4.05 Percentage increase and decrease
Here is a grid of 100 blue squares. Each small square represents 1\% of the total:
Choose the image that represents 3\% more than the original grid:
Describe what was done to the original grid to increase it by 3\%.
Write an expression to represent the 3\% increase in squares.
Choose the image that represents 6\% less than the original grid:
Describe what was done to the original grid to decrease it by 6\%.
Write an expression to represent the 6\% decrease in squares.
Bob wants to decrease 110 by 60\%.
Calculate 60\% of 110.
Should Bob add or subtract the amount from part (a) from 110? Explain your answer.
Hence, decrease 110 by 60\%.
Lucy wants to increase 70 by 60\%.
Calculate 60\% of 70.
Should Lucy add or subtract the amount from part (a) from 70? Explain your answer.
Hence, increase 70 by 60\%.
Increase:
80 by 5\%.
120 by 10\%.
72 by 40\%.
320 by 25\%.
\$140 by 9\%.
\$30\,000 by 20\%.
80\text{ km} by 15\%.
400\text{ mL} by 35\%.
Abed wants to increase 1500 by 30\%.
Calculate 30\% of 1500 and add the answer to 1500.
Calculate 130\% of 1500.
Are your answers to (a) and (b) the same? Explain why this is.
Tracy wants to increase 80 by 30\%.
What single percentage should she multiply 80 by?
Explain how you got your percentage in part (a).
What single percentage should a quantity be multiplied by in order to increase the quantity by:
Evaluate the following using a single percentage:
Increase 80 by 60\%
Increase 400 by 45\%
Increase 900 by 8\%
Increase 80 by 40\%
Increase 1200 by 45\%
Increase 1200 by 8\%
A bag of rice weighs 120 \text{ kg}. The company who makes these bags decides to increase their weight by 45\%. Find the new weight of the bag.
Decrease:
70 by 8\%.
260 by 10\%.
96 by 60\%.
250 by 20\%.
\$480 by 18\%.
\$55\,000 by 45\%.
200\text{ km} by 22\%.
650\text{ mL} by 30\%.
Derek wants to decrease 120 by 70\%.
What single percentage should he multiply 120 by?
Explain how you got your percentage in part (a).
What single percentage should a quantity be multiplied by in order to decrease the quantity by:
Evaluate the following using a single percentage:
Decrease 80 by 60\%
Decrease 400 by 45\%
Decrease 900 by 8\%
Decrease 80 by 40\%
Decrease 1200 by 45\%
Decrease 1200 by 8\%
A discus thrower has a personal best of 60 \text{ m}. In their most recent competition they fall short of their personal best by 30\%. Find the distance of their throw in this competition.
A percentage increase was applied to the number 60 in order to get 108.
Find how much was added to 60 to get 108.
Express the increase as a percentage of 60.
A percentage increase was applied to the number 180 in order to get 207.
Find how much was added to 180 to get 207.
Express the increase as a percentage of 180.
A percentage decrease was applied to the number 90 in order to get 27.
Find how much was subtracted from 90 to get 27.
Express the decrease as a percentage of 90.
A percentage decrease was applied to the number 180 in order to get 117.
Find how much was subtracted from 180 to get 117.
Express the decrease as a percentage of 180.
In training for her next marathon, Sally increased her practise route from 7000 \text{ m} to 7910 \text{ m}. What percentage has Sally increased the distance of her practice route by?
Luke's record for juggling a football was 70 keep ups. After buying some new football boots, this increased to 112. Express this increase as a percentage of the original record.
Sharon's daily pay was \$150. When she began working shorter hours in order to study, her pay decreased to \$90 per day. Express this decrease as a percentage of her original pay.
Jimmy had a bowling high score of 60 points. After practising for a week, this increased to 93. Express this increase as a percentage of his original high score.
Sophia is able to write 220 words in a minute. After sustaining a thumb injury, this decreased to 143 words a minute. Express this decrease as a percentage of her original rate.
During the editing phase when making a movie, the director ordered that the movie be cut down from 200 minutes to 124 minutes. What percentage did the movie's duration decrease by from its original length?