Common Core: 4th Grade Math : Use the Four Operations to Solve Word Problems Involving Various Measures: CCSS.Math.Content.4.MD.A.2

Study concepts, example questions & explanations for Common Core: 4th Grade Math

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Example Questions

Example Question #1 : Use The Four Operations To Solve Word Problems Involving Various Measures: Ccss.Math.Content.4.Md.A.2

On Saturday Jake raked leaves for \(\displaystyle 180\) minutes and on Sunday he raked leaves for \(\displaystyle 2\) hours. In hours, how much total time did he spend raking on both Saturday and Sunday?

Possible Answers:

\(\displaystyle 9\)

\(\displaystyle 8\)

\(\displaystyle 5\)

\(\displaystyle 7\)

\(\displaystyle 6\)

Correct answer:

\(\displaystyle 5\)

Explanation:

The first thing we need to do is put our minutes into hours because our final answer is asking for hours. We know that \(\displaystyle 1 hr=60min\). We can set up a proportion and cross multiply to solve. 

\(\displaystyle \frac{1hr}{60min}=\frac{x}{180min}\)

\(\displaystyle 60min(x)=1hr(180min)\)

Then we can divide to isolate the \(\displaystyle x\).

\(\displaystyle \frac{60min(x)}{60min}=\frac{1hr(180min)}{60min}\)

\(\displaystyle x=3hr\)

Now we can add our hours together to find the total. 

\(\displaystyle 3hr+2hr=5hr\)

Example Question #2 : Use The Four Operations To Solve Word Problems Involving Various Measures: Ccss.Math.Content.4.Md.A.2

Matt studied for \(\displaystyle 180\) minutes everyday from Monday-Friday. How many total hours did he spend studying?

Possible Answers:

\(\displaystyle 13\)

\(\displaystyle 14\)

\(\displaystyle 12\)

\(\displaystyle 11\)

\(\displaystyle 15\)

Correct answer:

\(\displaystyle 15\)

Explanation:

The first thing we need to do is put our minutes into hours because our final answer is asking for hours. We know that \(\displaystyle 1hr=60min\). We can set up a proportion and cross multiply to solve. 

\(\displaystyle \frac{1hr}{60min}=\frac{x}{180min}\)

\(\displaystyle 60min(x)=180min(1hr)\)

Then we can divide to isolate the \(\displaystyle x\).

\(\displaystyle \frac{60min(x)}{60min}=\frac{180min(1hr)}{60min}\)

\(\displaystyle x=3hr\)

Now we need to multiply \(\displaystyle 3\times5\) because Matt studied for \(\displaystyle 3\) hours each day. 

\(\displaystyle 3hr\times5=15hr\)

Example Question #1 : Use The Four Operations To Solve Word Problems Involving Various Measures: Ccss.Math.Content.4.Md.A.2

Today Jenny worked on homework for \(\displaystyle 120\) minutes when she got home from school and then worked on homework for \(\displaystyle 2\) hours after dinner. In minutes, what was the total time that Jenny spent working on homework?

Possible Answers:

\(\displaystyle 230\ \space minutes\)

\(\displaystyle 200\ \space minutes\)

\(\displaystyle 240\ \space minutes\)

\(\displaystyle 220\ \space minutes\)

\(\displaystyle 210\ \space minutes\)

Correct answer:

\(\displaystyle 240\ \space minutes\)

Explanation:

The first thing we need to do is put our hours into minutes because our final answer is asking for minutes. We know that \(\displaystyle 1 hr=60min\). We can set up a proportion and cross multiply to solve. 

\(\displaystyle \frac{1hr}{60min}=\frac{2hr}{x}\)

\(\displaystyle 1hr(x)=60min(2hr)\)

Then we can divide to isolate the \(\displaystyle x\).

\(\displaystyle \frac{1hr(x)}{1hr}=\frac{60min(2hr)}{1hr}\)

\(\displaystyle x=60min(2)\)

\(\displaystyle x=120 min\)

Now we can add our minutes from before and after dinner together to find our total. 

\(\displaystyle 120min+120min=240min\)

Example Question #4 : Use The Four Operations To Solve Word Problems Involving Various Measures: Ccss.Math.Content.4.Md.A.2

Jessica ran sprints for \(\displaystyle 120\) seconds, and Megan ran sprints for \(\displaystyle 7\) minutes. How many more minutes did Megan run than Jessica? 

Possible Answers:

\(\displaystyle 2\ \space minutes\)

\(\displaystyle 5\ \space minutes\)

\(\displaystyle 3\ \space minutes\)

\(\displaystyle 1\ \space minutes\)

\(\displaystyle 4\ \space minutes\)

Correct answer:

\(\displaystyle 5\ \space minutes\)

Explanation:

The first thing we need to do is put our seconds into minutes because our final answer is asking for minutes. We know that \(\displaystyle 1min=60sec\). We can set up a proportion and cross multiply to solve. 

\(\displaystyle \frac{1min}{60sec}=\frac{x}{120sec}\)

\(\displaystyle 60sec(x)=120sec(1min)\)

Then we can divide to isolate the \(\displaystyle x\).

\(\displaystyle \frac{60sec(x)}{60sec}=\frac{120sec(1min)}{60sec}\)

\(\displaystyle x=2min\)

Now we need to subtract to find our difference. 

\(\displaystyle 7min-2min=5min\)

Example Question #2 : Use The Four Operations To Solve Word Problems Involving Various Measures: Ccss.Math.Content.4.Md.A.2

Joe’s school is \(\displaystyle 7\) feet from his house, and his classroom is another \(\displaystyle 36\) inches once he gets to the school. In inches, how far does he walk to his classroom? 

Possible Answers:

\(\displaystyle 41\ \speace inches\)

\(\displaystyle 90\ \speace inches\)

\(\displaystyle 58\ \speace inches\)

\(\displaystyle 100\ \speace inches\)

\(\displaystyle 120\ \speace inches\)

Correct answer:

\(\displaystyle 120\ \speace inches\)

Explanation:

The first thing we need to do is put our feet into inches because our final answer is asking for inches. We know that \(\displaystyle 1ft=12in\). We can set up a proportion and cross multiply to solve. 

\(\displaystyle \frac{1ft}{12in}=\frac{7ft}{x}\)

\(\displaystyle 1ft(x)=7ft(12in)\)

Then we can divide to isolate the \(\displaystyle x\).

\(\displaystyle \frac{1ft(x))}{1ft}=\frac{7ft(12in)}{1ft}\)

\(\displaystyle x=84in\)

Now we can add our inches together to find our total. 

\(\displaystyle 84in+36in=120in\)

Example Question #5 : Use The Four Operations To Solve Word Problems Involving Various Measures: Ccss.Math.Content.4.Md.A.2

Tim has \(\displaystyle 2\) liters of soda. He pours \(\displaystyle 7\) milliliters into a glass and drinks it all. In milliliters, how much soda is left? 

Possible Answers:

\(\displaystyle 1\textup{,}800\ \space milliliters\)

\(\displaystyle 17\ \space milliliters\)

\(\displaystyle 9\ \space milliliters\)

\(\displaystyle 2\textup {,}000\ \space milliliters\)

\(\displaystyle 1\textup{,}993\ \space milliliters\)

Correct answer:

\(\displaystyle 1\textup{,}993\ \space milliliters\)

Explanation:

The first thing we need to do is put our liters into milliliters because our final answer is asking for milliliters. We know that \(\displaystyle 1l=1,000ml\). We can set up a proportion and cross multiply to solve. 

\(\displaystyle \frac{1l}{1,000ml}=\frac{2l}{x}\)

\(\displaystyle 1l(x)=1,000ml(2l)\)

Then we can divide to isolate the \(\displaystyle x\).

\(\displaystyle \frac{1l(x)}{1l}=\frac{1,000ml(2l)}{1l}\)

\(\displaystyle x=2,000ml\)

Now we can subtract to find out how much is left. 

\(\displaystyle 2,000ml-7ml=1,993\)

Example Question #841 : Ssat Middle Level Quantitative (Math)

Sarah walked \(\displaystyle 5\textup { feet}\) to the stop sign, and then \(\displaystyle 24\textup{ inches}\) to her friend’s house. In feet, how far did she walk?

Possible Answers:

\(\displaystyle 4ft\)

\(\displaystyle 3ft\)

\(\displaystyle 7ft\)

\(\displaystyle 6ft\)

\(\displaystyle 5ft\)

Correct answer:

\(\displaystyle 7ft\)

Explanation:

The first thing we need to do is put our inches into feet because our final answer is asking for feet. We know that \(\displaystyle 1ft=12in\). We can set up a proportion and cross multiply to solve. 

\(\displaystyle \frac{1ft}{12in}=\frac{x}{24in}\)

\(\displaystyle 12in(x)=1ft(24in)\)

Then we can divide to isolate the \(\displaystyle x\).

\(\displaystyle \frac{12in(x)}{12in}=\frac{1ft(24in)}{12in}\)

\(\displaystyle x=2ft\)

Now we can add our feet together to find our total. 

\(\displaystyle 5ft+2ft=7ft\)

Example Question #6 : Use The Four Operations To Solve Word Problems Involving Various Measures: Ccss.Math.Content.4.Md.A.2

Avery has \(\displaystyle 8\textup{ liters}\) of juice. She pours \(\displaystyle 3\textup{ liters}\) into a pitcher. In \(\displaystyle \textup{milliliters}\), how much of the juice is not in the pitcher? 

Possible Answers:

\(\displaystyle 5\textup,000ml\)

\(\displaystyle 7ml\)

\(\displaystyle 5ml\)

\(\displaystyle 13ml\)

\(\displaystyle 7\textup,000ml\)

Correct answer:

\(\displaystyle 5\textup,000ml\)

Explanation:

Because our systems of measurements are the same, the first thing we want to do is subtract. 

 \(\displaystyle 8l-3l=5l\)

Our answer is asking us for milliliters, so we need to convert \(\displaystyle 5l\) into milliliters. We know that \(\displaystyle 1l=1,000ml\). We can set up a proportion and cross multiply to solve. 

\(\displaystyle \frac{1l}{1,000ml}=\frac{5l}{x}\)

\(\displaystyle 1l(x)=1,000ml(2l)\)

Then we can divide to isolate the \(\displaystyle x\).

\(\displaystyle \frac{1l(x)}{1l}=\frac{1,000ml(5l)}{1l}\)

\(\displaystyle x=5,000ml\)

 

 

Example Question #183 : Ratio And Proportion

Hannah has a \(\displaystyle 4lb\) bag of peanuts that she is going to divide evenly between her four friends. How many ounces of peanuts does she give to each friend? 

Possible Answers:

\(\displaystyle 6oz\)

\(\displaystyle 1oz\)

\(\displaystyle 12oz\)

\(\displaystyle 16oz\)

\(\displaystyle 8oz\)

Correct answer:

\(\displaystyle 16oz\)

Explanation:

The first thing we need to do is put our pounds into ounces because our final answer is asking for ounces. We know that \(\displaystyle 1lb=16oz\). We can set up a proportion and cross multiply to solve. 

\(\displaystyle \frac{1lb}{16oz}=\frac{4lb}{x}\)

\(\displaystyle 1lb(x)=16oz(4lb)\)

Then we can divide to isolate the \(\displaystyle x\).

\(\displaystyle \frac{1lb(x)}{1lb}=\frac{16oz(4lb)}{1lb}\)

\(\displaystyle x=64oz\)

Now we need to divide our \(\displaystyle 64oz\) by \(\displaystyle 4\) because we are splitting the peanuts up equally between \(\displaystyle 4\) people. 

\(\displaystyle 64oz\div4=16oz\)

Example Question #184 : Ratio And Proportion

Molly has a \(\displaystyle 6lb\) bag of peanuts that she is going to divide evenly between her three friends. How many ounces of peanuts does she give to each friend? 

Possible Answers:

\(\displaystyle 32oz\)

\(\displaystyle 2oz\)

\(\displaystyle 24oz\)

\(\displaystyle 23oz\)

\(\displaystyle 3\)

Correct answer:

\(\displaystyle 32oz\)

Explanation:

The first thing we need to do is put our pounds into ounces because our final answer is asking for ounces. We know that \(\displaystyle 1lb=16oz\). We can set up a proportion and cross multiply to solve. 

\(\displaystyle \frac{1lb}{16oz}=\frac{6lb}{x}\)

\(\displaystyle 1lb(x)=16oz(6lb)\)

Then we can divide to isolate the \(\displaystyle x\).

\(\displaystyle \frac{1lb(x)}{1lb}=\frac{16oz(6lb)}{1lb}\)

\(\displaystyle x=96oz\)

Now we need to divide our \(\displaystyle 96oz\) by \(\displaystyle 3\) because we are splitting the peanuts up equally between \(\displaystyle 3\) people. 

\(\displaystyle 96oz\div3=32oz\)

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