same reservoir in &nbsp;12&nbsp; days, &nbsp;if drinks alone.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;How long will it take to empty the reservoir, &nbsp;if the elephant and the rhinoceros drink together?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 5. &nbsp;The tube can fill a reservoir with the water in &nbsp;3&nbsp; days.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;An elephant can drink all the water from the reservoir in &nbsp;4&nbsp; days.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;How long will it take to fill the reservoir, &nbsp;if the tube fills it and the elephant drinks the water at the same rates?

<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Using-fractions-to-solve-Travel-problems.lesson>Using fractions to solve Travel problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 1. &nbsp;The car covers the distance between two cities in &nbsp;20&nbsp; hours. &nbsp;The truck can cover this distance in &nbsp;30&nbsp; hours.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The car and the truck started moving simultaneously from these cities toward each other.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;When the car and the truck will get passing each other?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 2. &nbsp;The car covers the distance between two cities in &nbsp;4&nbsp; hours. &nbsp;The truck can cover this distance in &nbsp;6&nbsp; hours.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The car and the truck started moving simultaneously from these cities in one direction in a way that the car follows the truck.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;When the car will takeover the truck?

<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Calculations-with-fractions.lesson>Calculations with fractions</A>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 1. &nbsp;a) &nbsp;Calculate &nbsp;{{{1/2}}} - {{{1/3}}}. &nbsp;&nbsp;&nbsp;&nbsp;b) &nbsp;Calculate &nbsp;{{{1/3}}} - {{{1/4}}}. &nbsp;&nbsp;&nbsp;&nbsp;c) &nbsp;Calculate &nbsp;{{{1/4}}} - {{{1/5}}}. &nbsp;&nbsp;&nbsp;&nbsp;d) &nbsp;Calculate &nbsp;{{{1/5}}} - {{{1/6}}}. &nbsp;&nbsp;&nbsp;&nbsp;e) &nbsp;Calculate &nbsp;{{{1/6}}} - {{{1/7}}}. &nbsp;&nbsp;&nbsp;&nbsp;

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 2. &nbsp;Calculate &nbsp;&nbsp;&nbsp;{{{1/(2*3)}}} + {{{1/(3*4)}}} + {{{1/(4*5)}}} + {{{1/(5*6)}}} + {{{1/(6*7)}}}.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 3. &nbsp;a) &nbsp;Calculate &nbsp;{{{1/2}}} - {{{1/5}}}. &nbsp;&nbsp;b) &nbsp;Calculate &nbsp;{{{1/5}}} - {{{1/8}}}. &nbsp;&nbsp;c) &nbsp;Calculate &nbsp;{{{1/8}}} - {{{1/11}}}. &nbsp;&nbsp;d) &nbsp;Calculate &nbsp;{{{1/11}}} - {{{1/14}}}. &nbsp;&nbsp;e) &nbsp;Calculate &nbsp;{{{1/14}}} - {{{1/17}}}. &nbsp;&nbsp;

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 4. &nbsp;Calculate &nbsp;&nbsp;&nbsp;{{{1/(2*5)}}} + {{{1/(5*8)}}} + {{{1/(8*11)}}} + {{{1/(11*14)}}} + {{{1/(14*17)}}}.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 5. &nbsp;Calculate &nbsp;&nbsp;&nbsp;{{{1/(1*4)}}} + {{{1/(4*7)}}} + {{{1/(7*10)}}} + {{{1/(10*13)}}} + {{{1/(13*16)}}}.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 6. &nbsp;Calculate &nbsp;&nbsp;&nbsp;{{{1/(3*7)}}} + {{{1/(7*10)}}} + {{{1/(10*13)}}} + {{{1/(13*16)}}} + {{{1/(16*19)}}} &nbsp;&nbsp;on your own.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 7. &nbsp;Simplify &nbsp;&nbsp;{{{1/(3^(a-b) + 1)}}} + {{{1/(3^(b-a) + 1)}}}.

<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Advanced-problems-on-ratios.lesson>Advanced problems on ratios</A>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 1. &nbsp;Alan and Bob share a sum of money. &nbsp;If Alan gives &nbsp;1/4 &nbsp;of his money to Bob, &nbsp;Bob will have twice as much as Alan.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;What was the ratio of Alan's money to Bob's money at first.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 2. &nbsp;At an after school event, &nbsp;5/9&nbsp; of the students were 8th graders and the rest were 7th graders.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Of the students who were in 7th grade, &nbsp;the ratio of boys to girls is &nbsp;3:5.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;What fraction of ALL students at the after school event were boys who are in the 7th grade?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 3. &nbsp;In a condo complex, &nbsp;{{{2/3}}}&nbsp; of the men were married to &nbsp;{{{3/4}}}&nbsp; of the women. &nbsp;What is the ratio of married people

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 4. &nbsp;One night, &nbsp;a guest at an inn couldn't sleep and wanted a snack. &nbsp;He went down to the kitchen where he found a plate of cupcakes.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;He was hungry and ate &nbsp;1/6 &nbsp;of the cupcakes.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Later, &nbsp;his wife was hungry, &nbsp;couldn't sleep, &nbsp;and so she went to the kitchen and ate &nbsp;1/5&nbsp; of the remaining cupcakes.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;At 10, &nbsp;the oldest son ate &nbsp;1/4&nbsp; of what his mother had left.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;At 11, &nbsp;the second son ate &nbsp;1/3&nbsp; of the leftover cupcakes, &nbsp;and just after him,

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;the daughter ate &nbsp;1/2&nbsp; of what her brother had left, &nbsp;leaving only three cupcakes for the Inn Keeper's birthday party the next day.

<A HREF=https://www.algebra.com/algebra/homework/NumericFractions/Entertainment-problem-on-fractions.lesson>Entertainment problems on fractions</A>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 1. &nbsp;A container can hold either &nbsp;60 &nbsp;small boxes or &nbsp;48 &nbsp;big boxes.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;If there are already &nbsp;20 &nbsp;small and &nbsp;24 &nbsp;big boxes in the container,

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 2. &nbsp;Eleven fidget spinners cost less than &nbsp;$12. &nbsp;Twelve fidget spinners cost more than &nbsp;$13. &nbsp;How many cents does one fidget spinner cost?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 3. &nbsp;Brian had a sum of money. &nbsp;He spent an equal amount of money each day.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;After &nbsp;6 &nbsp;days he had &nbsp;3/5 &nbsp;of his money left. &nbsp;3 &nbsp;days later he had &nbsp;360 &nbsp;dollars left.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;How much did he have at first?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Solve the problem mentally, &nbsp;in your head, &nbsp;without using equation &nbsp;(use logical reasoning, &nbsp;only).

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 4. &nbsp;Find the sum of the series &nbsp;&nbsp;18/12 + 18/20 + 18/30 + 18/42 + ... + 18/1260.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Problem 5. &nbsp;The sum of the reciprocals of two numbers is &nbsp;7.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The larger reciprocal exceeds the smaller one by &nbsp;7/3. &nbsp;Find the numbers.