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Solve Percent Problems Using Proportional Reasoning

Students use proportional relationships to solve multistep percent problems including percent increase, percent decrease, simple interest, tax, tip, discount, markup, and percent error. They set up and solve proportions or use the equation part = percent × whole.

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Solve Percent Problems Using Proportional Reasoning

Grade 7 · Ratios and Proportional Relationships · question 1 of 3

0 of 20

20 rungs. A star at the top.

120 increased by 5% =

How it is taught

0:00 of 4:33

Simple interest is the principal times the rate times the years.

The interest is money earned, not the new balance.

Read it: Percent increase and decrease

120 increased by 15%: the tape is 120, 100%. 15% of 120 is 0.15 × 120 = 18, added on, so the answer is 120 + 18 = 138, which is 115% of 120: 1.15 × 120.

  1. Find the percent of the start: the percent as hundredths, times the start.
  2. Add it on for an increase, or take it away for a decrease.
  3. Or multiply once: 1.15 × 120 for 15% more, 0.85 × 120 for 15% less.

The start is always 100%, so 15% more is 115% of it.

A decrease of 15% leaves 85% of the start.

To work back to the start, divide by the multiplier: 138 ÷ 1.15 = 120.

15% more is × 1.15; 15% less is × 0.85.

Adding the percent itself: 120 + 15 = 135.

15% is a part of 120, not 15: 0.15 × 120 = 18, so 120 + 18 = 138.

260 increased by 35% = ___ — 351. 35% of 260 is 91, added on: 260 + 91 = 351, and 1.35 × 260 = 351.

25% off a $40 jacket

A jacket costs forty dollars and is twenty-five percent off. How much money do you save?

Twenty-five percent means twenty-five out of every hundred — the same as one out of four equal parts.

We can set up a proportion: part over whole equals percent over one hundred.

The whole is the original price — forty dollars.

The percent is twenty-five out of one hundred.

The part is what we want to find. Let's call it x.

Now cross-multiply: one hundred times x equals twenty-five times forty.

Twenty-five times forty is one thousand.

Divide both sides by one hundred. x equals ten.

You save ten dollars! The sale price is just thirty dollars.

$40 jacket — 25% offHow much do you save?25%25% = 25 out of 100=partwholepercent1004025100x100 · x = 25 · 40100x = 1,000x = 10YOU SAVE$10sale price $30
Grade 7 · Using part/whole = percent/100

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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