What is a ratio? — A comparison of two quantities by division.A ratio compares two quantities by division and can be written as a fraction, with a colon, or with the word "to."
Which is NOT a valid way to write the ratio 4 to 7? — 4 + 7.Ratios are written as fractions (4/7), with a colon (4:7), or with the word "to" (4 to 7). Addition (4+7) is not a ratio notation.
A unit rate always has what as the second quantity? — 1.A unit rate is a ratio where the second quantity is 1, making comparisons easy (e.g., miles per hour means miles per 1 hour).
A car travels 300 miles in 5 hours. What is the unit rate? — 60 mph.Unit rate = 300 ÷ 5 = 60 miles per hour.
Store A sells 3 pens for $2.10. What is the unit price? — $0.70.Unit price = $2.10 ÷ 3 = $0.70 per pen.
If a faucet drips 12 gallons in 4 hours, what is the drip rate per hour? — 3 gallons/hour.12 ÷ 4 = 3 gallons per hour.
A recipe calls for 2 cups of flour for every 3 cups of milk. Write this as a fraction ratio (flour to milk). — 2/3.Flour to milk = 2 to 3 = 2/3.
If the ratio of boys to girls is 5:4 and there are 20 boys, how many girls are there? — 16.Scale factor: 20 ÷ 5 = 4. Girls = 4 × 4 = 16.
What does "percent" literally mean? — Per hundred."Percent" comes from Latin "per centum," meaning per hundred. So 45% means 45 out of 100.
Convert 75% to a decimal. — 0.75.To convert a percent to a decimal, divide by 100 (move decimal two places left). 75% = 75 ÷ 100 = 0.75.
Convert 0.08 to a percent. — 8%.To convert a decimal to a percent, multiply by 100 (move decimal two places right). 0.08 × 100 = 8%.
What is 50% of 80? — 40.Part = (50/100) × 80 = 0.50 × 80 = 40.
What is 10% of 350? — 35.10% = 0.10. Part = 0.10 × 350 = 35.
18 is what percent of 90? — 20%.Percent = (Part ÷ Whole) × 100 = (18 ÷ 90) × 100 = 0.20 × 100 = 20%.
30 is 60% of what number? — 50.Whole = Part ÷ (Percent ÷ 100) = 30 ÷ 0.60 = 50.
A jacket costs $120 and is 20% off. What is the sale price? — $96.Discount = 0.20 × 120 = $24. Sale price = 120 − 24 = $96.
What is a conversion factor? — A fraction equal to 1 that changes units without changing the measurement.A conversion factor is a fraction where the numerator and denominator represent the same quantity in different units, so it equals 1.
How many feet are in 1 yard? (1 yard = 3 feet) — 3.1 yard = 3 feet is a standard conversion factor.
In dimensional analysis, when you multiply by a conversion factor, what happens to the unwanted unit? — It cancels out (appears in both numerator and denominator).When the unwanted unit appears in both numerator and denominator, it cancels, leaving only the desired unit.
Which conversion factor would you use to convert miles to kilometers, given 1 mile ≈ 1.6 km? — 1.6 km / 1 mile.To convert miles to kilometers, multiply by (1.6 km / 1 mile) so the "miles" unit cancels.
What does a ratio table contain? — Equivalent ratios organized in rows.A ratio table organizes equivalent ratios in rows, allowing easy scaling up or down.
The ratio of cats to dogs is 2:3. Fill in the table: if cats = 4, dogs = ? — 6.Scale factor = 4 ÷ 2 = 2. Dogs = 3 × 2 = 6.
In a tape diagram for the ratio 1:4, there are 5 total segments. If the total is 20, what does each segment represent? — 4.Total segments = 1 + 4 = 5. Each segment = 20 ÷ 5 = 4.
A ratio table shows: (2, 6), (4, 12), (6, 18). What is the ratio? — 1:3.Each row: second value = 3 × first value. Ratio = 1:3 (or 2:6 scaled down).
The ratio of red to blue tiles is 3:5. If there are 15 red tiles, how many blue tiles are there? — 25.Scale factor = 15 ÷ 3 = 5. Blue = 5 × 5 = 25.
To create equivalent ratios in a ratio table, what must you do to both values? — Multiply (or divide) both by the same number.To keep ratios equivalent (proportional), multiply or divide both values by the same non-zero number.
In a tape diagram, if boys:girls = 2:3 and there are 30 total students, how many are boys? — 12.Total segments = 2 + 3 = 5. Each segment = 30 ÷ 5 = 6. Boys = 2 × 6 = 12.
What formula is used to calculate percent change? — (New − Original) / Original × 100%.Percent change = (New − Original) / Original × 100%. A positive result is an increase; negative is a decrease.
A price goes from $20 to $25. Is this a percent increase or decrease? — Increase.New ($25) > Original ($20), so this is a percent increase.
What is the percent change if a value goes from 50 to 75? — 50%.(75 − 50) / 50 × 100% = 25/50 × 100% = 50% increase.
A test score drops from 80 to 64. What is the percent decrease? — 20%.(64 − 80) / 80 × 100% = −16/80 × 100% = −20%. The decrease is 20%.
What does percent error measure? — How close a measured value is to the true value.Percent error compares the measured value to the known true value, showing how accurate the measurement is.
The formula for percent error uses which type of value in the numerator? — Absolute value of (Measured − True).Percent error = |Measured − True| / True × 100%. The absolute value ensures percent error is always positive.
A population grew from 200 to 250. What is the percent increase? — 25%.(250 − 200) / 200 × 100% = 50/200 × 100% = 25%.
A measurement of 48 cm is taken. The true value is 50 cm. What is the percent error? — 4%.|48 − 50| / 50 × 100% = 2/50 × 100% = 4%.
If percent error is 0%, what does that mean? — The measurement exactly equals the true value.Percent error of 0% means |Measured − True| = 0, so the measured value equals the true value exactly.