← SSAT® Middle Level

Number Concepts and Operations: Ratios, Rates and Estimation

Ratios as a divided bar, proportions, rates, averages, and the rounding that replaces the calculator you are not allowed to bring.

6 topics · 28 questions

Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.

Ratios as a Divided Bar

  1. How it worksHow does a 2 to 3 ratio show up as one bar chopped into five equal parts?
  2. How it worksHow do you move from a part-to-part ratio to a part-to-whole fraction?
  3. Worked exampleFind how many girls sit in a class of 30 when the boy to girl ratio is 2 to 3.
  4. Worked exampleFind the new ratio after a 3 to 4 paint mix is doubled in size.
  5. Common mistakeWhy isn't a 2 to 3 ratio the same statement as 2 out of 3?
Your turneasy1 of 3
A class holds 5 times 11 students, and the ratio of boys to girls is 2 to 3. How many girls are in the class?

Proportions and Scaling

  1. How it worksHow does setting two fractions equal and cross multiplying answer a scaling question?
  2. Worked exampleFind how much flour 10 people need when 4 people need 6 cups.
  3. Worked exampleFind the height of a flagpole casting a 12 foot shadow when a 5 foot boy casts a 4 foot shadow.
Your turneasy1 of 3
A recipe for 4 people needs 6 cups of flour. How many cups does the same recipe need for 19 people?

Rates, Unit Rates and Speed

  1. How it worksHow does dividing a total by the number of units collapse any rate down to a per-one rate?
  2. Worked exampleFind which costs less per ounce: 12 ounces for 3 dollars, or 20 ounces for 4.60 dollars.
  3. Worked exampleFind how long a 150 mile drive takes at a steady 50 miles per hour.
  4. Worked exampleFind the average speed for 60 miles at 30 miles per hour then 60 miles at 60 miles per hour.
  5. Common mistakeWhy isn't the average of 30 and 60 miles per hour the average speed for that whole trip?
Your turnhard1 of 3
A box holds 20 ounces of cereal and costs 7 dollars. What is the price per ounce, in dollars? Round to three decimal places.

Arithmetic Word Problems

  1. How it worksHow do words like each, total, left over and share point straight at one of the four operations?
  2. How it worksHow does drawing the quantities as bars make a two-step word problem obvious?
  3. Worked exampleFind the change from 20 dollars after buying 3 notebooks at 2.75 dollars each.
  4. Worked exampleFind how many buses 133 students need when each bus holds 40 of them.
  5. Common mistakeWhy isn't the answer to a bus-loading problem ever a decimal like 3.3 buses?
Your turneasy1 of 3
You pay with a 20 dollar note for 3 notebooks costing 3.59 dollars each. How much change do you get? Round to two decimal places.

Averages and Missing Values

  1. How it worksHow does an average level uneven bars out until every bar stands the same height?
  2. How it worksHow does total equal average times count, and why does that unlock most average questions?
  3. Worked exampleFind the fifth test score needed to average 88 when the first four were 84, 90, 79 and 95.
  4. Worked exampleFind the average of 12, 15, 18 and 23.
  5. Going furtherWhat happens to an average when you add one more value exactly equal to it?
Your turnhard1 of 3
A student scores 84, 90, 79 and 90 on the first four tests. What score is needed on the fifth test for an average of 88?

Estimation and Rounding

  1. How it worksHow does rounding each number to its leading digit land you inside the right ballpark?
  2. How it worksHow can you tell whether your rounding pushed the estimate too high or too low?
  3. Worked exampleFind the closest estimate for 398 times 21 by rounding both numbers first.
  4. Worked exampleFind roughly what 61 percent of 298 comes to, using friendly numbers.
  5. Common mistakeWhy isn't an estimate trustworthy when you round both numbers in the same direction?
Your turneasy1 of 3
Estimate 398 times 31 by rounding 398 up to 400 first. What is your estimate?

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