Working with Fractions Reinforcement Questions

1.

A tray of sandwiches is being passed around a family gathering. The tray has 34 sandwiches, to begin with. Brian takes 2, then Stewie takes 3, and then Meg takes 4. What percentage of the original total is left after each of the guests has taken their sandwiches? What is the total percentage sandwich loss at the party?

Brian takes 2 sandwiches so there begin mathsize 14px style fraction numerator 34 space minus space 2 over denominator 34 end fraction space cross times space 100 space equals space 94.11 percent sign space end style are  of the sandwiches left.

Stewie takes 3 sandwiches, so there are begin mathsize 14px style fraction numerator 32 space minus space 3 over denominator 34 end fraction space cross times space 100 space equals space 85.29 percent sign space end style of the sandwiches left after Brian and Stewie have taken their sandwiches.

Meg takes 4 sandwiches, so there are begin mathsize 14px style fraction numerator 29 space minus space 4 over denominator 34 end fraction space cross times space 100 space equals space 73.53 percent sign end style of the sandwiches left after all three guests have taken their sandwiches.

The total percentage sandwich loss at the party is begin mathsize 14px style 100 space minus space 73.53 space equals space 26.47 percent sign end style.

2.

What is begin mathsize 14px style bevelled fraction numerator 2 over denominator 9 t h s end fraction end style of 35 multiplied by begin mathsize 14px style bevelled fraction numerator 5 over denominator 7 t h s end fraction end style of 18?

begin mathsize 14px style open parentheses 35 over 9 space cross times space 2 close parentheses space cross times space open parentheses 18 over 7 space cross times space 5 close parentheses space equals space 100 end style

3.

Process A produces 23.325 kg of product from 31.1 kg of raw material.

Process B produces 3.75 L of product from 15 L of raw material.

What is the ratio of the process losses between process A and B?

The yield of process A is begin mathsize 14px style open parentheses fraction numerator 23.325 over denominator 31.1 end fraction space cross times space 100 space equals space 75 percent sign space close parentheses end style so the loss is begin mathsize 14px style 100 space minus space 75 space equals space 25 percent sign end style

The yield of process B is begin mathsize 14px style open parentheses fraction numerator 3.75 over denominator 15 end fraction space cross times space 100 space equals space 25 percent sign close parentheses end style so the loss is begin mathsize 14px style 100 space minus space 25 space equals space 75 percent sign end style

This gives a ratio loss ratio of 25:75, which can be reduced to 1:3 by dividing by 25

4.

You need to clean some process equipment using a 2.5% detergent solution. What volume of 35% detergent would you use to make 1,500 L of 2.5% detergent.

First, we work out what 2.5% of 1,500 is:

begin mathsize 14px style fraction numerator 2.5 over denominator 100 end fraction space cross times space 1 comma 500 space equals space 37.5 space L end style

If our detergent solution was 100%, we could add 37.5 L, but we have 35% detergent.

We therefore multiply the volume at 100% by 100 and divide by 35:

begin mathsize 14px style fraction numerator 37.5 space L space cross times space 100 percent sign over denominator 35 percent sign end fraction space equals space 107.14 space L end style

Or simply:

begin mathsize 14px style fraction numerator 1 comma 500 space L space cross times space 0.025 over denominator 0.35 end fraction space equals space 107.14 space L end style

5.

You are sitting a maths exam. The total marks for the course are made up of 35% for part A and 65% for part B. You need 60% to pass the test, and you got 72% in part A. The maximum possible number of marks from part B is 76. How many marks do you need to get in part B to pass the course?

First, we find what percentage of the total marks we got in part A:

begin mathsize 14px style fraction numerator 72 percent sign over denominator 100 percent sign end fraction space cross times space 35 percent sign space equals space 25.2 percent sign end style

So we have 25.2% after part A and need a total of 60% to pass. We therefore need to gain:

begin mathsize 14px style 60 percent sign space – space 25.2 percent sign space equals space 34.8 percent sign space o f space t h e space t o t a l space m a r k s space f r o m space p a r t space B. end style

Part B is worth 65% of the total marks, so in part B, you need to get:

begin mathsize 14px style fraction numerator 34.8 percent sign over denominator 65 percent sign end fraction space cross times space 100 percent sign space equals space 53.5 percent sign end style

There is a maximum of 76 marks for part B, so you need to get:

begin mathsize 14px style fraction numerator 53.5 percent sign over denominator 100 percent sign end fraction space cross times space 76 space m a r k s space equals space 40.7 space m a r k s space o r space 41 space t o space b e space o n space t h e space s a f e space s i d e end style

Next, we find out more about squares and other exponents.

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