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7th Grade · 7.RP.A.3

Percent increase in 7th grade math

Percent increase in 7th grade math measures how much an amount grows, compared with where it started. It is one of many percent problems your child solves this year, along with sales tax, tips, discounts and simple interest. All of them rest on one idea: a percent is always a percent of some starting amount.

What the standard says

The official Common Core wording, quoted exactly. The plain version follows.

7.RP.A.3 Use proportional relationships to solve multistep ratio and percent problems.

What it means, in plain words

A percent is a number out of 100, so 30% is 30100\frac{30}{100}, or 0.30. In 7th grade, your child uses percents in real situations. Examples are sales tax on a price, a tip on a restaurant bill, a markup when a store raises a price and a discount when it lowers one. Simple interest is another: money in a bank earns the same percent of the starting amount every year.

Percent increase and decrease compare a change with the starting amount. First find the change: subtract the smaller amount from the larger one. Then divide the change by the original amount, never the new one. The result, written as a percent, is the percent increase when the amount went up and the percent decrease when it went down.

Many percent word problems take more than one step. A price may drop by a discount and then go up by sales tax. Each new percent is taken of the amount at that moment, so two percents in a row cannot just be added. One decimal per step keeps the work short: a 20% discount means paying 80% of the price, so multiply by 0.80.

Your child should be able to:

  • Find a percent of an amount, such as a 15% tip on a bill
  • Find the percent increase or decrease from an old amount to a new amount
  • Solve percent word problems about tax, tips, markups, discounts and simple interest
  • Work through a problem with two percent changes in a row

Example

A school club had 40 members last year and has 52 members this year. What is the percent increase?

  1. The change is 52−40=1252 - 40 = 12 members.
  2. Divide the change by the starting amount: 1240=0.30\frac{12}{40} = 0.30.
  3. 0.30=30%0.30 = 30\%.
  4. The club's membership went up by 30%.

Example

A family's restaurant bill is 40 dollars, and the family leaves a 15% tip. How much does the family pay in total?

  1. 15% is 0.15, so the tip is 0.15×40=60.15 \times 40 = 6 dollars.
  2. Add the tip to the bill: 40+6=4640 + 6 = 46 dollars.
  3. One step gives the same answer, because paying the bill plus the tip is paying 115%: 1.15×40=461.15 \times 40 = 46.
  4. The family pays 46 dollars in total.

Where children usually get stuck

  • For a club that grew from 40 to 52 members, your child divides 12 by 52 and gets about 23%.

    Both numbers are in the problem, and the child picks the new one. A percent change is always measured against the starting amount.

    What helps. Before any dividing, ask "a percent of what?" The answer is the starting amount. That number goes on the bottom of the fraction.

  • Your child says a price that drops 20% and then rises 20% ends up where it started.

    The two percents look like they cancel. The second 20% is taken of a smaller amount, so it adds back less than the first one took away.

    What helps. Try it with 50 dollars. 20% off gives 40 dollars, and 20% of 40 is 8 dollars, so the price ends at 48 dollars, not 50.

  • Your child finds a 6-dollar tip on a 40-dollar bill and writes 6 dollars as the total paid.

    Finding the percent feels like the whole job, so the last step, adding the tip to the bill, gets skipped.

    What helps. Ask whether the question wants the tip or the amount paid. Have your child underline the last sentence of the problem before starting.

Try four practice questions

Real 7th grade questions from our question bank, easiest first. Answer them right here, check each one, and see a worked solution for any question.

  1. 1Warm-up
    Which amount is the notebook's selling price?
    ItemCostMarkup
    Notebook$20.0025%
    A
    $5.00
    B
    $20.00
    C
    $25.00
    D
    $45.00
    Show the answer and how to solve it

    The selling price is $25.00 because 25% of $20.00 is $5.00, and $20.00 + $5.00 = $25.00.

    1. 1Look at the table. The notebook has a cost of $20.00 and a markup of 25%.
    2. 2Change 25% to 0.25 and find the markup amount.
    3. 3Add the markup to the cost to find the selling price.

    Common mistake. A common mistake is selecting $5.00, which is only the markup amount. You must add the markup to the cost to find the selling price.

    The idea underneath. A markup is a percent of the cost, so you first find that percent amount and then add it to the cost to get the selling price.

  2. 2On level
    An $80 backpack is marked down 25%, then a 10% surcharge is added. Look at Leila's work and select the statement that best describes it.
    Step 1
    80×0.75\displaystyle 80 \times 0.75
    =\displaystyle =
    60\displaystyle 60
    Step 2
    60+(80×0.10)\displaystyle 60 + (80 \times 0.10)
    =\displaystyle =
    68\displaystyle 68
    Final
    Final price\displaystyle \text{Final price}
    =\displaystyle =
    68\displaystyle 68
    A
    Leila used the wrong multiplier for the 25% markdown.
    B
    Leila used the original $80 instead of the sale price $60 to calculate the 10% surcharge.
    C
    Leila treated the 10% surcharge as a flat $10 addition instead of 10% of the sale price.
    D
    No mistake; Leila's work is correct.
    Show the answer and how to solve it

    Leila used the original $80 instead of the sale price $60 for the 10% surcharge. The correct final price is $66.

    1. 1Look at Leila's work. Step 1 is correct: a 25% markdown means keeping 75% of the original price, so 80×0.75=6080 \times 0.75 = 60.
    2. 2After the markdown, the backpack costs $60. The 10% surcharge must be calculated from $60, not the original $80.
    3. 3The correct final price is $66, not $68.
    4. 4Leila used the original $80 for the surcharge calculation in Step 2 instead of the sale price $60.

    Common mistake. A common mistake is applying the second percent to the original price because it is still visible in the problem. After the 25% markdown, the new base is $60, so the 10% surcharge must come from $60.

    The idea underneath. After each percent change, the amount itself changes, so the next percent must be taken from the new amount.

  3. 3On level
    A grocery store sells two bags of granola. Complete the table. Enter each unit price in dollars per ounce and mark the better buy.
    OfferPriceSizeUnit price ($ per oz)Better buy
    Bag A$4.8016 oz
    Bag B$6.481.5 lb
    Show the answer and how to solve it

    Enter 0.30 for Bag A and 0.27 for Bag B, then select Bag B because 0.27 dollars per ounce is less than 0.30 dollars per ounce.

    1. 1The header asks for dollars per ounce, so convert Bag B to ounces first. Since 1 lb = 16 oz, 1.5 lb = 24 oz.
    2. 2Find Bag A's price per ounce.
    3. 3Find Bag B's price per ounce.
    4. 4Compare the unit prices. Since 0.27 is less than 0.30, Bag B is the better buy.

    Common mistake. A common mistake is choosing Bag A because $4.80 is less than $6.48. Better buy depends on the lower price for 1 ounce, not the lower total price of the whole bag.

    The idea underneath. To compare two offers fairly, rewrite both as the cost for the same 1 unit and then compare those unit rates.

  4. 4Stretch
    A bookstore buys a paperback from a publisher for $160.00. The book's price goes through three changes before the clearance event, as shown in the table below.
    StepActionPrice
    StartStore's cost for the paperback$160.00
    MarkupRaise shelf price by25%
    Weekend saleLower shelf price by15%
    ClearanceLower clearance price by20%
    What is the paperback's clearance price?
    A
    $170.00
    B
    $184.00
    C
    $144.00
    D
    $136.00
    Show the answer and how to solve it

    The answer is $136.00 because the store's $160.00 cost becomes a $200.00 shelf price after the 25% markup, then $170.00 after the 15% weekend sale, and finally $136.00 after the 20% clearance.

    1. 1Read the rows in order: start with the store's cost, apply the markup, then the weekend sale, then the clearance. Each percent is taken from the updated price on the row above it, so the base changes after every step.
    2. 2Markup: the shelf price increases by 25%. Keep 100% of $160.00 and add 25%, so multiply by 1.25. The shelf price is $200.00.
    3. 3Weekend sale: the price decreases by 15%. Keep 85% of the new shelf price, $200.00, so multiply by 0.85. The price after the weekend sale is $170.00.
    4. 4Clearance: the price decreases by 20%. Keep 80% of $170.00, so multiply by 0.80. The clearance price is $136.00.
    5. 5The paperback's clearance price is $136.00, so that is the correct choice.

    Common mistake. A common mistake is combining all three percent changes into one net −10% applied to $160.00, giving $144.00. Each percent must be taken from the current price — the 15% sale applies to the $200.00 shelf price, and the 20% clearance applies to the $170.00 sale price.

    The idea underneath. In successive percent changes, each new percent is taken from the current price, so the base changes after every step. The 20% clearance is taken from the sale price of $170.00, not from the original $160.00 or the shelf price of $200.00.