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PSAT Math : Solving Word Problems with Multiple Unit Conversions

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Example Questions

Example Question #1 : Conversions

How many $\textup { centimeters}$ $\displaystyle \textup { centimeters}$ are in $5\textup { meters?}$ $\displaystyle 5\textup { meters?}$

Possible Answers:

$5\textup,000\textup { centimeters}$ $\displaystyle 5\textup,000\textup { centimeters}$

$50\textup { centimeters}$ $\displaystyle 50\textup { centimeters}$

$500\textup { centimeters}$ $\displaystyle 500\textup { centimeters}$

$5\textup { centimeters}$ $\displaystyle 5\textup { centimeters}$

$1.5\textup { centimeters}$ $\displaystyle 1.5\textup { centimeters}$

Correct answer:

$500\textup { centimeters}$ $\displaystyle 500\textup { centimeters}$

Explanation:

To solve this problem we can make proportions.

We know that $1\ centimeter= .01\ meters$ $\displaystyle 1\ centimeter= .01\ meters$ and we can use $\displaystyle x$ as our unknown.

$\frac{1\ centimeter}{.01\ meter}=\frac{x\ centimeters}{5\ meters}$ $\displaystyle \frac{1\ centimeter}{.01\ meter}=\frac{x\ centimeters}{5\ meters}$

Next, we want to cross multiply and divide to isolate the on one side.

$1\ centimeter\times 5\ meters=.01\ meter\times x\ centimeters$ $\displaystyle 1\ centimeter\times 5\ meters=.01\ meter\times x\ centimeters$

$\frac{1\ centimeter\times 5\ meters}{.01\ meter}= x\ centimeters$ $\displaystyle \frac{1\ centimeter\times 5\ meters}{.01\ meter}= x\ centimeters$

The meters $\displaystyle meters$ will cancel and we are left with $500\ centimeters$ $\displaystyle 500\ centimeters$

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Example Question #2 : Conversions

How many $\textup{centimeters}$ $\displaystyle \textup{centimeters}$ are in $13\textup { meters?}$ $\displaystyle 13\textup { meters?}$

Possible Answers:

$.0013\textup { centimeters}$ $\displaystyle .0013\textup { centimeters}$

$13\textup,000\textup { centimeters}$ $\displaystyle 13\textup,000\textup { centimeters}$

$1\textup,300\textup { centimeters}$ $\displaystyle 1\textup,300\textup { centimeters}$

$130\textup { centimeters}$ $\displaystyle 130\textup { centimeters}$

$1.3\textup{ centimeters}$ $\displaystyle 1.3\textup{ centimeters}$

Correct answer:

$1\textup,300\textup { centimeters}$ $\displaystyle 1\textup,300\textup { centimeters}$

Explanation:

To solve this problem we can make proportions.

We know that $1\ centimeter= .01\ meters$ $\displaystyle 1\ centimeter= .01\ meters$ and we can use $\displaystyle x$ as our unknown.

$\frac{1\ centimeter}{.01\ meter}=\frac{x\ centimeters}{13\ meters}$ $\displaystyle \frac{1\ centimeter}{.01\ meter}=\frac{x\ centimeters}{13\ meters}$

Next, we want to cross multiply and divide to isolate the on one side.

$1\ centimeter\times 13\ meters=.01\ meter\times x\ centimeters$ $\displaystyle 1\ centimeter\times 13\ meters=.01\ meter\times x\ centimeters$

$\frac{1\ centimeter\times 13\ meters}{.01\ meter}= x\ centimeters$ $\displaystyle \frac{1\ centimeter\times 13\ meters}{.01\ meter}= x\ centimeters$

The meters $\displaystyle meters$ will cancel and we are left with $1,300\ centimeters$ $\displaystyle 1,300\ centimeters$

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PSAT Math : Solving Word Problems with Multiple Unit Conversions

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1 : Conversions

Example Question #2 : Conversions

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